Fundamentals of Financial ManagementX

Appendix A Solutions to Self-Test Questions and Problems A-3

multiply $735.03 by 1.08 to get $793.83, and compare $793.83 with the lump sum of
$750. You would then take your father’s offer to make the payments of $221.92
rather than take the lump sum on January 1, 2007.

d. 1/1/06 I=? 1/1/07 1/1/08 1/1/09 1/1/10

Ϫ750 1‚000

Using a financial calculator, input N ϭ 3, PV ϭ Ϫ750, PMT ϭ 0, FV ϭ 1000, and

I/YR ϭ ? Solve for I/YR ϭ 10.0642%.

e. 1/1/06 I=? 1/1/07 1/1/08 1/1/09 1/1/10

Ϫ200 Ϫ200 Ϫ200 Ϫ200
FV=1,000

Using a financial calculator, input N ϭ 4, PV ϭ 0, PMT ϭ Ϫ200, FV ϭ 1000, and
I/YR ϭ ? Solve for I/YR ϭ 15.09%.

You might be able to find a borrower willing to offer you a 15 percent interest
rate, but there would be some risk involved—he or she might not actually pay you
your $1,000!

f. 1/1/06 4% 1/1/07 1/1/08 1/1/09 1/1/10

Ϫ400 ? ? ? ? ??
Find the future value of the original $400 deposit: FV=1,000

FV6 ϭ PV 11.04 2 6 ϭ $400 11.2653 2 ϭ $506.13

This means that on January 1, 2010, you need an additional sum of $493.87:

$1,000.00 Ϫ $506.13 ϭ $493.87

This will be accumulated by making 6 equal payments that earn 8 percent com-
pounded semiannually, or 4 percent each 6 months. Using a financial calculator, input
N ϭ 6, I/YR ϭ 4, PV ϭ 0, FV ϭ 493.87, and PMT ϭ ? Solve for PMT ϭ Ϫ$74.46.

Alternatively, input N ϭ 6, I/YR ϭ 4, PV ϭ Ϫ400, FV ϭ 1000, and PMT ϭ ? Solve
for PMT ϭ Ϫ$74.46.

INOM M
M
g. Effective annual rate ϭ a1 ϩ b Ϫ 1.0

0.08 2
2
ϭ a1 ϩ b Ϫ 1 ϭ 11.04 2 2 Ϫ 1

ϭ 1.0816 Ϫ 1 ϭ 0.0816 ϭ 8.16%

APR ϭ IPER ϫ M
ϭ 0.04 ϫ 2 ϭ 0.08 ϭ 8%

ST-4 Bank A’s effective annual rate is 8.24 percent:

Effective annual rate ϭ a1 ϩ 0.08 b 4 Ϫ 1.0
4

ϭ 11.02 2 4 Ϫ 1 ϭ 1.0824 Ϫ 1

ϭ 0.0824 ϭ 8.24%

Now Bank B must have the same effective annual rate:

a1 ϩ INOM 12 Ϫ 1.0 ϭ 0.0824
12
b

a1 ϩ INOM 12 ϭ 1.0824
12
b

A-4 Appendix A Solutions to Self-Test Questions and Problems

1 ϩ INOM ϭ 11.0824 2 1>12
12

1 ϩ INOM ϭ 1.00662
12

INOM ϭ 0.00662
12

INOM ϭ 0.07944 ϭ 7.94%

Thus, the two banks have different quoted rates—Bank A’s quoted rate is 8 percent,
while Bank B’s quoted rate is 7.94 percent; however, both banks have the same effec-
tive annual rate of 8.24 percent. The difference in their quoted rates is due to the dif-
ference in compounding frequency.

CHAPTER 3

ST-2 a. EBIT $5,000,000
Interest 1,000,000
EBT
Taxes (40%) $4,000,000
Net income 1,600,000

$2,400,000

b. NCF ϭ NI ϩ DEP and AMORT
ϭ $2,400,000 ϩ $1,000,000 ϭ $3,400,000

c. NOPAT ϭ EBIT(1 Ϫ T)
ϭ $5,000,000(0.6)
ϭ $3,000,000

d. OCF ϭ NOPAT ϩ DEP and AMORT
ϭ EBIT(1 Ϫ T) ϩ DEP and AMORT
ϭ $5,000,000(0.6) ϩ $1,000,000
ϭ $4,000,000

e. NOWC ϭ Current assets Ϫ Non-interest-bearing current liabilities
ϭ $14,000,000 Ϫ $4,000,000
ϭ $10,000,000

f. Operating capitalBOY ϭ $24,000,000

Operating capitalEOY ϭ NOWC ϩ Net fixed assets
ϭ $10,000,000 ϩ $15,000,000
ϭ $25,000,000

⌬ in Operating capital ϭ $25,000,000 Ϫ $24,000,000
ϭ $1,000,000

Note that the investment in operating capital must include depreciation so the
investment is calculated as follows:

Investment in operating capital ϭ $1,000,000 ϩ $1,000,000
ϭ $2,000,000

FCF ϭ Operating cash flow Ϫ Investment in operating capital
ϭ $4,000,000 Ϫ $2,000,000
ϭ $2,000,000

g. Retained earnings at the end of the year can be calculated as follows:

Balance of retained earningsBOY $4,500,000
Add: Net income* 2,400,000
Less: Common dividends 1,200,000

Balance of retained earningsEOY $5,700,000

*Net income was calculated in part a.

Appendix A Solutions to Self-Test Questions and Problems A-5

CHAPTER 4

ST-2 Billingsworth paid $2 in dividends and retained $2 per share. Because total retained
earnings rose by $12 million, there must be 6 million shares outstanding. With a book
value of $40 per share, total common equity must be $40(6 million) ϭ $240 million. Since
Billingsworth has $120 million of debt, its debt ratio must be 33.3 percent:

Debt ϭ Debt ϭ $120 $120 million million
Assets Debt ϩ Equity million ϩ $240

ϭ 0.333 ϭ 33.3%

ST-3 a. In answering questions such as this, always begin by writing down the relevant def-

initional equations, then start filling in numbers. Note that the extra zeros indicating

millions have been deleted in the calculations below.

(1) DSO ϭ Accounts receivable
Sales>365

A>R
40.55 ϭ Sales>365

A>R ϭ 40.55 1$2.73972 ϭ $111.1 million

(2) Current ratio ϭ Current assets ϭ 3.0
Current liabilities

ϭ Current assets ϭ 3.0
$105.5

Current assets ϭ 3.0 1$105.52 ϭ $316.5 million

(3) Total assets ϭ Current assets ϩ Fixed assets
ϭ $316.5 ϩ $283.5 ϭ $600 million

(4) ROA ϭ Profit margin ϫ Total assets turnover

ϭ Net income ϫ Sales
Sales Total assets

ϭ $50 ϫ $1,000
$1,000 $600

ϭ 0.05 ϫ 1.667 ϭ 0.083333 ϭ 8.3333%

(5) ROE ϭ ROA ϫ Assets
Equity

12.0% ϭ 8.3333% ϫ $600
Equity

Equity ϭ 18.3333% 2 1$6002

12.0%

ϭ $416.67 million

(6) Current assets ϭ Cash and equivalents ϩ Accounts receivable ϩ Inventories

$316.5 ϭ $100.0 ϩ $111.1 ϩ Inventories

Inventories ϭ $105.4 million

Quick ratio ϭ Current assets Ϫ Inventories
Current liabilities

ϭ $316.5 Ϫ $105.4 ϭ 2.00
$105.5

A-6 Appendix A Solutions to Self-Test Questions and Problems

(7) Total assets ϭ Total claims ϭ $600 million
Current liabilities ϩ Long-term debt ϩ Equity ϭ $600 million
$105.5 ϩ Long-term debt ϩ $416.67 ϭ $600 million
Long-term debt ϭ $600 Ϫ $105.5 Ϫ $416.67 ϭ $77.83 million

Note: We could have found equity as follows:

ROE ϭ Net income
Equity

12.0% ϭ $50
Equity

Equity ϭ $50>0.12

ϭ $416.67 million

Then we could have gone on to find long-term debt.

b. Kaiser’s average sales per day were $1,000/365 ϭ $2.74 million. Its DSO was 40.55,
so A/R ϭ 40.55($2.74) ϭ $111.1 million. Its new DSO of 30.4 would cause A/R ϭ
30.4($2.74) ϭ $83.3 million. The reduction in receivables would be $111.1 Ϫ $83.3 ϭ
$27.8 million, which would equal the amount of cash generated.

(1) New equity ϭ Old equity Ϫ Stock bought back

ϭ $416.7 Ϫ $27.8

ϭ $388.9 million

Thus,

New ROE ϭ Net income
New equity

ϭ $50
$388.9

ϭ 12.86% 1versus old ROE of 12.0% 2

(2) New ROA ϭ Total Net income in A>R
assets Ϫ Reduction

ϭ $50
$600 Ϫ $27.8

ϭ 8.74% 1versus old ROA of 8.33% 2

(3) The old debt is the same as the new debt:

Debt ϭ Total claims Ϫ Equity
ϭ $600 Ϫ $416.7 ϭ $183.3 million

New total assets ϭ Old total assets Ϫ Reduction in A>R
ϭ $600 Ϫ $27.8
ϭ $572.2 million

Therefore,

Old Debt ϭ $183.3 ϭ 30.6%
total assets $600

while

New debt ϭ $183.3 ϭ 32.0%
New total assets $572.2

Appendix A Solutions to Self-Test Questions and Problems A-7

CHAPTER 6

ST-2 a. Average inflation over 4 years ϭ (2% ϩ 2% ϩ 2% ϩ 4%)/4 ϭ 2.5%

b. T4 ϭ rRF ϩ MRP4
ϭ r* ϩ IP4 ϩ MRP4
ϭ 3% ϩ 2.5% ϩ 10.12 3%
ϭ 5.8%

c. C4, BBB ϭ r* ϩ IP4 ϩ MRP4 ϩ DRP ϩ LP
ϭ 3% ϩ 2.5% ϩ 0.3% ϩ 1.3% ϩ 0.5%
ϭ 7.6%

d. T8 ϭ r* ϩ IP8 ϩ MRP8
ϭ 3% ϩ 13 ϫ 2% ϩ 5 ϫ 4% 2>8 ϩ 0.7%
ϭ 3% ϩ 3.25% ϩ 0.7%
ϭ 6.95%

e. C8, BBB ϭ r* ϩ IP8 ϩ MRP8 ϩ DRP ϩ LP
ϭ 3% ϩ 3.25% ϩ 0.7% ϩ 1.3% ϩ 0.5%
ϭ 8.75%

f. T9 ϭ r* ϩ IP9 ϩ MRP9
7.3% ϭ 3% ϩ IP9 ϩ 0.8%
IP9 ϭ 3.5%
3.5% ϭ 13 ϫ 2% ϩ 5 ϫ 4% ϩ X2>9

31.5% ϭ 6% ϩ 20% ϩ X
5.5% ϭ X
X ϭ Inflation in Year 9 ϭ 5.5%

ST-3 T1 ϭ 6%; T2 ϭ 6.2%; T3 ϭ 6.3%; MRP ϭ 0
a. Yield of 1-year security, 1 year from now is calculated as follows:

2 ϫ 6.2% ϭ 6% ϩ X
12.4% ϭ 6% ϩ X
6.4% ϭ X

b. Yield of 1-year security, 2 years from now is calculated as follows:

3 ϫ 6.3% ϭ 2 ϫ 6.2% ϩ X
18.9% ϭ 12.4% ϩ X
6.5% ϭ X

c. Yield of 2-year security, 1 year from now is calculated as follows:

3 ϫ 6.3% ϭ 6% ϩ 2X
18.9% ϭ 6% ϩ 2X
12.9% ϭ 2X
6.45% ϭ X

A-8 Appendix A Solutions to Self-Test Questions and Problems

CHAPTER 7

ST-2 a. Pennington’s bonds were sold at par; therefore, the original YTM equaled the
coupon rate of 12 percent.

b. VB ϭ 50 $120>2 ϩ $1,000

a a1 ϩ 0.10 t a1 ϩ 0.10 50
2 2
tϭ1 b b

With a financial calculator, input the following: N ϭ 50, I/YR ϭ 5, PMT ϭ 60,
FV ϭ 1000, and PV ϭ ? Solve for PV ϭ $1,182.56.

c. Current yield ϭ Annual coupon payment/Price

ϭ $120/$1,182.56

ϭ 0.1015 ϭ 10.15%
Capital gains yield ϭ Total yield – Current yield

ϭ 10% – 10.15% ϭ –0.15%

Total return ϭ 10%

d. With a financial calculator, input the following: N ϭ 13, PV ϭ Ϫ916.42, PMT ϭ 60,
FV ϭ 1000, and rd/2 ϭ I/YR ϭ ? Calculator solution ϭ rd/2 ϭ 7.00%; therefore,
rd ϭ YTM ϭ 14.00%.

Current yield ϭ $120/$916.42 ϭ 13.09%

Capital gains yield ϭ 14% – 13.09% ϭ 0.91%

e. The following time line illustrates the years to maturity of the bond:

1/1/05 7/1/05 1/1/06 7/1/06 1/1/07 12/31/11

3/1/05

Thus, on March 1, 2005, there were 132/3 periods left before the bond matured. Bond
traders actually use the following procedure to determine the price of the bond:

(1) Find the price of the bond on the next coupon date, July 1, 2005. Using a
financial calculator, input N ϭ 13, I/YR ϭ 7.75, PMT ϭ 60, FV ϭ 1000, and
PV ϭ ? Solve for PV ϭ $859.76.

(2) Add the coupon, $60, to the bond price to get the total value, TV, of the bond on
the next interest payment date: TV ϭ $859.76 ϩ $60.00 ϭ $919.76.

(3) Discount this total value back to the purchase date (March 1, 2005):
Using a financial calculator, input N ϭ 4/6, I/YR ϭ 7.75, PMT ϭ 0, FV ϭ 919.76,
and PV ϭ ? Solve for PV ϭ $875.11.

(4) Therefore, you would have written a check for $875.11 to complete the transac-
tion. Of this amount, (1/3)($60) ϭ $20 would represent accrued interest and
$855.11 would represent the bond’s basic value. This breakdown would affect
both your taxes and those of the seller.

(5) This problem could be solved very easily using a spreadsheet or a financial
calculator with a bond valuation function, such as the HP-12C or the HP-17BII.
This is explained in the calculator manual under the heading “Bond
Calculations.”

ST-3 a. (1) $100,000,000/10 ϭ $10,000,000 per year, or $5 million each 6 months. Because
the $5 million will be used to retire bonds immediately, no interest will be
earned on it.

(2) VDC will purchase bonds on the open market if they’re selling at less than par.
So, the sinking fund payment will be less than $5,000,000 each period.

b. The debt service requirements will decline. As the amount of bonds outstanding
declines, so will the interest requirements (amounts given in millions of dollars). If
the bonds are called at par, the total bond service payments are calculated as follows:

Appendix A Solutions to Self-Test Questions and Problems A-9

Semiannual Sinking Outstanding Interest Total
Payment Fund Bonds on Which Paymenta Bond
Period Interest Is Paid Service
Payment (4)
(1) (3) (2) ؉ (4) ‫( ؍‬5)
(2)

1 $5 $100 $6.0 $11.0

2 5 95 5.7 10.7

3 5 90 5.4 10.4

.. . ..

.. . ..

.. . ..

20 5 5 0.3 5.3

a Interest is calculated as (0.5)(0.12)(Column 3); for example: Interest in Period 2 ϭ
(0.5)(0.12)($95) ϭ $5.7.

The company’s total cash bond service requirement will be $21.7 million per year for
the first year. For both options, interest will decline by 0.12($10,000,000) ϭ $1,200,000
per year for the remaining years. The total debt service requirement for the open
market purchases cannot be precisely determined, but the amounts would be less
than what’s shown in Column 5 of the table above.

c. Here we have a 10-year, 7 percent annuity whose compound value is $100 million,
and we are seeking the annual payment, PMT. The solution can be obtained with a
financial calculator. Input N ϭ 10, I/YR ϭ 7, PV ϭ 0, and FV ϭ 100000000, and
press the PMT key to obtain $7,237,750. This amount is not known with certainty as
interest rates over time will change, so the amount could be higher (if interest rates
fall) or lower (if interest rates rise).

d. Annual debt service costs will be $100,000,000(0.12) ϩ $7,237,750 ϭ $19,237,750.

e. If interest rates rose, causing the bond’s price to fall, the company would use open
market purchases. This would reduce its debt service requirements.

CHAPTER 8

ST-2 a. The average rate of return for each stock is calculated simply by averaging the
returns over the 5-year period. The average return for Stock A is

rAvg A ϭ (–24.25% + 18.50% + 38.67% + 14.33% + 39.13%)/5
ϭ 17.28%

The average return for Stock B is

rAvg B ϭ (5.50% + 26.73% + 48.25% + –4.50% + 43.86%)/5
ϭ 23.97%

The realized rate of return on a portfolio made up of Stock A and Stock B would be
calculated by finding the average return in each year as rA(% of Stock A) ϩ rB(% of
Stock B) and then averaging these annual returns:

Year Portfolio AB’s Return, rAB

2001 (9.38%)
2002 22.62
2003 43.46
2004
2005 4.92
41.50
rAvg ϭ 20.62%

b. The standard deviation of returns is estimated, using Equation 8-3a, as follows:

N (8-3a)

a 1 ៮rt Ϫ ៮rAvg 2 2
Estimated ␴ ϭ S ϭ R tϭ1 N Ϫ 1

A-10 Appendix A Solutions to Self-Test Questions and Problems

For Stock A, the estimated ␴ is 25.84 percent:

␴A ϭ B 1Ϫ24.25% Ϫ 17.25% 2 2 ϩ 118.50% Ϫ 17.28% 2 2 ϩ 138.67% Ϫ 17.28% 2 2 ϩ 114.33% Ϫ 17.28% 2 2 ϩ 139.13% Ϫ 17.28% 2 2

5Ϫ1

ϭ 25.84%

The standard deviations of returns for Stock B and for the portfolio are similarly
determined, and they are as follows:

Stock A Stock B Portfolio AB

Standard deviation 25.84% 23.15% 22.96%

c. Because the risk reduction from diversification is small (␴AB falls only to 22.96 per-
cent), the most likely value of the correlation coefficient is 0.8. If the correlation coef-
ficient were Ϫ0.8 the risk reduction would be much larger. In fact, the correlation
coefficient between Stocks A and B is 0.76.

d. If more randomly selected stocks were added to a portfolio, ␴p would decline to
somewhere in the vicinity of 20 percent; see Figure 8-8. ␴p would remain constant
only if the correlation coefficient were ϩ1.0, which is most unlikely. ␴p would
decline to zero only if the correlation coefficient, ␳, were equal to zero and a large
number of stocks were added to the portfolio, or if the proper proportions were held
in a two-stock portfolio with ␳ ϭ Ϫ1.0.

ST-3 a. b ϭ (0.6)(0.70) + (0.25)(0.90) + (0.1)(1.30) + (0.05)(1.50)

ϭ 0.42 + 0.225 + 0.13 + 0.075 ϭ 0.85
b. rRF ϭ 6%; RPM ϭ 5%; b ϭ 0.85

r ϭ 6% + (5%)(0.85)
ϭ 10.25%

c. bN ϭ (0.5)(0.70) + (0.25)(0.90) + (0.1)(1.30) + (0.15)(1.50)
ϭ 0.35 + 0.225 + 0.13 + 0.225
ϭ 0.93

r ϭ 6% + (5%)(0.93)
ϭ 10.65%

CHAPTER 9

ST-2 a. This is not necessarily true. Because G plows back two-thirds of its earnings, its
ST-3 growth rate should exceed that of D, but D pays higher dividends ($3 versus $1). We
cannot say which stock should have the higher price.

b. Again, we just do not know which price would be higher.

c. This is false. The changes in rd and rs would have a greater effect on G; its price
would decline more.

d. The total expected return for D is rˆD ϭ D1/P0 ϩ g ϭ 12% ϩ 0% ϭ 12%. The total
expected return for G will have D1/P0Ͻ 12% and g Ͼ 0%, but rˆG should be neither
greater nor smaller than D’s total expected return, 12 percent, because the two
stocks are stated to be equally risky.

e. We have eliminated a, b, c, and d, so e should be correct. On the basis of the
available information, D and G should sell at about the same price, $25; thus,
rˆsϭ 12% for both D and G. G’s current dividend yield is $1/$25 ϭ 4%. Therefore,
g ϭ 12% Ϫ 4% ϭ 8%.

The first step is to solve for g, the unknown variable, in the constant growth equation.
Since D1 is unknown but D0 is known, substitute D0(1 ϩ g) as follows:

Pˆ0 ϭ P0 ϭ D1 g ϭ D0 11 ϩ g 2
rs Ϫ rs Ϫ g

$36 ϭ $2.40 11 ϩ g2
0.12 Ϫ g

Appendix A Solutions to Self-Test Questions and Problems A-11

Solving for g, we find the growth rate to be 5 percent:

$4.32 Ϫ $36g ϭ $2.40 ϩ $2.40g

$38.4g ϭ $1.92

g ϭ 0.05 ϭ 5%

The next step is to use the growth rate to project the stock price 5 years hence:

Pˆ5 ϭ D0 11 ϩ g 2 6
rs Ϫ g

$2.40 11.05 2 6
ϭ

0.12 Ϫ 0.05

ST-4 ϭ $45.95
1Alternatively, Pˆ5 ϭ $36 11.05 2 5 ϭ $45.95 2
Therefore, the firm’s expected stock price 5 years from now, Pˆ5, is $45.95.

a. (1) Calculate the PV of the dividends paid during the supernormal growth period:

D1 ϭ $1.1500 11.15 2 ϭ $1.3225

D2 ϭ $1.3225 11.15 2 ϭ $1.5209

D3 ϭ $1.5209 11.13 2 ϭ $1.7186

PV D ϭ $1.3225 ϩ $1.5209 ϩ $1.7186
1.12 11.12 2 2 11.12 2 3

ϭ $1.1808 ϩ $1.2125 ϩ $1.2233

ϭ $3.6166 Ϸ $3.62
(2) Find the PV of the firm’s stock price at the end of Year 3:

Pˆ3 ϭ D4 g ϭ D3 11 ϩ g 2
rs Ϫ rs Ϫ g

$1.7186 11.062
ϭ 0.12 Ϫ 0.06

ϭ $30.36

PV Pˆ3 ϭ $30.36 ϭ $21.61
11.12 2 3

(3) Sum the two components to find the value of the stock today:

Pˆ0 ϭ $3.62 ϩ $21.61 ϭ $25.23
Alternatively, the cash flows can be placed on a time line as follows:

0 12% 1 234

g=15% g=13% g=6%

1.3225 1.5209 1.7186 1.8217

30.3617 = $1.8217
32.0803 0.12 Ϫ 0.06

Enter the cash flows into the cash flow register and I/YR ϭ 12, and press the NPV
key to obtain P0 ϭ $25.23.

A-12 Appendix A Solutions to Self-Test Questions and Problems

b. Pˆ1 ϭ $1.5209 ϩ $1.7186 ϩ $30.36
1.12 11.12 2 2 11.12 2 2

ϭ $1.3579 ϩ $1.3701 ϩ $24.2028

ϭ $26.9308 Ϸ $26.93

(Calculator solution: $26.93)

Pˆ2 ϭ $1.7186 ϩ $30.36
1.12 1.12

ϭ $1.5345 ϩ $27.1071

ϭ $28.6416 Ϸ $28.64

(Calculator solution: $28.64)
c.

Year Dividend Yield ؉ Capital Gains Yield ‫ ؍‬Total Return

1 $1.3225 Ϸ 5.24% $26.93 Ϫ $25.23 Ϸ 6.74% Ϸ 12%
$25.23 $25.23

2 $1.5209 Ϸ 5.65% $28.64 Ϫ $26.93 Ϸ 6.35% Ϸ 12%
$26.93 $26.93

3 $1.7186 Ϸ 6.00% $30.36 Ϫ $28.64 Ϸ 6.00% Ϸ 12%
$28.64 $28.64

CHAPTER 10

ST-2 a. Component costs are as follows:

Common: rs ϭ D1 ϩ g ϭ D0 11 ϩ g2 ϩ g
P0 P0

$3.60 11.092
ϭ $54 ϩ 0.09

ϭ 0.0727 ϩ 0.09 ϭ 16.27%

Preferred: rp ϭ Preferred dividend ϭ $11 ϭ 11.58%
Pp $95
Debt at rd ϭ 12%:
b. WACC calculation: rd 11 Ϫ T 2 ϭ 12% 10.6 2 ϭ 7.20%

WACC ϭ wdrd 11 Ϫ T 2 ϩ wprp ϩ wcrs

ϭ 0.25 17.2% 2 ϩ 0.15 111.58% 2 ϩ 0.60 116.27% 2 ϭ 13.30%

c. LEI should accept Projects A, B, C, and D. It should reject Project E because its rate
of return does not exceed the WACC of funds needed to finance it.

CHAPTER 11

ST-2 a. Net present value (NPV):

NPVX ϭ Ϫ$10,000 ϩ $6,500 ϩ $3,000 ϩ $3,000 ϩ $1,000 ϭ $966.01
11.12 2 1 11.12 2 2 11.12 2 3 11.12 2 4

NPVY ϭ Ϫ$10,000 ϩ $3,500 ϩ $3,500 ϩ $3,500 ϩ $3,500 ϭ $630.72
11.12 2 1 11.12 2 2 11.12 2 3 11.12 2 4

Alternatively, using a financial calculator, input the cash flows into the cash flow
register, enter I/YR ϭ 12, and then press the NPV key to obtain NPVX ϭ $966.01
and NPVY ϭ $630.72.

Appendix A Solutions to Self-Test Questions and Problems A-13

Internal rate of return (IRR):
To solve for each project’s IRR, find the discount rates that equate each NPV to zero:

IRRX ϭ 18.0%

IRRY ϭ 15.0%

Modified internal rate of return (MIRR):
To obtain each project’s MIRR, begin by finding each project’s terminal value (TV) of
cash inflows:

TVX ϭ $6,500(1.12)3 ϩ $3,000(1.12)2 ϩ $3,000(1.12)1 ϩ $1,000 ϭ $17,255.23

TVY ϭ $3,500(1.12)3 ϩ $3,500(1.12)2 ϩ $3,500(1.12)1 ϩ $3,500 ϭ $16,727.65

Now, each project’s MIRR is the discount rate that equates the PV of the TV to each proj-
ect’s cost, $10,000:

MIRRX ϭ 14.61%

MIRRY ϭ 13.73%

Payback:
To determine the payback, construct the cumulative cash flows for each project:

CUMULATIVE CASH FLOWS

Year Project X Project Y

0 ($10,000) ($10,000)

1 (3,500) (6,500)

2 (500) (3,000)

3 2,500 500

4 3,500 4,000

PaybackX ϭ 2 ϩ $500 ϭ 2.17 years
$3,000

PaybackY ϭ 2 ϩ $3,000 ϭ 2.86 years
$3,500

Discounted payback:
To determine the discounted payback, construct the cumulative discounted cash flows at
the firm’s WACC of 12 percent for each project:

Project X

Years 0 1 2 3 4

Cash flow Ϫ10,000 6,500 3,000 3,000 1,000
Discounted cash flow Ϫ10,000 2,135.34 635.52
Cumulative discounted cash flow Ϫ10,000 5,803.57 2,391.58 ϩ330.49
ϩ966.01
Ϫ4,196.43 Ϫ1,804.85
4
Project Y Discounted PaybackX ϭ 2 ϩ $1,804.85/$2,135.34 ϭ 2.85 years
Years 0 1 2 3

Cash flow Ϫ10,000 3,500 3,500 3,500 3,500
Discounted cash flow Ϫ10,000 2,224.31
Cumulative discounted cash flow Ϫ10,000 3,125.00 2,790.18 2,491.23 ϩ630.72

Ϫ6,875.00 Ϫ4,084.82 Ϫ1,593.59

Discounted PaybackY ϭ 3 ϩ $1,593.59/$2,224.31 ϭ 3.72 years
b. The following table summarizes the project rankings by each method:

Project That Ranks Higher

NPV X
IRR X
MIRR X
Payback X
Discounted payback X

A-14 Appendix A Solutions to Self-Test Questions and Problems

Note that all methods rank Project X over Project Y. In addition, both projects are
acceptable under the NPV, IRR, and MIRR criteria. Thus, both projects should be
accepted if they are independent.

c. In this case, we would choose the project with the higher NPV at r ϭ 12%, or
Project X.

d. To determine the effects of changing the cost of capital, plot the NPV profiles of each
project. The crossover rate occurs at about 6 to 7 percent (6.2 percent). See the
accompanying graph.
If the firm’s cost of capital is less than 6.2 percent, a conflict exists because NPVY Ͼ
NPVX, but IRRX Ͼ IRRY. Therefore, if r were 5 percent, a conflict would exist. Note,
however, that when r ϭ 5.0%, MIRRX ϭ 10.64% and MIRRY ϭ 10.83%; hence, the
modified IRR ranks the projects correctly, even if r is to the left of the crossover
point.

e. The basic cause of the conflict is differing reinvestment rate assumptions between
NPV and IRR. NPV assumes that cash flows can be reinvested at the cost of capital,
while IRR assumes reinvestment at the (generally) higher IRR. The high reinvest-
ment rate assumption under IRR makes early cash flows especially valuable, and
hence short-term projects look better under IRR.

NPV Profiles for Projects X and Y

NPV
($)

4,000 NPVY

3,000 Crossover Rate = 6.2%

NPVX
2,000

1,000

0 5 10 15 20 Cost of Capital
Ϫ1,000 IRRY (%)
IRRx

Cost of Capital NPVX NPVY

0% $3,500 $4,000
4 2,545 2,705
8 1,707 1,592
12 966 631
16 307 (206)
18 5 (585)

Appendix A Solutions to Self-Test Questions and Problems A-15

CHAPTER 12

ST-2 a. Estimated investment requirements:

Price ($55,000)

Installation (10,000)

Change in net operating working capital (2,000)

Total investment ($67,000)

b. Depreciation schedule:
Equipment cost ϭ $65,000; MACRS 3-year class

YEARS

12 3

MACRS depreciation rates 33% 45% 15%
Equipment depreciation expense $21,450 $29,250 $9,750

Note that the remaining book value of the equipment at the end of the project’s life
is 0.07 ϫ $65,000 ϭ $4,550.

c. Terminal cash flow:

Salvage value $10,000
Tax on salvage valuea (2,180)
Net operating working capital recovery 2,000
Termination cash flow
$ 9,820

a Sales price $10,000
Less book value 4,550
Taxable income
Tax at 40% $ 5,450
$ 2,180

Book value ϭ Depreciable basis Ϫ Accumulated depreciation
ϭ $65,000 Ϫ $60,450 ϭ $4,550

d. Net operating cash flows:

Revenues (4,000 ϫ $50) Year 1 Year 2 Year 3
Variable costs (70%)
Fixed costs $200,000 $200,000 $200,000
Depreciation 140,000 140,000 140,000
EBIT 30,000 30,000 30,000
Taxes (40%) 21,450 29,250 9,750
NOPAT
Add back: Depreciation $ 8,550 $ 750 $ 20,250
Operating cash flow 3,420 300 8,100

e. Project cash flows: $ 5,130 $ 450 $ 12,150
21,450 29,250 9,750

$ 26,580 $ 29,700 $ 21,900

0 11% 1 2 3

Operating cash flows Ϫ67,000 26,580 29,700 21,900
Terminal cash flow Ϫ67,000 26,580 29,700 9,820
Project cash flows
31,720

f. From the time line shown in part e, the project’s NPV can be calculated as follows:

NPV ϭ Ϫ$67,000 ϩ $26,580/(1.11)1 ϩ $29,700/(1.11)2 ϩ $31,720/(1.11)3

ϭ $4,245

Alternatively, using a financial calculator, you would enter the following data: CF0
ϭ Ϫ67000; CF1 ϭ 26580; CF2 ϭ 29700; CF3 ϭ 31720; I/YR ϭ 11; and then solve for
NPV ϭ $4,245.

Since the NPV is positive, the project should be accepted.

g. Project analysis if unit sales turned out to be 20 percent below forecast:
Initial projection ϭ 4,000 units; however, if unit sales turn out to be only 80 percent
of forecast then unit sales ϭ 3,200.

A-16 Appendix A Solutions to Self-Test Questions and Problems

Year 0 Year 1 Year 2 Year 3
Ϫ$65,000
Equipment purchase $160,000 $160,000 $160,000
Change in NOWC Ϫ2,000 112,000 112,000 112,000
Revenues (3,200 ϫ $50) 30,000 30,000 30,000
Variable costs (70%) Ϫ$67,000 21,450 29,250 9,750
Fixed costs Ϫ$67,000
Depreciation Ϫ$ 3,450 Ϫ$ 11,250 $ 8,250
EBIT Ϫ1,380 Ϫ4,500 3,300
Taxes (40%)
NOPAT Ϫ$ 2,070 Ϫ$ 6,750 $ 4,950
Add back: Depreciation 21,450 29,250 9,750
Operating cash flow
Terminal cash flow $ 19,380 $ 22,500 $ 14,700
Project cash flows 9,820
$ 19,380 $ 22,500
Project NPV: $ 24,520

0 11% 1 2 3
22‚500 24‚520
Ϫ67‚000 19‚380

NPV ϭ Ϫ$67,000 ϩ $19,380/(1.11)1 ϩ $22,500/(1.11)2 ϩ $24,520/(1.11)3
ϭ Ϫ$13,350

Alternatively, using a financial calculator, you would enter the following data: CF0
ϭ Ϫ67000; CF1 ϭ 19380; CF2 ϭ 22500; CF3 ϭ 24520; I/YR ϭ 11; and then solve for
NPV ϭ Ϫ$13,350.

Since the NPV is negative, the project should not be accepted. If unit sales were
20 percent below the forecasted level, the project would no longer be accepted.
h. Best-case scenario: Unit sales ϭ 4,800, Variable cost % ϭ 65%.

Year 0 Year 1 Year 2 Year 3
Ϫ$65,000
Equipment purchase $240,000 $240,000 $240,000
Change in NOWC Ϫ2,000 156,000 156,000 156,000
Revenues (4,800 ϫ $50) 30,000 30,000 30,000
Variable costs (65%) Ϫ$67,000 21,450 29,250 9,750
Fixed costs Ϫ$67,000
Depreciation $ 32,550 $ 24,750 $ 44,250
EBIT 13,020 9,900 17,700
Taxes (40%)
NOPAT $ 19,530 $ 14,850 $ 26,550
Add back: Depreciation 21,450 29,250 9,750
Operating cash flows
Terminal cash flow $ 40,980 $ 44,100 $ 36,300
Project cash flows 9,820
$ 40,980 $ 44,100
$ 46,120

Project NPV:

0 11% 1 2 3
Ϫ67‚000 40‚980 44‚100 46‚120

NPV ϭ Ϫ$67,000 ϩ $40,980/(1.11)1 ϩ $44,100/(1.11)2 ϩ $46,120/(1.11)3
ϭ $39,434

Alternatively, using a financial calculator, you would enter the following data:
CF0 ϭ Ϫ67000; CF1 ϭ 40980; CF2 ϭ 44100; CF3 ϭ 46120; I/YR ϭ 11; and then solve
for NPV ϭ $39,434.

Base-case scenario: The NPV was calculated in part f as $4,245.

Worst-case scenario: Unit sales ϭ 3,200; Variable cost % ϭ 75%.

Appendix A Solutions to Self-Test Questions and Problems A-17

Year 0 Year 1 Year 2 Year 3
Ϫ$65,000
Equipment purchase $160,000 $160,000 $160,000
Change in NOWC Ϫ2,000 120,000 120,000 120,000
Revenues (3,200 ϫ $50) 30,000 30,000 30,000
Variable costs (75%) Ϫ$67,000 21,450 29,250 9,750
Fixed costs Ϫ$67,000
Depreciation Ϫ$ 11,450 Ϫ$ 19,250 $ 250
EBIT Ϫ4,580 Ϫ7,700 100
Taxes (40%)
NOPAT Ϫ$ 6,870 Ϫ$ 11,550 $ 150
Add back: Depreciation 21,450 29,250 9,750
Operating cash flows
Terminal cash flow $ 14,580 $ 17,700 $ 9,900
Project cash flows 9,820
$ 14,580 $ 17,700
Project NPV: $ 19,720

0 11% 1 2 3
Ϫ67‚000 14‚580 17‚700 19‚720

NPV ϭ Ϫ$67,000 ϩ $14,580/(1.11)1 ϩ $17,700/(1.11)2 ϩ $19,720/(1.11)3
ϭ Ϫ$25,080

Alternatively, using a financial calculator, you would enter the following data:
CF0 ϭ Ϫ67000; CF1 ϭ 14580; CF2 ϭ 17700; CF3 ϭ 19720; I/YR ϭ 11; and then solve
for NPV ϭ Ϫ$25,080.

Scenario Probability NPV

Best case 25% $39,434
Base case 50 4,245
Worst case 25 Ϫ25,080

Expected NPV ϭ $ 5,711

␴NPV ϭ [0.25[$39,434 Ϫ $5,711]2 ϩ 0.50[$4,245 Ϫ $5,711]2 ϩ 0.25[Ϫ$25,080 Ϫ
$5,711]2]1/2

␴NPV ϭ [$284,310,182 ϩ $1,074,578 ϩ $237,021,420]1/2
␴NPV ϭ $22,856
CVNPV ϭ $22,856/$5,711 ϭ 4.0

i. The project’s CV ϭ 4.0, which is significantly larger than the firm’s typical project
CV. So, the WACC for this project should be adjusted upward, 11% ϩ 3% ϭ 14%.
To calculate the expected NPV, standard deviation, and coefficient of variation
you would recalculate each scenario’s NPV by discounting the project cash flows by
14 percent rather than 11 percent.

Best-case scenario:

0 14% 1 2 3

Ϫ67‚000 40‚980 44‚100 46‚120

NPV ϭ Ϫ$67,000 ϩ $40,980/(1.14)1 ϩ $44,100/(1.14)2 ϩ $46,120/(1.14)3
ϭ $34,011

Alternatively, using a financial calculator, you would enter the following data:
CF0 ϭ Ϫ67000; CF1 ϭ 40980; CF2 ϭ 44100; CF3 ϭ 46120; I/YR ϭ 14; and then solve
for NPV ϭ $34,011.

Base-case scenario:

0 14% 1 2 3

Ϫ67‚000 26‚580 29‚700 31‚720

NPV ϭ Ϫ$67,000 ϩ $26,580/(1.14)1 ϩ $29,700/(1.14)2 ϩ $31,720/(1.14)3
ϭ $579

A-18 Appendix A Solutions to Self-Test Questions and Problems

Alternatively, using a financial calculator, you would enter the following data:
CF0 ϭ Ϫ67000; CF1 ϭ 26580; CF2 ϭ 29700; CF3 ϭ 31720; I/YR ϭ 14; and then solve
for NPV ϭ $579.

Worst-case scenario:

0 14% 1 2 3
Ϫ67‚000 14‚580 17‚700 19‚720

NPV ϭ Ϫ$67,000 ϩ $14,580/(1.14)1 ϩ $17,700/(1.14)2 ϩ $19,720/(1.14)3
ϭ Ϫ$27,281

Alternatively, using a financial calculator, you would enter the following data:
CF0 ϭ Ϫ67000; CF1 ϭ 14580; CF2 ϭ 17700; CF3 ϭ 19720; I/YR ϭ 14; and then solve
for NPV ϭ Ϫ$27,281.

Scenario Probability NPV

Best case 25% $34,011
Base case 50 579
Worst case 25 Ϫ27,281

Expected NPV ϭ $ 1,972

␴NPV ϭ [0.25[$34,011 Ϫ $1,972]2 ϩ 0.50[$579 Ϫ $1,972]2 ϩ 0.25[Ϫ$27,281 Ϫ $1,972]2]1/2
␴NPV ϭ [$256,624,380 ϩ $970,225 ϩ $213,934,502]1/2
␴NPV ϭ $21,715
CVNPV ϭ $21,715/$1,972 ϭ 11.0

The expected NPV of the project is still positive so the project would still be accepted.

CHAPTER 13

ST-2 a. No abandonment considered; WACC ϭ 12%.
ST-3
Years 0 1 23 NPV

25% Ϫ25,000 18,000 18,000 18,000 $18,233

50 Ϫ25,000 12,000 12,000 12,000 3,822

25 Ϫ25,000 Ϫ8,000 Ϫ8,000 Ϫ8,000 Ϫ44,215

Expected NPV ϭ Ϫ$ 4,585

b. Abandonment considered; WACC ϭ 12 percent.

Years 0 1 23 NPV

25% Ϫ25,000 18,000 18,000 18,000 $18,233

50 Ϫ25,000 12,000 12,000 12,000 3,822

25 Ϫ25,000 Ϫ8,000

Abandon project 15,000 0 Ϫ20,185

Expected NPV ϭ $ 1,423

c. Value of the abandonment option:

NPV with abandonment $1,423
NPV without abandonment (4,585)
Value of abandonment option $6,008

a. Machine W:

0 10% 1 2

Ϫ500,000 300,000 300,000

NPVW ϭ Ϫ$500,000 ϩ $300,000 ϩ $300,000
11.10 2 1 11.10 2 2

ϭ $20,661.16

Appendix A Solutions to Self-Test Questions and Problems A-19

Machine WW:
0 10% 1 2 3 4

Ϫ500,000 165,000 165,000 165,000 165,000

NPVWW ϭ Ϫ $500,000 ϩ $165,000 ϩ $165,000 ϩ $165,000 ϩ $165,000
11.10 2 1 11.10 2 2 11.10 2 3 11.10 2 4

ϭ $23,027.80.

Since the projects are independent and both have positive NPVs, both projects
should be accepted.

b. Since the projects are mutually exclusive, only one project can be accepted. There-
fore, Machine WW has the higher NPV and should be chosen.

c(1). Machine W’s NPV needs to be recalculated under the assumption that it is repeated
in Year 2.

Replacement chain analysis:
Machine W:

0 10% 1 2 3 4

Ϫ500,000 300,000 300,000
Ϫ500,000
Ϫ200,000 300,000 300,000

NPVW ϭ Ϫ $500,000 ϩ $300,000 ϩ Ϫ $200,000 $300,000 $300,000
11.10 2 1 11.10 2 2 ϩ 11.10 2 3 ϩ 11.10 2 4

ϭ NPVW ϭ $37,736.49

Machine WW:

NPVWW ϭ $23,027.80 (NPV remains the same since it’s calculated over a 4-year life.)

Since the projects are mutually exclusive but repeatable, Machine W should be chosen
because its 4-year NPV is higher than Machine WW’s.

c(2). Equivalent annual annuity analysis:

Machine W:
Using a financial calculator, enter the following data: N ϭ 2; I/YR ϭ 10;
PV ϭ Ϫ20661.16; FV ϭ 0; and then solve for EAAW ϭ PMT ϭ $11,904.76.

Machine WW:
Using a financial calculator, enter the following data: N ϭ 4; I/YR ϭ 10;
PV ϭ Ϫ23027.80; FV ϭ 0; and then solve for EAAWW ϭ PMT ϭ $7,264.60.

The equivalent annual annuity analysis arrives at the same decision as the replace-
ment chain method. EAAW ϭ $11,904.76 and EAAWW ϭ $7,264.60; therefore, Machine W
should be chosen if the projects are mutually exclusive and can be repeated indefinitely.

d. Yes. If the two projects can be repeated indefinitely over time but the cash flows are
expected to change, then the replacement chain analysis can be used. The analysis
would be similar to what was done in part c(1) except that the repeated cash flows
would not be identical to the original cash flows.

CHAPTER 14

ST-2 a. The following information is given in the problem:

Q ϭ Units of output (sales) ϭ 5,000
P ϭ Average sales price per unit of output ϭ $100
F ϭ Fixed operating costs ϭ $200,000
V ϭ Variable costs per unit ϭ $50
EBIT ϭ Operating income ϭ $50,000
Total assets ϭ $500,000
Common equity ϭ $500,000

A-20 Appendix A Solutions to Self-Test Questions and Problems

(1) Determine the new EBIT level if the change is made:

New EBIT ϭ P2(Q2) Ϫ F2 Ϫ V2(Q2)
New EBIT ϭ $95(7,000) Ϫ $250,000 Ϫ $40(7,000)

ϭ $135,000

(2) Determine the incremental EBIT:

⌬EBIT ϭ $135,000 Ϫ $50,000 ϭ $85,000
(3) Estimate the approximate rate of return on the new investment:

⌬ROA ϭ ⌬EBIT ϭ $85,000 ϭ 21.25%
Investment $400,000

Since the ROA exceeds Olinde’s average cost of capital, this analysis suggests that
the firm should go ahead and make the investment.

b. The change would increase the breakeven point. Still, with a lower sales price, it
might be easier to achieve the higher new breakeven volume.

Old: QBE ϭ P F V ϭ $200,000 ϭ 4,000 units
Ϫ $100 Ϫ $50

New: QBE ϭ P2 F V2 ϭ $250,000 ϭ 4,545 units
Ϫ $95 Ϫ $40

c. The incremental ROA is

ROA ϭ ⌬Profit ϫ ⌬Sales
⌬Sales ⌬Assets

Using debt financing, the incremental profit associated with the investment is equal
to the incremental profit found in part a minus the interest expense incurred as a
result of the investment:

⌬Profit ϭ New profit Ϫ Old profit Ϫ Interest
ϭ $135,000 Ϫ $50,000 Ϫ 0.10($400,000)
ϭ $45,000

The incremental sales is calculated as:

⌬Sales ϭ P2Q2 Ϫ P1Q1
ϭ $95(7,000) Ϫ $100(5,000)

ϭ $665,000 Ϫ $500,000

ϭ $165,000

ROA ϭ $45,000 ϫ $165,000 ϭ 11.25%
$165,000 $400,000

The return on the new equity investment still exceeds the average cost of capital, so
the firm should make the investment.

ST-3 a. EBIT $4,000,000
Interest ($2,000,000 ϫ 0.10) 200,000
Earnings before taxes (EBT)
Taxes (35%) $3,800,000
Net income 1,330,000

$2,470,000

EPS ϭ $2,470,000/600,000 ϭ $4.12

P0 ϭ $4.12/0.15 ϭ $27.47
b. Equity ϭ 600,000 ϫ $10 ϭ $6,000,000

Debt ϭ $2,000,000

Total capital ϭ $8,000,000

WACC ϭ wdrd(1 Ϫ T) ϩ wcrs
ϭ (2/8)(10%)(1 Ϫ 0.35) ϩ (6/8)(15%)

ϭ 1.63% ϩ 11.25%

ϭ 12.88%

Appendix A Solutions to Self-Test Questions and Problems A-21

c. EBIT $4,000,000
Interest ($10,000,000 ϫ 0.12) 1,200,000
Earnings before taxes (EBT)
Taxes (35%) $2,800,000
Net income 980,000

Shares bought and retired: $1,820,000

⌬N ϭ ⌬Debt/P0 ϭ $8,000,000/$27.47 ϭ 291,227

New outstanding shares:
N1 ϭ N0 Ϫ ⌬N ϭ 600,000 Ϫ 291,227 ϭ 308,773

New EPS:

EPS ϭ $1,820,000/308,773 ϭ $5.89

New price per share:

P0 ϭ $5.89/0.17 ϭ $34.65 versus $27.47

Therefore, Gentry should change its capital structure.
d. In this case, the company’s net income would be higher by (0.12 Ϫ 0.10)($2,000,000)

(1 Ϫ 0.35) ϭ $26,000 because its interest charges would be lower. The new price
would be

P0 ϭ 1$1,820,000 ϩ $26,0002>308,773 ϭ $35.17

0.17

In the first case, in which debt had to be refunded, the bondholders were compen-
sated for the increased risk of the higher debt position. In the second case, the old
bondholders were not compensated; their 10 percent coupon perpetual bonds would
now be worth

$100/0.12 ϭ $833.33

or $1,666,667 in total, down from the old $2 million, or a loss of $333,333. The stock-
holders would have a gain of

($35.17 Ϫ $34.65)(308,773) ϭ $160,562

This gain would, of course, be at the expense of the old bondholders. (There is no
reason to think that bondholders’ losses would exactly offset stockholders’ gains.)

e. TIE ϭ EBIT
I

Original TIE ϭ $4,000,000 ϭ 20 times
$200,000

New TIE ϭ $4,000,000 ϭ 3.33 times
$1,200,000

CHAPTER 15

ST-2 a. Projected net income $2,000,000
Less projected capital investments 800,000
Available residual
$1,200,000
Shares outstanding
200,000

DPS ϭ $1,200,000/200,000 shares ϭ $6 ϭ D1

A-22 Appendix A Solutions to Self-Test Questions and Problems

b. EPS ϭ $2,000,000/200,000 shares ϭ $10
Payout ratio ϭ DPS/EPS ϭ $6/$10 ϭ 60% or
Total dividends/NI ϭ $1,200,000/$2,000,000 ϭ 60%

c. Currently, P0 ϭ D1 g ϭ 0.14 $6 0.05 ϭ $6 ϭ $66.67
rs Ϫ Ϫ 0.09

Under the former circumstances, D1 would be based on a 20 percent payout on $10
EPS, or $2. With rs ϭ 14% and g ϭ 12%, we solve for P0:

P0 ϭ D1 g ϭ $2 ϭ $2 ϭ $100
rs Ϫ 0.14 Ϫ 0.12 0.02

Although CMC has suffered a severe setback, its existing assets will continue to pro-
vide a good income stream. More of these earnings should now be passed on to the
shareholders, as the slowed internal growth has reduced the need for funds. How-
ever, the net result is a 33 percent decrease in the value of the shares.

d. If the payout ratio were continued at 20 percent, even after internal investment
opportunities had declined, the price of the stock would drop to $2/(0.14 Ϫ 0.06) ϭ
$25 rather than to $66.67. Thus, an increase in the dividend payout is consistent with
maximizing shareholder wealth.
Because of the diminishing nature of profitable investment opportunities, the
greater the firm’s level of investment, the lower the average ROE. Thus, the more
money CMC retains and invests, the lower its average ROE will be. We can deter-
mine the average ROE under different conditions as follows:

Old situation (with founder active and a 20 percent payout):

g ϭ (1.0 Ϫ Payout ratio)(Average ROE)

12% ϭ (1.0 Ϫ 0.2)(Average ROE)

Average ROE ϭ 12%/0.8 ϭ 15% Ͼ rs ϭ 14%

Note that the average ROE is 15 percent, whereas the marginal ROE is presumably
equal to 14 percent.

New situation (with founder retired and a 60 percent payout):

g ϭ 6% ϭ (1.0 Ϫ 0.6)(ROE)

ROE ϭ 6%/0.4 ϭ 15% Ͼ rs ϭ 14%

This suggests that the new payout is appropriate and that the firm is taking on
investments down to the point at which marginal returns are equal to the cost of
capital. Note that if the 20 percent payout was maintained, the average ROE would
be only 7.5 percent, which would imply a marginal ROE far below the 14 percent
cost of capital.

CHAPTER 16

ST-2 The Calgary Company: Alternative Balance Sheets

Restricted Moderate Relaxed
(40%) (50%) (60%)

Current assets $1,200,000 $1,500,000 $1,800,000
Fixed assets 600,000 600,000 600,000
Total assets
$1,800,000 $2,100,000 $2,400,000

Debt $ 900,000 $1,050,000 $1,200,000
Equity 900,000 1,050,000 1,200,000
Total liabilities and equity
$1,800,000 $2,100,000 $2,400,000

Appendix A Solutions to Self-Test Questions and Problems A-23

The Calgary Company: Alternative Income Statements

Restricted Moderate Relaxed

Sales $3,000,000 $3,000,000 $3,000,000

EBIT $ 450,000 $ 450,000 $ 450,000
Interest (10%) 90,000 105,000 120,000
Earnings before taxes
Taxes (40%) $ 360,000 $ 345,000 $ 330,000
Net income 144,000 138,000 132,000

$ 216,000 $ 207,000 $ 198,000

ROE 24.0% 19.7% 16.5%

ST-3 a. and b.

Income Statements for Year Ended December 31, 2005 (Thousands of Dollars)

VANDERHEIDEN PRESS HERRENHOUSE PUBLISHING

ab ab

EBIT $ 30,000 $ 30,000 $ 30,000 $ 30,000
Interest 12,400 14,400 10,600 18,600
Taxable income
Taxes (40%) $ 17,600 $ 15,600 $ 19,400 $ 11,400
Net income 7,040 6,240 7,760 4,560

$ 10,560 $ 9,360 $ 11,640 $ 6,840

Equity $100,000 $100,000 $100,000 $100,000
Return on equity 10.56% 9.36% 11.64% 6.84%

The Vanderheiden Press has a higher ROE when short-term interest rates are high,
whereas Herrenhouse Publishing does better when rates are lower.

c. Herrenhouse’s position is riskier. First, its profits and return on equity are much
more volatile than Vanderheiden’s. Second, Herrenhouse must renew its large short-
term loan every year, and if the renewal comes up at a time when money is very
tight, when its business is depressed, or both, then Herrenhouse could be denied
credit, which could put it out of business.

CHAPTER 17

ST-2 To solve this problem, we will define ⌬S as the change in sales and g as the growth rate
ST-3 in sales, and then we use the three following equations:

⌬S ϭ S0g
S1 ϭ S0(1 ϩg)
AFN ϭ (A*/S0)(⌬S) Ϫ (L*/S0)(⌬S) Ϫ MS1(RR)

Set AFN ϭ 0, substitute in known values for A*/S0, L*/S0, M, RR, and S0, and then solve
for g:

0 ϭ 1.6($100g) Ϫ 0.4($100g) Ϫ 0.10[$100(1 ϩ g)](0.55)
0 ϭ $160g Ϫ $40g Ϫ 0.055($100 ϩ $100g)
0 ϭ $160g Ϫ $40g Ϫ $5.5 Ϫ $5.5g
$114.5g ϭ $5.5
g ϭ $5.5/$114.5 ϭ 0.048 ϭ 4.8%

ϭ Maximum growth rate without external financing

Assets consist of cash, marketable securities, receivables, inventories, and fixed assets.
Therefore, we can break the A*/S0 ratio into its components—cash/sales, inventories/
sales, and so forth. Then,

A* ϭ A* Ϫ Inventories ϩ Inventories ϭ 1.6
S0 S0 S0

A-24 Appendix A Solutions to Self-Test Questions and Problems

We know that the inventory turnover ratio is sales/inventories ϭ 3 times, so invento-
ries/sales ϭ 1/3 ϭ 0.3333. Further, if the inventory turnover ratio can be increased to
4 times, then the inventory/sales ratio will fall to 1/4 ϭ 0.25, a difference of 0.3333 Ϫ
0.2500 ϭ 0.0833. This, in turn, causes the A*/S0 ratio to fall from A*/S0 ϭ 1.6 to
A*/S0 ϭ 1.6 Ϫ 0.0833 ϭ 1.5167.

This change has two effects: First, it changes the AFN equation, and second, it means
that Weatherford currently has excessive inventories. Because it is costly to hold excess
inventories, Weatherford will want to reduce its inventory holdings by not replacing
inventories until the excess amounts have been used. We can account for this by setting
up the revised AFN equation (using the new A*/S0 ratio), estimating the funds that will
be needed next year if no excess inventories are currently on hand, and then subtracting
out the excess inventories that are currently on hand:

Present conditions:

Sales ϭ $100 ϭ 3
Inventories Inventories

so
Inventories ϭ $100/3 ϭ $33.3 million at present

New conditions:

Sales ϭ $100 ϭ 4
Inventories Inventories

so
New level of inventories ϭ $100/4 ϭ $25 million

Therefore,
Excess inventories ϭ $33.3 Ϫ $25 ϭ $8.3 million

Forecast of funds needed next year:
⌬S in first year ϭ 0.2($100 million) ϭ $20 million

AFN ϭ 1.5167($20) Ϫ 0.4($20) Ϫ 0.1(0.55)($120) Ϫ $8.3
ϭ $30.3 Ϫ $8 Ϫ $6.6 Ϫ $8.3
ϭ $7.4 million

CHAPTER 18

ST-2 V ϭ P[N(d1)] Ϫ XeϪrRFt [N(d2)]
ϭ [$33(0.63369)] Ϫ [$33(0.95123)(0.55155)]
ϭ $20.91 Ϫ $17.31
ϭ $3.60

CHAPTER 19

ST-2 Euro ϭ Euros ϫ US$
C$ US$ C$

ϭ 1.1215 ϫ $1 ϭ 1.1215 ϭ 0.7334 euro per Canadian dollar
$1 1.5291 1.5291

Appendix A Solutions to Self-Test Questions and Problems A-25

CHAPTER 20

ST-2 a. Cost of leasing:

BEGINNING OF YEAR
0 1 23

Lease payment (AT)a ($ 6,000) ($6,000) ($6,000) ($6,000)
Total PV cost of leasing ϭ ($22,038)

aAfter-tax payment ϭ $10,000(1 Ϫ T) ϭ $10,000(0.6) ϭ $6,000

Using a financial calculator, input the following data after switching your calculator
to “BEG” mode: N ϭ 4, I/YR ϭ 6, PMT ϭ 6000, and FV ϭ 0. Then press the PV
key to arrive at the answer of ($22,038). Now, switch your calculator back to
“END” mode. Note that the interest rate used is the after-tax cost of debt,
10% (1 Ϫ T) ϭ 6%.

b. Cost of owning:

Depreciable basis ϭ $40,000

Here are the cash flows under the borrow-and-buy alternative:

0 END OF YEAR 3 4
12
($40,000)
1. Depreciation schedule ($40,000) $40,000 $40,000 $40,000 $40,000
(a) Depreciable basis 0.33 0.45 0.15 0.07
(b) Allowance
(c) Depreciation 13,200 18,000 6,000 2,800

2. Cash flows 5,280a 7,200 2,400 1,120
(d) Net purchase price (600) (600) (600) (600)
(e) Depreciation tax savings
(f) Maintenance (AT) $ 4,680 $ 6,600 $ 1,800 6,000
(g) Salvage value (AT) $ 6,520
(h) Total cash flows

Total PV cost of owning ϭ ($23,035)

aDepreciation(T) ϭ $13,200(0.40) ϭ $5,280
Input the cash flows for the individual years into the cash flow register and enter I/YR ϭ 6,
then press the NPV key to arrive at the answer of ($23,035). Because the present value of
the cost of leasing is less than that of owning, the truck should be leased: $23,035 Ϫ
$22,038 ϭ $997, net advantage to leasing.

c. The discount rate is based on the cost of debt because most cash flows are fixed by
contract and, consequently, are relatively certain. Thus, the lease cash flows have
about the same risk as the firm’s debt. Also, leasing is considered to be a substitute
for debt. We use an after-tax cost rate because the cash flows are stated net of taxes.

d. The firm could increase the discount rate on the salvage value cash flow. This would
increase the PV cost of owning and make leasing even more advantageous.

CHAPTER 21

ST-2 Time line numbers are in millions of dollars:

0 12% 1 2 3 4

PV = ? 1.5 2.0 3.0 5.0
TV = 75.0*

80.0

A-26 Appendix A Solutions to Self-Test Questions and Problems

rs ϭ 6% ϩ 4% 11.5 2
ϭ 12%
$5 11.052

*Terminal CF ϭ 0.12 Ϫ 0.5 ϭ $75.00
To solve this problem, use your financial calculator to enter the following input data:
CF0 ϭ 0; CF1 ϭ 1.5; CF2 ϭ 2.0; CF3 ϭ 3.0; CF4 ϭ 80; and I/YR ϭ 12. Then, solve for
NPV ϭ $55.91 million.

APPENDIX B

Answers to Selected End-of-Chapter Problems

We present here some intermediate steps and final 3-10 a. $2,400,000,000.
answers to selected end-of-chapter problems. Please b. $4,500,000,000.
note that your answer may differ slightly from ours due c. $5,400,000,000.
to rounding differences. Also, although we hope not, d. $1,100,000,000.
some of the problems may have more than one correct
solution, depending on what assumptions are made in 3-12 a. $592 million.
working the problem. Finally, many of the problems b. RE04 ϭ $1,374 million.
involve some verbal discussion as well as numerical c. $1,600 million.
calculations; this verbal material is not presented here. d. $15 million.
e. $620 million.
2-2 PV ϭ $1,292.10.
2-4 N ϭ 11.01 years. 3-14 a. $2,400,000.
2-6 FVA5 ϭ $1,725.22; FVA5 Due ϭ $1,845.99. b. NI ϭ 0; NCF ϭ $3,000,000.
2-8 PMT ϭ $444.89; EAR ϭ 12.6825%. c. NI ϭ $1,350,000; NCF ϭ $2,100,000.
2-10 a. $895.42.
4-2 D/A ϭ 58.33%.
b. $1,552.92. 4-4 M/B ϭ 4.2667.
c. $279.20. 4-6 ROE ϭ 8%.
d. $499.99; $867.13. 4-8 15.31%.
2-12 b. 7%. 4-10 NI/S ϭ 2%; D/A ϭ 40%.
c. 9%. 4-12 TIE ϭ 2.25.
d. 15%. 4-14 ROE ϭ 23.1%.
2-14 a. $6,374.97. 4-16 7.2%.
d(1). $7,012.47. 4-18 6.0.
2-16 PV7% ϭ $1,428.57; PV14% ϭ $714.29. 4-20 $405,682.
2-18 a. Stream A: $1,251.25. 4-22 A/P ϭ $90,000; Inv ϭ $90,000; FA ϭ $138,000.
2-20 Contract 2; PV ϭ $10,717,847.14. 4-24 a. TIE ϭ 11; EBITDA coverage ϭ 9.46;
2-22 a. $802.43.
c. $984.88. Profit margin ϭ 3.40%; ROE ϭ 8.57%.
2-24 a. $279.20.
b. $276.84. 6-2 2.25%.
c. $443.72. 6-4 1.5%.
2-26 $17,290.89; $19,734.26. 6-6 21.8%.
2-28 INOM ϭ 7.8771%. 6-8 8.5%.
2-30 a. E ϭ 63.74 yrs.; K ϭ 41.04 yrs. 6-10 6.0%.
b. $35,825.33. 6-12 0.35%.
2-32 $496.11. 6-14 a. r1 in Year 2 ϭ 6%.
2-34 a. PMT ϭ $10,052.87.
b. Yr 3: Int/Pymt ϭ 9.09%; b. I1 ϭ 2%; I2 ϭ 5%.
6-16 14%.
Princ/Pymt ϭ 90.91%. 6-18 a. r1 ϭ 9.20%; r5 ϭ 7.20%.
2-36 a. $5,308.12.
7-2 a. 7.11%.
b. $4,877.09. b. 7.22%.
2-38 $309,015. c. $988.46.
2-40 $9,385.
7-4 YTM ϭ 6.62%; YTC ϭ 6.49%;
3-2 $2,500,000. most likely yield ϭ 6.49%.
3-4 $20,000,000.
3-6 $89,100,000. 7-6 a. C0 ϭ $1,012.79; Z0 ϭ $693.04;
3-8 NI ϭ $450,000; NCF ϭ $650,000; C1 ϭ $1,010.02; Z1 ϭ $759.57;
C2 ϭ $1,006.98; Z2 ϭ $832.49;
OCF ϭ $650,000. C3 ϭ $1,003.65; Z3 ϭ $912.41;
C4 ϭ $1,000.00; Z4 ϭ $1,000.00.

A-27

A-28 Appendix B Answers to Selected End-of-Chapter Problems

7-8 15.03%. 10-12 a. rs ϭ 14.40%.
7-10 a. YTM ϭ 9.69%. b. WACC ϭ 10.62%.
10-14
b. CY ϭ 8.875%; CGY ϭ 0.816%. 10-16 c. Project A.
7-12 a. YTM ϭ 8%; YTC ϭ 6.1%.
7-14 10.78%. 10-18 11.94%.
7-16 $987.87.
7-18 8.88%. 10-20 a. g ϭ 8%.
7-20 a. 8.35%.
b. D1 ϭ $2.81.
b. 8.13%. c. rs ϭ 15.81%.
a. rd ϭ 7%; rp ϭ 10.20%; rs ϭ 15.72%.
8-2 bp ϭ 1.12. b. WACC ϭ 13.86%.
8-4 rM ϭ 11%; r ϭ 12.2%.
8-6 a. rˆY ϭ 14%. c. Projects 1 and 2 will be accepted.

b. ␴X ϭ 12.20%. a. rd(1 Ϫ T) ϭ 5.4%; rs ϭ 14.6%.
8-8 b ϭ 1.33. b. WACC ϭ 10.92%.
8-10 4.2%.
8-12 rM Ϫ rRF ϭ 4.375%. 11-2 IRR ϭ 16%.
8-14 bN ϭ 1.16. 11-4
8-16 rp ϭ 11.75%. 11-6 4.34 years.
8-18 a. $0.5 million.
11-8 a. 5%: NPVA ϭ $3.52; NPVB ϭ $2.87.
d(2). 15%. 11-10 10%: NPVA ϭ $0.58; NPVB ϭ $1.04.
8-20 a. rA ϭ 11.30%. 11-12 15%: NPVA ϭ Ϫ$1.91; NPVB ϭ Ϫ$0.55.
11-14
c. ␴A ϭ 20.8%; ␴p ϭ 20.1%. b. IRRA ϭ 11.10%; IRRB ϭ 13.18%.
11-16 c. 5%: Choose A; 10%: Choose B; 15%: Do not
9-2 Pˆ0 ϭ $6.25.
9-4 b. $37.80. 11-18 choose either one.

c. $34.09. 11-20 a. Without mitigation: NPV ϭ $12.10 million;
9-6 rp ϭ 8.33%. 11-22
9-8 a. $125. With mitigation: NPV ϭ $5.70 million.

b. $83.33. Project A; NPVA ϭ $30.16.
9-10 $23.75. IRRL ϭ 11.74%.
9-12 a(1). $9.50. a. HCC; PV of costs ϭ Ϫ$805,009.87.

a(2). $13.33. c. HCC; PV of costs ϭ Ϫ$767,607.75.
a(3). $21.00.
a(4). $44.00. LCC; PV of costs ϭ Ϫ$686,627.14.
b(1). Undefined.
b(2). Ϫ$48.00, which is nonsense. a. NPVA ϭ $14,486,808; NPVB ϭ $11,156,893;
9-14 Pˆ3 ϭ $27.32. IRRA ϭ 15.03%; IRRB ϭ 22.26%.
9-16 P0 ϭ $19.89.
9-18 6.25%. b. Crossover rate ഠ 12%.
9-20 a. P0 ϭ $54.11; D1/P0 ϭ 3.55%;
a. No; PVOld ϭ Ϫ$89,910.08; PVNew ϭ Ϫ$94,611.45.
CGY ϭ 6.45%. b. $2,470.80.
9-22 $35.00.
9-24 a. $2.01; $2.31; $2.66; $3.06; $3.52. c. 22.94%.

b. P0 ϭ $39.43. $10,239.20.
c. D1/P0 2006 ϭ 5.10%; CGY2006 ϭ 6.9%;
$250.01.
D1/P0 2011 ϭ 7.00%; CGY2011 ϭ 5%.
12-2 a. $2,600,000.
10-2 rp ϭ 8%.
10-4 rs ϭ 15%; re ϭ 16.11%. 12-4 b. Accelerated method; $12,781.64.
10-6 a. rs ϭ 16.3%.
b. rs ϭ 15.4%. 12-6 a. Ϫ$178,000.
10-8 c. rs ϭ 16%.
10-10 d. rs AVG ϭ 15.9%. b. $52,440; $60,600; $40,200.
rs ϭ 16.51%; WACC ϭ 12.79%.
WACC ϭ 11.4%. c. $48,760.

d. NPV ϭ Ϫ$19,549; Do not purchase.

12-8 a. Expected CFA ϭ $6,750;
Expected CFB ϭ $7,650; CVA ϭ 0.0703.

b. NPVA ϭ $10,036; NPVB ϭ $11,624.
12-10 a. NPV ϭ $37,035.13.

b. NPV ϭ ϩ20%: $77,975.63;

Ϫ20%: NPV ϭ Ϫ$3,905.37.

c. E(NPV) ϭ $34,800.21;

␴NPV ϭ $35,967.84;
CV ϭ 1.03.

13-2 a. Project B; NPVB ϭ $2,679.46.
b. Project A; NPVA ϭ $3,773.65.
c. Project A; EAAA ϭ $1,190.48.

Appendix B Answers to Selected End-of-Chapter Problems A-29

13-4 A; EAAA ϭ $1,407.85. 17-2 AFN ϭ $610,000.
13-6 NPVA ϭ $9.93 million. 17-4 a. $133.50 million.
13-8 EAAY ϭ $7,433.12. b. 39.06%.
13-10 No, NPV3 ϭ $1,307.29. 17-6 $67 million; 5.01.
13-12 a. NPV ϭ $4.6795 million. 17-8 a. $480,000.
b. $18,750.
b. No, NPV ϭ $3.2083 million. 17-10 $34.338 million; 34.97 ഠ 35 days.
17-12 a. $2,500,000,000.
c. 0. b. 24%.
17-14 c. $24,000,000.
14-2 30% debt and 70% equity. a. 33%.
14-4 b. AFN ϭ $2,549.
14-6 bU ϭ 1.0435.
a(1). Ϫ$60,000. 18-2 $27.00; $37.00.
14-8 18-4 $1.82.
14-10 b. QBE ϭ 14,000. 18-6 b. Futures ϭ ϩ$4,180,346; Bond ϭ Ϫ$2,203,701;
rs ϭ 17%.
14-12 a. FCA ϭ $80,000; VA ϭ $4.80/unit; Net ϭ $1,976,645.

PA ϭ $8.00/unit.
a. EPSOld ϭ $2.04; New: EPSD ϭ $4.74;

EPSS ϭ $3.27.
b. 339,750 units.

c. QNew, Debt ϭ 272,250 units.

15-2 P0 ϭ $60. 19-2 27.2436 yen per shekel.
15-4 D0 ϭ $3.44. 19-4 1 euro ϭ $0.68966 or $1 ϭ 1.45 euros.
15-6 Payout ϭ 31.39%. 19-8 15 kronas per pound.
19-10 rNOM-U.S. ϭ 4.6%.
15-8 a. 12%. 19-12 b. $1.6488.
19-14 ϩ$250,000.
b. 18%. 19-16 $468,837,209.

c. 6%; 18%. 20-2 $196.36.
20-4 a. D/AJ-H ϭ 50%; D/AM-E ϭ 67%.
d. 6%. 20-6 a. EV ϭ Ϫ$3; EV ϭ $0; EV ϭ $4; EV ϭ $49.

e. 28,800 new shares; $0.13 per share. d. 9%; $90.
20-8 a. PV cost of owning ϭ Ϫ$185,112;
16-2 73 days; 30 days; $1,178,082.
16-4 PV cost of leasing ϭ Ϫ$187,534;
16-6 a. 83 days.
Purchase loom.
16-8 b. $356,250.
16-10 c. 4.87ϫ. 21-2 P0 ϭ $43.48.
21-4 a. 16.8%.
a. 32 days.
b. V ϭ $14.93 million.
b. $288,000.
21-6 a. 14%.
c. $45,000. b. TV ϭ $1,143.4; V ϭ $877.2.

d(1). 30.

d(2). $378,000.
a. ROET ϭ 11.75%; ROEM ϭ 10.80%;

ROER ϭ 9.16%.
a. October loan ϭ $22,800.

C APPENDIX

Selected Equations and Data

CHAPTER 2

FVN ϭ PV 11 ϩ I 2 N

PV ϭ FVN
11 ϩ I2N

11 ϩ I2N Ϫ 1
FVAN ϭ PMT c I d

FVADue ϭ FVAOrdinary 11 ϩ I 2

1Ϫ 1 I2N §
PVAN ϭ PMT £ 11 ϩ

I

PVAN Due ϭ PVAOrdinary 11 ϩ I 2

PV of a perpetuity ϭ PMT
I

PVUneven stream ϭ N CFt
11 ϩ I2t
a

tϭ1

IPER ϭ I
M

APR ϭ 1IPER 2 M
Number of periods ϭ NM

INOM M
M
EFF% ϭ a1 ϩ b Ϫ 1.0

CHAPTER 3

EBIT ϭ Sales revenues Ϫ Operating costs

Net cash flow ϭ Net income ϩ Depreciation and amortization

Net operating All current assets All non-interest-bearing
working capital ϭ required in operations Ϫ current liabilities

Net operatingworking Cash ((
Accounts
( (capital payable ϩAccruals
ϭ and cash ϩ Accounts Inventories Ϫ
equivalents receivable ϩ

Total operating capital ϭ Net operating working capital ϩ Net fixed assets
NOPAT ϭ EBIT 11 Ϫ Tax rate2
Operating cash flow ϭ NOPAT ϩ Depreciation and amortization

FCF ϭ c EBIT 11 Ϫ T2 ϩ Depreciation and d Ϫ c Capital ϩ ¢Net operating d
amortization expenditures working capital

A-30

Appendix C Selected Equations and Data A-31

Free cash flow ϭ Operating cash flow Ϫ Investment in operating capital

MVA ϭ Market value of stock Ϫ Equity capital supplied by shareholders

ϭ 3 1Shares outstanding2 1Stock price2 4 Ϫ Total common equity

EVA ϭ NOPAT Ϫ Annual dollar cost of capital

ϭ 1EBIT2 11 Ϫ T2 Ϫ a Total investor-supplied ϫ After-tax percentage b
operating capital cost of capital

CHAPTER 4

Current ratio ϭ Current assets
Current liabilities

Quick, or acid test, ratio ϭ Current assets Ϫ Inventories
Current liabilities

Inventory turnover ratio ϭ Sales
Inventories

DSO ϭ Days sales outstanding ϭ Receivables day ϭ Receivables
Average sales per Annual sales>365

Fixed assets turnover ratio ϭ Net Sales
fixed assets

Total assets turnover ratio ϭ Sales
Total assets

Debt ratio ϭ Total debt
Total assets

D>E
D>A ϭ 1 ϩ D>E

Debt ratio ϭ 1 Ϫ Equity 1
multiplier

D>A
D>E ϭ 1 Ϫ D>A

Times-interest-earned 1 TIE 2 ratio ϭ EBIT
Interest charges

EBITDA ϩ Lease payments
EBITDA coverage ratio ϭ Interest ϩ Principal payments ϩ Lease payments

Profit margin on sales ϭ Net income
Sales

Return on total assets 1ROA 2 ϭ Net income
Total assets

Basic earning power 1 BEP 2 ratio ϭ EBIT
Total assets

ROA ϭ Profit margin ϫ Total assets turnover

ROA ϭ Net income ϫ Sales
Sales Total assets

Return on common equity 1 ROE 2 ϭ Net income
Common equity

A-32 Appendix C Selected Equations and Data

ROE ϭ ROA ϫ Equity multiplier

ϭ Profit margin ϫ Total assets turnover ϫ Equity multiplier

ϭ Net income ϫ Sales ϫ Total assets
Sales Total assets Common equity

Return on investors’ capital ϭ Net income ϩ Interest
Debt ϩ Equity

Price per share
Price>earnings 1P>E2 ratio ϭ Earnings per share

Price per share
Price>cash flow ratio ϭ Cash flow per share

Common equity
Book value per share ϭ Shares outstanding

Market price per share
Market>book 1M>B2 ratio ϭ Book value per share

EVA ϭ Net income Ϫ a Equity capital ϫ % Cost of equity capital b
EVA ϭ Equity capital ϫ 1ROE Ϫ % Cost of equity capital2

CHAPTER 6

r ϭ r* ϩ IP ϩ DRP ϩ LP ϩ MRP

rRF ϭ r* ϩ IP

Considering cross term, rRF ϭ r* ϩ I ϩ 1r* ϫ I 2 . Assume no cross term, unless specified.

r ϭ rRF ϩ DRP ϩ LP ϩ MRP

IPN ϭ I1 ϩ I2 ϩ. . . ϩ IN
N

CHAPTER 7

VB ϭ N INT ϩ M
11 ϩ rd 2 t 11 ϩ rd 2 N
a

tϭ1

Price of callable bond ϭ N INT ϩ Call price
11 ϩ rd 2 t 11 ϩ rd 2 N
a

tϭ1

Current yield ϭ Annual interest
Bond’s current price

VB ϭ 2N INT>2 ϩ M
11 ϩ rd>2 2 2N
a 11 ϩ rd>2 2 t

tϭ1

Appendix C Selected Equations and Data A-33

CHAPTER 8

N

Expected rate of return ϭ ˆr ϭ a Piri
iϭ1
N

Variance ϭ ␴2 ϭ a 1ri Ϫ ˆr 2 2Pi
iϭ1

N ˆr 2 2Pi

Standard deviation ϭ ␴ ϭ B a 1ri Ϫ

iϭ1

N

a 1rt Ϫ rAvg 2 2
tϭ1
Estimated ␴ ϭ S ϭ N Ϫ 1
R

CV ϭ ␴
ˆr

N

ˆrp ϭ a wi ˆri
iϭ1

N rˆp 2 2Pj

␴p ϭ B a 1rpj Ϫ

jϭ1

N

bp ϭ a wibi
iϭ1

RPi ϭ 1rM Ϫ rRF 2 bi ϭ 1RPM 2 bi

SML ϭ ri ϭ rRF ϩ 1rM Ϫ rRF 2 bi

CHAPTER 9

Pˆ0 ϭ PV of expected future dividends ϭ ϱ 11 Dt
ϩ rs 2 t
a

tϭ1

Pˆ0 ϭ D0 11 ϩ g 2 ϭ D1
rs Ϫ g rs Ϫ g

ˆrs ϭ D1 ϩ g
P0

Capital gains yield ϭ Pˆ1 Ϫ P0
P0

Dividend yield ϭ D1
P0

For a constant growth stock, PˆN ϭ P0 11 ϩ g 2 N

For a zero growth stock, Pˆ0 ϭ D
rs

Horizon value ϭ PˆN ϭ DNϩ1
rs Ϫ g

VCompany ϭ FCF1 ϩ FCF2 ϩ...ϩ FCFϱ
11 ϩ WACC 2 1 11 ϩ WACC 2 2 11 ϩ WACC 2 ϱ

Terminal value ϭ VCompany at tϭN ϭ FCFNϩ1
WACC Ϫ gFCF

A-34 Appendix C Selected Equations and Data

Vp ϭ Dp
rp

rˆp ϭ Dp
Vp

CHAPTER 10

After-tax component cost of debt ϭ rd 11 Ϫ T 2
Dp

Component cost of preferred stock ϭ rp ϭ Pp

rs ϭ rˆs ϭ rRF ϩ RP ϭ D1>P0 ϩ g

rs ϭ Bond yield ϩ Risk premium

re ϭ D1 F2 ϩ g
P0 11 Ϫ

g ϭ 1Retention rate2 1ROE 2 ϭ 11.0 Ϫ Payout rate2 1ROE2

REBreakpoint ϭ Addition to retained earnings

Equity fraction

WACC ϭ wdrd 11 Ϫ T 2 ϩ wprp ϩ wcrs

CHAPTER 11

NPV ϭ CF0 ϩ CF1 ϩ CF2 ϩ . . . ϩ CFN
11 ϩ r21 11 ϩ r22 11 ϩ r2N

ϭ N CFt
11 ϩ r2t
a

tϭ0

IRR: N 11 CFt ϭ 0
ϩ IRR 2 t
a

tϭ0

MIRR: PV costs ϭ PV terminal value

N

N COF ϭ a CIFt 11 ϩ r 2 NϪt
11 ϩ r2t
a tϭ0

tϭ0 11 ϩ MIRR 2 N

PV costs ϭ 11 TV
ϩ MIRR 2 N

Payback ϭ Number of years prior to full recovery ϩ Unrecovered cost at start of full recovery year

Cash flow during full recovery year

CHAPTER 14

EBIT ϭ PQ Ϫ VQ Ϫ F

QBE ϭ P F V
Ϫ

Appendix C Selected Equations and Data A-35

1S Ϫ FC Ϫ VC Ϫ I2 11 Ϫ T2 1EBIT Ϫ I2 11 Ϫ T 2
EPS ϭ Shares outstanding ϭ Shares outstanding
bL ϭ bU 3 1 ϩ 11 Ϫ T 2 1D>E 2 4
bU ϭ bL > 3 1 ϩ 11 Ϫ T 2 1D>E 2 4
rs ϭ rRF ϩ Premium for business risk ϩ Premium for financial risk

CHAPTER 15

Dividends ϭ Net income Ϫ 3 1Target equity ratio2 1Total capital budget2 4

CHAPTER 16

Inventory Average Payables Cash

conversion ϩ collection Ϫ deferral ϭ conversion

period period period cycle

Inventory
Inventory conversion period ϭ Cost of goods sold>365

Average collection period ϭ DSO ϭ Receivables
Sales>365

Payables
Payables deferral period ϭ Cost of goods sold>365

Accounts receivable ϭ Credit sales per day ϫ Length of collection period

ADS ϭ 1Units sold2 1Sales price2 ϭ Annual sales
365 365

Receivables ϭ 1ADS2 1DSO2

Nominal annual cost of trade credit ϭ Discount % % ϫ Days credit is 365 Ϫ Discount period
100 Ϫ Discount outstanding

Simple interest rate per day ϭ Nominal rate
Days in year

Simple interest charge for period ϭ 1Days in period2 1Rate per day2 1Amount of loan2

Interest paid
Approximate annual rateAdd-on ϭ 1Amount received 2 >2

APR ϭ 1Periods per year2 1Rate per period2

Effective annual rateAdd-on ϭ 11 ϩ rd 2 N Ϫ 1.0

CHAPTER 17

Required Spontaneous Increase in

AFN ϭ asset Ϫ liability Ϫ retained

increase increase earnings

ϭ 1A*>S0 2 ⌬S Ϫ 1L*>S0 2 ⌬S Ϫ MS1 1RR 2

A-36 Appendix C Selected Equations and Data

Full capacity sales ϭ Percentage of capacity Actual sales assets were operated
at which fixed

Target FA>Sales ratio ϭ Actual fixed assets
Full capacity sales

Required level of FA ϭ 1Target FA>Sales ratio2 1Projected sales2

CHAPTER 18

Exercise value ϭ Current price of stock Ϫ Strike price
V ϭ P 3 N 1d1 2 4 Ϫ XeϪrRFt 3 N 1d2 2 4
d1 ϭ ln 1P>X 2 ϩ 3 rRF ϩ 1␴2>2 2 4 t

␴ 2t
d2 ϭ d1 Ϫ ␴ 2t

Values of the Areas under the Standard Normal Distribution Function

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319 .0359
0.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .0753
0.2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1103 .1141
0.3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .1517
0.4 .1554 .1591 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .1879
0.5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 .2157 .2190 .2224

0.6 .2257 .2291 .2324 .2357 .2389 .2422 .2454 .2486 .2517 .2549
0.7 .2580 .2611 .2642 .2673 .2704 .2734 .2764 .2794 .2823 .2852
0.8 .2881 .2910 .2939 .2967 .2995 .3023 .3051 .3078 .3106 .3133
0.9 .3159 .3186 .3212 .3238 .3264 .3289 .3315 .3340 .3365 .3389
1.0 .3413 .3438 .3461 .3485 .3508 .3531 .3554 .3577 .3599 .3621

1.1 .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .3830
1.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 .4015
1.3 .4032 .4049 .4066 .4082 .4099 .4115 .4131 .4147 .4162 .4177
1.4 .4192 .4207 .4222 .4236 .4251 .4265 .4279 .4292 .4306 .4319
1.5 .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .4441

1.6 .4452 .4463 .4474 .4484 .4495 .4505 .4515 .4525 .4535 .4545
1.7 .4554 .4564 4573 .4582 .4591 .4599 .4608 .4616 .4625 .4633
1.8 .4641 .4649 .4656 .4664 .4671 .4678 .4686 .4693 .4699 .4706
1.9 .4713 .4719 .4726 .4732 .4738 .4744 .4750 .4756 .4761 .4767
2.0 .4773 .4778 .4783 .4788 .4793 .4798 .4803 .4808 .4812 .4817

2.1 .4821 .4826 .4830 .4834 .4838 .4842 .4846 .4850 .4854 .4857
2.2 .4861 .4864 .4868 .4871 .4875 .4878 .4881 .4884 .4887 .4890
2.3 .4893 .4896 .4898 .4901 .4904 .4906 .4909 .4911 .4913 .4916
2.4 .4918 .4920 .4922 .4925 .4927 .4929 .4931 .4932 .4934 .4936
2.5 .4938 .4940 .4941 .4943 .4945 .4946 .4948 .4949 .4951 .4952

2.6 .4953 .4955 .4956 .4957 .4959 .4960 .4961 .4962 .4963 .4964
2.7 .4965 .4966 .4967 .4968 .4969 .4970 .4971 .4972 .4973 .4974
2.8 .4974 .4975 .4976 .4977 .4977 .4978 .4979 .4979 .4980 .4981
2.9 .4981 .4982 .4982 .4982 .4984 .4984 .4985 .4985 .4986 .4986
3.0 .4987 .4987 .4987 .4988 .4988 .4989 .4989 .4989 .4990 .4990

Appendix C Selected Equations and Data A-37

CHAPTER 19

Forward exchange rate ϭ 1 ϩ rh
Spot exchange rate 1 ϩ rf

Ph ϭ 1Pf 2 1Spot rate 2

Spot rate ϭ Ph
Pf

CHAPTER 20

Price paid for bond with warrants ϭ Straight-debt value of bond ϩ Value of warrants

Conversion price ϭ Pc ϭ Par value of bond given up

Shares received

Conversion ratio ϭ CR ϭ Par value of bond given up

Pc

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A INDEX

Abandonment option, 417–419 B
Accounting profit, 75
Accounts payable (See also Current assets Balance sheet (See also Financial statements), 68–72
Bank loans, 537–541
and Working capital), 534–537
stretching, 536 add-on interest, 540–541
Accounts receivable (See also Current assets cost, 539–541
prime rate, 539
and Working capital), 530–534 promissory note, 537–538
credit policy, 530–532 regular (simple) interest, 539–540
Accruals, 542 secured, 542
Acid test, 104 simple (regular) interest, 539–540
Acquiring company, 689 Bankruptcy (See also Reorganization), 233–234
Actual (realized) rate of return (Ϫr ), 258, 294 Base-case NPV, 398
Additional funds needed (AFN), 556 Base-case scenario, 400
Add-on interest, 540–541 Basic EPS, 674
Adjustable rate preferred stock, 652 Basic earning power ratio, 114
Agency theory, 16 Behavioral finance, 167
Aging schedule, 533–534 a closer look at theory, 168
Airbus, 357–358 Benchmarking, 121
Amazon.com, 648–649 Benefits of diversifying overseas, 270
American depository receipts (ADRs), 636 Best Buy Company, 512
American terms, 625 Best-case scenario, 400
Amortization, 74 Beta coefficient (See also Capital Asset Pricing
Amortization schedule, 54
Amortized loans, 52–54 Model), 266
Annual compounding, 48 changes in, 277
Annual depreciation rates, 413 concept of, 266–269
Annual percentage rate (APR), 50 concerns about, and the CAPM, 277–278
Annual report, 66 unlevered (bU), 452
Annuity, 35–36 Beta risk, 264, 397
annuity due, 36 Bid price, 156
finding payments, periods, and interest Bird-in-the-hand theory, 481
Black-Scholes option pricing model, 592–596
rates, 40–42 Boeing, 357–358
ordinary (deferred), 36 Bonds, 207, 208–237
Apple Computer, 552 assessing riskiness, 223–227
Appreciation of a currency, 622 changes in values over time, 218–222
Arbitrage, 628, 704 convertible, 212
risk, 704 corporate, 209
Arbitrageurs, 704 debenture, 228–229
Arrearages, 650 default risk, 227–234
Ask price, 156 discount, 215
Asset management ratios (See also Financial duration, 223
eurobond, 631
ratios), 104–107 floating rate, 210
days sales outstanding, 106 foreign, 209
fixed assets turnover ratio, 106–107 income, 212
inventory turnover ratio, 105 indenture, 228
total assets turnover ratio, 107 indexed (purchasing power), 213
Asymmetric information, 460 investment grade, 229
Average collection period (ACP), junk, 229
key characteristics, 209–213
106, 514 markets, 234–236
Average-risk stock, 266

I-2 Index

Bonds, (continued) modified IRR, 371–373
mortgage, 228 multiple IRRs, 369–371
municipal, 209 net present value (NPV) criterion, 360–362
new issue, 218 optimal capital budget, 424–425
original issue discount, 210 payback period, 373–375
premium, 216 post-audit, 378–379
putable, 212 practices in the Asian/Pacific region, 402
seasoned issue, 218 project analysis, 390–394
semiannual coupons, 222–223 project background, 388–390
sizing up risk in market, 207–208 project classifications, 359–360
subordinated debenture, 229 real options and other topics in, 415–426
treasury, 209 replacement analysis, 395
valuation, 213–216 using capital budgeting techniques in other
warrant, 212
who issues, 208–209 contexts, 377–378
yields, 216–218 Capital component, 331
zero coupon, 210 Capital gains yield, 219, 294
Capital intensity ratio, 558
Bond valuation (See also Valuation), 213–216 Capital markets, 145
semiannual coupons, 222–223 Capital rationing, 425
Capital structure and leverage, 436–466
Bond-yield-plus-risk-premium approach, 339
Book value per share, 70, 117 business and financial risk, 439–450
Breakup value, 687 checklist for decisions, 462–464
Business climate, 637 different, 403
Business cycles, 300 determining optimal, 450–456
Business ethics, 12, 13–15 Hamada equation, 452–453
Business risk (See also Risk), 439–441 international, 638–639
optimal, 331, 437
C taking a look at global capital structures, 465
target (optimal), 331, 437–438
Call option, 584 theory, 456–462
Call premium, 211 variations in, 465–466
Call protection, 211 Captive finance companies, 532
Call provision, 211 Carve-out, 707
Cannibalization effect, 396 Cash budget, 521, 522–525
Capital, 358 Cash conversion cycle, 513–517
Capital allocation process overview, 143–144 Cash equivalents, 68
Capital Asset Pricing Model (CAPM), 264 Cash flow, 44
estimation and risk analysis, 387–405
approach for cost of capital, 336 free, 84–85
beta coefficient, 266 future value of uneven stream, 46–47
market risk premium, 186 incremental, 395
required rate of return, 294 massaging, 78
Security Market Line, 274 net, 75
Capital budgeting, 357, 358–379 operating, 84
basics, 357–379 other points on analysis, 394–397
comparing mutually exclusive projects with statement, 75, 76–78
uneven, 44–46
unequal lives, 422–424 Certainty equivalent, 404
comparison of NPV and IRR methods, 364–369 Chairman of the board, 17
competition in the aircraft industry, 357–358 Chief executive officer, CEO, 18
conclusions on methods, 375–376 Chief financial officer, CFO, 18
decision criteria used in practice, 376–377 Chief operating officer, COO, 18
estimating project risk, 397–398 Citigroup, 2–3
externality, 396 built to compete in a changing environment, 154
generating ideas for capital projects, 358–359 Classified stock, 292
incorporating risk into, 403–404
internal rate of return (IRR), 363–364
international, 636–637

Index I-3

Class life, 413 Conversion price, 667
Clientele effect, 482–483 Conversion ratio, 667
Clienteles, 482 Conversion value, 669
Closely held corporation, 157 Convertible bond, 212
Coefficient of variation (CV), 254–255 Convertible security, 667–673
Collateralized mortgage obligations, 601
Collection policy, 530 comparison with warrants, 673–674
Commercial bank, 150 reporting earnings when outstanding, 674–675
Commercial paper, 541–542 Corporate alliance, 706
Commodity futures, 597 Corporate bonds, 209
Common equity, 69 Corporate objectives, 554
Common life (replacement chain) approach, Corporate raider, 17
Corporate (within-firm) risk, 397
422–423 Corporate scope, 553
Common size analysis, 103 Corporate strategies, 554
Common stock, 289–317 Corporate valuation (total company) model, 305
Corporation, 5
classified, 292 closely held, 157
constant growth, 296–298 multinational (global), 616–619
cost of new, 335, 340–343 publicly owned, 157
evaluating stocks that don’t pay dividends, 304 S, 5
expected rate of return on constant growth stock, Correlation, 259
Correlation coefficient (␳), 259
299–300 Cost of capital, 328–349
founders’ shares, 292 adjusting for risk, 346–348
investing in international stocks, 313 after-tax cost of debt, rd(1 – T), 332
legal rights and privileges, 290–292 basic definitions, 331–332
market efficiency, 163–169 bond-yield-plus-risk-premium approach, 339
market equilibrium, 310–313 CAPM approach, 336
market for, 157–160 composite, or weighted average, WACC, 331,
markets and returns, 160–162
nonconstant growth, 300 343–344
other approaches to valuing, 308–309 cost of debt, rd(1 – T), 332–333
oversubscribed, 158 cost of new common stock (re), 335, 340–343
searching for the right stock, 289 cost of preferred stock (rp), 333–334
types, 292 cost of retained earnings, rs, 335–339
valuation, 292–295 creating value at GE, 328–329
valuing stocks expected to grow at a nonconstant DCF approach, 336–339
factors affecting, 344–345
rate, 300–303 global variations in, 345
valuing the entire corporation, 305–310 how much does it cost to raise external
zero growth stock, 298
Common equity, 69 capital, 340
Company-specific risk (See also Risk), 264 overview of weighted average cost of capital,
Comparative ratios and benchmarking, 121–124
Comparing interest rates, 50–51 329–330
Compensation committee, 17 problems with estimates, 348–349
Compensation package, 16 risk-adjusted, 398
Compounding, 26 weighted average (WACC), 331, 343–344
annual, 48 Cost of money, 175–176
semiannual, 48 Costly trade credit, 536
Compound interest, 27 Counterparties, 582
Concerns about beta and the CAPM, 277–278 Country risk, 199
Conflicts between managers and stockholders, 16–17 measuring, 198
Congeneric merger, 687 Coupon interest rate, 210
Conglomerate merger, 687 Coupon payment, 210
Consol, 42 Credit (See also Trade credit), 534–543
Constant growth (Gordon) model, 296 line of, 538
Constant growth stocks, 296–298 revolving agreement, 538–539

I-4 Index

Credit instruments create new opportunities and EBITDA coverage ratio, 111–112
risk, 603 times-interest-earned (TIE) ratio, 110–111
Decision tree, 417–418
Credit policy, 530 Declaration date, 490
collection policy, 530 Default risk, 227–234
discount, 530 Default risk premium, 183
five Cs of credit, 531 Defensive merger, 686
period, 530 Deferred (ordinary) annuity, 36
score, 531 Deferred call, 211
standards, 530 Demand deposits, 526–527
terms, 531 Depreciation, 74
Depreciation of a currency, 622
Credit unions, 150 Derivative, 147, 581
Cross rate, 624–625 and risk management, 578–611
Crossover rate, 365 background on, 582–584
Cumulative, 650 Barings and Sumitomo suffer large losses in
Cumulative voting, 290
Currency, 526 derivatives market, 583
Currency board arrangement, 623 Black-Scholes option pricing model, 592–596
Currency swap, 601 credit instruments create new opportunities and
Current assets, 68, 511–534
risks, 603
accounts receivable, 530–534 expensing executive stock options, 590
alternative financing policies, 518–521 forward and futures contracts, 596–600
alternative investment policies, 517–518 introduction to option pricing models, 589–592
cash and marketable securities, 525–528 Microsoft’s goal: manage every risk, 606
cash budget, 521, 522–525 options, 584–589
cash conversion cycle, 513–517 other types, 600–603
financing policy, 518 reasons to manage risk, 579–582
inventories, 528–529 risk management, 603–604, 605–607
maturity matching (“self-liquidating”) using to reduce risks, 607–611
Detachable warrant, 664
approach, 519 Determinants of market interest rates, 180–187
moderate policy, 518 Determinants of shape of yield curve, 189–193
permanent, 518 expectations theory, 193
relaxed investment policy, 518 Devaluation of a currency, 622
restricted policy, 518 Diluted EPS, 675
temporary, 518 Direct investments, 631
Current ratio, 103–104 Direct quotation, 625
Current yield, 218 Direct transfers, 143
Discount, 530
D Discount bond, 215
Discount on forward rate, 627
Days sales outstanding, 106 Discounted cash flow analysis (See also Time value
Dealer market, 156
Debenture, 228–229 of money), 24–54, 336–339
Discounted payback period, 374
subordinated, 229 Discounting, 32
Debt (See also Bonds; Current asset financing; Diversifiable risk, 246, 263, 264–266
Diversification, benefits more important than ever, 263
Short-term financing), 207–237
bonds, 207, 208–237 benefits of overseas, 270
collateralized obligations, 602 Divestitures, 707–710
cost of, 332–333 Dividend policy, 478–502
floating-rate, 210
interest only, 602 bird-in-the-hand theory, 481
principal only, 602 declaration date, 490–491
ratio, 110 establishing in practice, 483–492
rocket or anchor?, 436–437 ex-dividend date, 491–492
Debt management ratios (See also Financial ratios), holder-of-record date, 491

108–112
debt ratio, 110

Index I-5

irrelevance theory, 480 Expectations theory, 193
low-regular-dividend-plus-extras, 489 Expected rate of return, rˆs, 248–250, 294
optimal policy, 480
other issues, 482–483 constant growth stock, 299–300
payment date, 492 Expected return on a portfolio (rˆp), 258–259
reinvestment plans, 493–494 Expected total return, 294
residual dividend model, 483–484, 485–489 Expensing executive stock options, 590
reverse splits, 496 Externalities, 396–397
stock dividends and splits, 495–496, 497–498
stock repurchases, 498–502 F
summary of factors influencing, 494–495
target payout ratio, 479 Factors that affect the WACC, 344–345
versus capital gains, 479–481 Factors that influence interest rate levels, 196–199
Dividend yield, 294 FASB #13, 656
around the world, 488 Federal income tax system, 87–89
Due diligence, 694 Federal Reserve policy, 196
Du Pont equations, 118–121 Fidelity, 64
basic, 118 Finance, role in the organization, 17–18
extended, 120 Financial analysis on the internet, 80
Duration, 223 Financial asset markets, 145
Financial calculators, hints on using, 29
E Financial futures, 597–598
Financial institutions, 148–153
Earnings per share (EPS), 72, 73 Financial intermediaries, 143
basic, 674 Financial lease, 655
diluted, 675 Financial leverage, 108, 445
primary, 674 Financial management overview, 2–19

EBITDA, 74 important trends, 11–12
coverage ratio, 111–112 striking the right balance, 2–3
Financial markets, 145–147
Economic Value Added (EVA), 86 Financial markets and institutions, 141–169
and ROE, 126–127 Financial merger, 692
Financial plan, 554
Effective annual rate (EAR), 50 Financial planning and forecasting, 552–567
Efficient Markets Hypothesis (EMH), 163 AFN equation, 556–559
Emerging markets, 316 forecasted financial statements, 560–563
Enron, 100–101 pro forma financial statements, 553
Equilibrium, 10, 311 sales forecast, 555–556
Equity (See also Common stock), 69 strategic planning, 553–555
Equity multiplier, 120 using individual ratios in forecasting process,
Equity residual method, 692
Equivalent annual annuity (EAA) method, 423–424 565–566
Equivalent annual rate, 50 using regression to improve financial forecasts,
Ethics, 13
Estimating the market risk premium, 272 563–565
Eurobond, 631 Financial ratios (See also the specific type of ratios),
Eurocredits, 631
Eurodollar, 631 100–129
European terms, 625 analysis, 102–103
Exchange rate, 621 asset management, 104–107
comparative ratios and benchmarking, 121–124
fixed, 621 debt management, 108–112
floating (flexible), 622 liquidity, 103–104
forward, 621, 626 looking beyond the numbers, 128
spot, 621, 626 market value, 115–117
Exchange rate risk, 199, 637 problems with ROE, 125–127
Ex-dividend date, 491–492 profitability, 112–115
Exercise (strike) price, 584 trend analysis, 118
Exercise value, 586–589 tying together: the Du Pont equations, 118–121
uses and limitations of, 124–125

I-6 Index

Financial risk (See also Risk), 444–450 financial, 597–598
Financial services corporation, 150 interest rate, 597
Financial statements, 64–89 Futures markets, 145
FVAN, 36
analysis, 110–129
and reports, 66–67 G
annual report, 66
balance sheet, 68–72 General Electric, 328–329
doing your homework with, 64 Global accounting standards, 113
forecasted, 560–563 Global capital structures, 465
history, 65–66 Global corporations, 616–619
income statement, 72–74 Global perspectives boxes, 113, 270, 316, 345, 402,
lessons learned from Enron and WorldCom,
465, 488, 583
100–101 Global variations in the cost of capital, 345
looking for warning signs with, 123 Going public, 157
more than just, 697 Golden parachutes, 698, 702
pro forma, 553 Goodwill, 699
ratio analysis, 102–103 Governments divesting state-owned businesses to
statement of cash flows, 75, 76–78
statement of retained earnings, 78–79 spur economic efficiency, 708
uses and limitations of, 79–81 Greenmail, 500
Financial system, 141–142 Growth, 294–303
Financing policies (current assets), 518–521
aggressive approach, 519 constant growth (Gordon) model, 296
choosing between, 521 constant (normal), 296–298
conservative approach, 519 nonconstant (supernormal), 300
maturity matching, 519 option, 420–421
Fixed assets turnover ratio, 106–107 rate (g), 294
Fixed peg arrangement, 623 zero, 298
Flexibility option, 421–422
Float, 527 H
collection, 527
net, 527 Half-year convention, 413
payment, 527 Hamada equation, 452–453
Floating exchange rates, 622 Hedge funds, 151
Floating-rate bond, 210 Hedging, 607
Flotation cost, F, 341 Holder-of-record date, 491
Foreign bond, 209, 634 Home Depot, 387–388
Foreign trade deficit, 197 Horizon date, 301
Forms of business organization, 4–5 Horizon (terminal) value, 301
Forward contract, 596–597 Horizontal merger, 687
Forward exchange rate, 621, 626 Hostile merger, 689
Founders’ shares, 292 Hostile takeover, 17
Fractional time periods, 52 Humped yield curve, 189
Free cash flow, 84–85 Hurdle rate, 346
Freely-floating regime, 622 Hybrid financing (See individual entries, such as
Free trade credit, 536
Friendly merger, 689 Preferred stock; Leasing; Warrants;
Future value (See also Time value of money), 26–31 Convertibles), 648–675
annuity due, 38–39
ordinary (deferred) annuity, 36–38 I
uneven cash flow stream, 46–47
Futures contract, 596–597, 598–600 Incentive signaling, 482
commodity, 582, 597 Income bond, 212
exchange rate, 582 Income statement (See also Financial statements),

72–74
Incremental cash flow, 395
Indenture, 228
Independent projects, 362
Indexed (purchasing power) bond, 213

Index I-7

Indirect quotation, 625 Investment banking house, 143, 149
Inflation, 175 Investment-grade bonds, 229
Inflation premium, 182–183, 275 Investment horizon, 226
Information content (signaling) hypothesis, 482 Investment timing options, 419–420
Initial public offering (IPO) market, 158
Insolvent (See also Bankruptcy and Reorganization), J

233 Joint venture, 706
Intangible assets, 74 Junk bonds, 229
Interest (also see Bank loans), 537–541
K
add-on, 540–541
regular (simple), 539–540 Kellogg Co., 436–437
Interest rate parity, 627–629
Interest rates, 174–201 L
annual percentage rate, 50
business decisions affected by, 199–200 Leasing, 653–661
comparing, 50–51 FASB #13, 656
compound, 27 financial (capital), 655
cost of money, 175–176 off balance sheet financing, 656
coupon, 210 operating, 654
determinants of market, 180–187 residual value, 661
effective annual rate (EAR), 50 sale and leaseback, 653
encourage investment and stimulate consumer service, 654

spending, 174 Lessee, 654
expectations theory, 193 Lessor, 654
factors that influence levels, 196–199 Leverage, 441–445
finding, 34–35
levels, 176–180 financial, 108, 445
links between expected inflation, 192 operating, 441–444
nominal, 50 Leveraged buyout, 706–707
nominal (quoted) risk-free rate, 182 Life insurance companies, 150
periodic, 52 Line of credit, 538
prime, 539 Liquid asset, 103
real risk-free rate, 181 Liquidation, 233, 707
risk, 186, 223–225 Liquidity, 5
simple, 27 Liquidity premium, 186
simple versus compound, 27 Liquidity ratios, 103–104
swap, 581–582, 600 acid test, 104
term structure, 187–189 current ratio, 103–104
Internal rate of return (IRR) method, 363–364 quick ratio, 104
comparison with NPV, 364–369 Loans (See also Bank loans), 537–541, 542–543
IRR, 363–364 bank, 537–541
modified, 371–373 secured, 542
multiple, 369–371 Lockbox, 526
reinvestment rate assumption, 368 London Inter Bank Offer Rate, 631
International monetary system, 621–623 Long hedges, 607
Intrinsic value (Pˆ0), 8, 293 Long-term equity anticipation security, 586
stock prices, and compensation plans, 8–11 Low-regular-dividend-plus-extras, 489
Inventory, 528–529
conversion period, 514 M
turnover ratio, 105
Inverse floater, 602–603 Maintenance margin, 599
Inverted (abnormal) yield curve, 188 Managed-float regime, 622
Investing in emerging markets, 316 Margin, 599
Investing overseas, 199 Marginal investor, 10, 310
Market auction (money market) preferred

stock, 652
Market/book ratio, 116–117

I-8 Index

Market multiple analysis, 695 dividends, 480
Market portfolio, 264 Yogi Berra on the M&M proposition, 457
Market price (P0), 10, 293 Money market fund, 151
Market risk (See also Risk), 246, 263, 264–266, 397 Money markets, 145
Market risk premium, 271 Monte Carlo simulation, 401–403
Mortgage bond, 228
estimating, 272 Multinational (global) corporations, 616–619
Market Value Added (MVA), 86 Multinational financial management, 615–643
Market value ratios, 115–117 American terms, 625
capital budgeting, 636–637
market/book ratio, 116–117 capital structures, 638–639
price/cash flow ratio, 116 cross rate, 624–625
price/earnings ratio, 116 currency board arrangement, 623
Marketable securities, 527–528 direct quotation, 625
Maturity date, 210–211 eurobond, 631
Maturity matching (self-liquidating) eurocredits, 631
eurodollar, 631
approach, 519 European terms, 625
Maturity risk premium, 186 exchange rate, 621
Measuring the market, 164–165 fixed peg arrangement, 623
Mergers and acquisitions, 683–684, 685–710 foreign bond, 634
foreign exchange rate quotations, 623–626
analysis, 691–699 freely-floating regime, 622
congeneric, 687 hungry for a Big Mac?, 632–633
conglomerate, 687 indirect quotation, 625
corporate alliances, 706 inflation, interest rates, and exchange rates, 630–631
defensive, 686 international monetary system, 621–623
divestitures, 707–710 international money and capital markets, 631–636
do mergers create value? empirical evidence, interest rate parity, 627–629
managed-float regime, 622
704–706 multinational (global) corporations, 616–619
financial, 692 purchasing power parity, 629–630
financial reporting, 699–701 trading in foreign exchange, 626–627
friendly, 689 versus domestic financial management, 619–621
governments divesting to spur economic vertically integrated investment, 618
working capital management, 639–642
efficiency, 708 Multiple internal rates of return, 369–371
horizontal, 687 Municipal bonds or munis, 209
hostile, 689 Mutual funds, 150
hostile versus friendly takeovers, 689–690 Mutually exclusive projects, 361
level of activity, 687–689 comparing mutually exclusive projects with
leveraged buyout, 706
more than just financial statements, 697 unequal lives, 422–424
operating, 692 Mutual savings banks, 150
rationale for, 685–687 MVA and EVA, 86–87
regulation, 690–691
role of investment bankers, 702–704 N
synergy, 685
tempest in a teapot?, 701 Nasdaq, 156–157
track record of recent large mergers, 705 National Association of Securities Dealers, 156
types, 687 Natural hedges, 582
vertical, 687 Net cash flow, 75
Microsoft, 478–479 Net float, 527
goal: manage every risk, 606 Net operating profit after taxes, 84
Mission statement, 553 Net operating working capital, 82, 513
Moderate current asset investment policy, 518 Net present value (NPV), 360–362
Modified internal rate of return (MIRR), 371–373
Modifying accounting data for investor and base-case, 398

managerial decisions, 81–85
Modigliani-Miller model, 456–458, 480

capital structure, 456–458

Index I-9

comparison with IRR, 364–369 Original maturity, 211
profiles, 364 Over-the-counter (OTC) market, 156
reinvestment rate assumption, 368
Net working capital, 69, 513 P
Net worth, 69
New issue, 218 Par value, 210
New York Stock Exchange (NYSE), 153–155 Partnership, 4
Nominal (quoted) interest rate, 50 Payables deferral period, 514
Nominal (quoted) risk-free interest rate, 182 Payback period, 373–375
Nonconstant growth, 300
Nondiversifiable risk, 264 discounted, 374
Nonoperating assets, 83 Payment (PMT), 44
Normal, or constant, growth (Gordon) model, 296 Payment date, 492
Normal yield curve, 188 Payoff matrix, 248
NYSE and Nasdaq combine forces with the leading Pension funds, 150
Perfect hedge, 608
online trading systems, 155 Periodic interest rate, 52
Permanent current assets, 518
O Perpetuities, 42–44, 315
Physical asset markets, 145
Off balance sheet financing, 656 Physical location exchanges, 154–155
Operating assets, 83 Poison pill, 702
Operating breakeven, 441 Political risk, 619, 637
Operating capital, 83 Portfolio, 245
Operating cash flow, 84 Portfolio investments, 631
Operating lease, 654 Post-audit, 378–379
Operating leverage, 441–444 Preemptive right, 291–292
Operating merger, 692 Preferred stock, 315, 650–653
Operating plan, 554
Opportunity cost, 32, 396 adjustable rate, 652
Opportunity cost principle, 335 arrearages, 650
Opportunity cost rate, 368 cost of, 333–334
Optimal capital budget, 424–425 cumulative, 650
Optimal dividend policy, 480 funny-named, 334, 654–655
Optimal (target) capital structure, 331, 450–456 market auction (money market), 652
Premium bond, 216
determining, 450–456 Premium on forward rate, 627
Options, 584–589 Present value (See also Time value of money), 26,

abandonment/shutdown, 417–419 31–34
call, 584 annuity due, 39–40
covered, 584 ordinary annuity, 39–40
equilibrium value, 595 uneven cash flow stream, 45–46
expensing executive stock options, 590 Price/cash flow ratio, 116
expiration date, 585 Price/earnings ratio, 116
fair (equilibrium) price, 591, 595 Primary EPS, 674
flexibility, 421–422 Primary markets, 145
growth, 420–421 Prime rate, 539
in-the-money, 584 Private markets, 146
introduction to real options, 416–417 Probability distributions, 247–248
investment timing, 419–420 Procter & Gamble, 578–579, 683–684
long-term equity anticipation security, 586 Production opportunities, 175
naked, 584 Profitability ratios (See also Financial ratios),
out-of-the-money, 584
put, 585 112–115
real, 416 basic earning power ratio, 114
value, 418 profit margin on sales, 112–114
Ordinary (deferred) annuity, 36 return on common equity (ROE), 115
Original issue discount bond, 210 return on total assets (ROA), 114
Profit margin on sales, 112–114

I-10 Index

Pro forma financial statements, 553 Retention ratio, 558
Programmed trading, 594 Retirement ability, 24
Projects, mutually exclusive with unequal lives, Return on common equity (ROE), 115

422–424 EVA and, 126–127
Promissory note, 537–538 problems with, 125–127
Proprietorship, 4 Return on total assets (ROA), 114
Proxy, 290 Revaluation of a currency, 622
Proxy fight, 291, 690 Revolving credit agreement, 538–539
Public markets, 146 Risk, 175, 246
Publicly owned corporation, 157 adjusted cost of capital, 398
Purchase accounting, 699–700 adjusted discount rate, 404
Purchasing power parity, 629–630 adjusting cost of capital for, 346–348
Pure expectations theory, 193 and rates of return, 244–280
Putable bond, 212 arbitrage, 704
Put option, 585 aversion, 255
PVAN, 39 beta, 264, 397
business, 439–441
Q business and financial, 439–450
certainty equivalent, 404
Quick ratio, 104 company-specific, 264
corporate (within-firm), 397
R country, 199
default, 227–234
re, 335, 340–343 demand, 604
Ratio analysis (See also Financial ratios), 102–103 diversifiable, 246, 263, 264–266
environmental, 604
comparative, 121–124 estimating project, 397–398
looking beyond the numbers, 128 exchange rate, 199, 637
problems with ROE, 125–127 financial, 444–450, 604
uses and limitations of, 124–125 implications for corporate managers and investors,
Realized rate of return (Ϫr ), 258, 294
Real options, 415, 416–422 278–279
abandonment/shutdown, 417–419 input, 604
flexibility, 421–422 insurable, 604
growth, 420–421 interest rate, 186, 223–225
introduction to, 416–417 liability, 604
investment timing, 419–420 management, 578–582, 603, 604–607
Real risk-free rate of interest (r*), 181 market, 246, 263, 264–266, 397
Refunding operation, 211 measuring country, 198
Regular (simple) interest, 539–540 measuring stand-alone, 398–403
Reinvestment rate assumption, 368 Microsoft’s goal: managing every risk, 606
Reinvestment rate risk, 186, 225–226 nondiversifiable, 264
Relaxed current asset investment policy, 518 no pain no gain, 244–245
Relevant risk, 265 personnel, 604
Reorganization (See also Bankruptcy), 233–234 political, 619, 637
Repatriation of earnings, 636 portfolio context, 245, 257–271
Replacement analysis, 395 premium, 256
Replacement project, 395 property, 604
Replacement chain (common life) approach, pure, 604
reasons to manage, 579–582
422–423 reinvestment rate, 186, 225–226
Required rate of return, rs, 294 relationship between, and rates of return, 271–277
Reserve borrowing capacity, 461 relevant, 265
Residual dividend model, 483, 484–492 speculative, 604
Residual value, 661 stand-alone, 246–257, 397–403
Restricted current asset investment policy, 518 systematic, 264
Retained earnings, 69

breakpoint, 342
statement of, 78–79

Index I-11

trade-off between, and return, 256–257 international, 635–636
unsystematic, 264 reporting, 160–162
Risk-adjusted cost of capital, 398 Stock prices and shareholder value, 6–7
Risk-adjusted discount rate, 404 Stock repurchases, 498–502
Risk-free rate, 182 soar in 2004, 499
Riskless hedge, 589 Stocks (See individual entries, such as Common
Riskless Treasury bonds, 184–185
stock; Preferred stock), 289–317
S Stock splits, 496

Sale and leaseback, 653 reverse, 496
Sales forecast, 555–556 Strategic alliances, 706
Salvage value calculations, 391–392 Strategic business plan, 359
Savings and loan associations, 150 Strategic planning, 553–555
Scenario analysis, 400–401 Stretching accounts payable, 536
S Corporation, 5 Strike (exercise) price, 584
Seasoned issue, 218 Structured note, 601–602
Secondary markets, 145 Subordinated debenture, 229
Secured financing, 543 Sunk cost, 395–396
Secured loan, 542 Supernormal (nonconstant) growth, 300
Securitization, 601 Supply chain management, 529
Security Market Line (SML), 274 Swap, 600–601, 609–610
Security Market Line (SML) equation, 273
Security markets, 145–147, 153–160 currency, 601
interest rate, 581–582, 600
efficient markets hypothesis, 163 Symmetric information, 460
equilibrium, 10, 311 Synergy, 685
Semiannual compounding, 48 Systematic risk, 264
Sensitivity analysis, 398–400
Short hedges, 607 T
Shutdown options, 417–419
Side payments, 601 Takeover, 291
Signal, 461, 482 Tangible assets, 74
Signaling theory, 460–461 Target cash balance, 522
Simple interest, 27 Target (optimal) capital structure, 331
Sinking fund provision, 211–212 Target company, 689
Soft currency, 622 Target payout ratio, 479
Speculation, 607 Tax depreciation, 413–414
Spin-off, 707 Taxes, 87–89
Spontaneous funds, 542 Temporary current assets, 518
Spot markets, 145 Tender offer, 500, 689
Spot rate, 621, 626 Terminal date, 301
Stand-alone risk, 246–257, 397 Terminal value, 301
measuring, 398–403 Term structure of interest rates, 187–189
Standard deviation, 250, 251–252 Time lines, 25–26
Statement of cash flows, 75, 76–78 Time preferences for consumption, 175
Statement of retained earnings, 78–79 Times-interest-earned (TIE) ratio, 110–111
Stepped-up exercise price, 664 Time value of money, 24–54
Stock dividends, 496–497
Stockholders’ equity, 68–69 amortized loans, 52–54
Stockholder wealth maximization, 6 annuity, 35–36
a worldwide goal?, 12 annuity due, 36
Stock market, 153–157 comparing interest rates, 50–51
and returns, 160–162 compounding, 26
efficiency, 163–169 finding annuity payments, periods, and interest
equilibrium, 310–313
indices around the world, 634–635 rates, 40–42
finding the interest rate, 34–35
finding the number of years, 35
fractional time periods, 52
future value (FV), 26–31

I-12 Index

Time value of money, (continued) reporting earnings when outstanding, 674–675
future value of an ordinary annuity, 36–38 stepped-up exercise price, 664
future value of an annuity due, 38–39 weak currency, 622
future value of an uneven cash flow stream, Weighted average (composite) cost of capital
46–47
ordinary (deferred) annuity, 36 (WACC), 331, 343–344
perpetuities, 42–44 factors affecting, 344–345
present value (PV), 26, 31–34 overview of, 329–330
present value of an ordinary annuity, 39–40 Whistle-blowers, 15
semiannual and other compounding periods, White knight, 691, 702
48–50 White squire, 702
solving for I with uneven cash flows, 47–48 Window dressing techniques, 124
time lines, 25–26 Within-firm risk (corporate), 397
uneven cash flows, 44–46 Working capital, 512, 513–543
accounts payable (trade credit), 534–537
Total assets turnover ratio, 107 accounts receivable, 530–534
Total company (corporate valuation) model, 305 accruals, 542
Trade credit, 534 alternative financing policies, 518–521
alternative investment policies, 517–518
costly, 536 average collection period, 514
free, 536 bank loans, 537–541
stretching accounts payable, 536 cash and marketable securities, 525–528
Trade-off between risk and return, 256–257 cash budget, 521, 522–525
Trade-off theory, 459–460 cash conversion cycle, 513–517
Treasury bonds, 209 commercial paper, 541–542
almost riskless, 184–185 inventories, 528–529
Treasury stock, 498 inventory conversion period, 514
Trend analysis, 118 loans, 513
Tying the ratios together: the Du Pont equations, management, 512–543
multinational, 639–642
118–121 negative working capital, some firms operate

U with, 516
net, 69, 513
Uneven cash flows, 44–46 net operating, 82, 513
future value, 46–47 payables deferral period, 514
solving for I, 47–48 supply chain management, 529
terminology, 513
Unlevered beta (bU), 452 trade credit, 534–537
Unsystematic risk, 264 use of security in short-term financing, 542–543
Uses and limitations of ratio analysis, 124–125 WorldCom, 100–101
Worst-case scenario, 400
V
Y
Valuation, 213–216, 289–317
bond valuation, 213–216 Yield curve, 187
common stock valuation, 289–317 determinants of its shape, 189–193
corporation, 305–310 humped, 189
preferred stock valuation, 315 inverted, 188
normal, 188
Variance, 251 using to estimate future interest rates, 193–195
Vertically integrated investment, 618
Vertical merger, 687 Yield to call, 217–218
Vignettes, 2–3, 24, 64, 100–101, 141–142, 174, 207–208, Yield to maturity, 216–217
Yogi Berra on the M&M proposition, 457
244–245, 289, 328–329, 357–358, 387–388, 415,
436–437, 512, 552, 578–579, 615–616, 648–649, Z
683–684
Zero coupon bond, 210
W Zero growth stock, 298

Warrant, 212, 661–667
comparison with convertibles, 673–674
detachable, 664

FREQUENTLY USED SYMBOLS/ABBREVIATIONS

ACP Average collection period
ADR American depository receipt
APR Annual percentage rate
A/R Accounts receivable
Beta coefficient, a measure of an asset’s riskiness
b Levered beta
bL Unlevered beta
bU Basic earning power
BEP Book value per share
BVPS Capital Asset Pricing Model
CAPM Cash conversion cycle
CCC Cash flow; CFt is the cash flow in Period t
CF Cash flow per share
CFPS Conversion ratio
CR Coefficient of variation
CV Dividend of preferred stock
Dp Dividend in Period t
Dt Discounted cash flow
DCF Debt-to-equity ratio
D/E Dividends per share
DPS Dividend reinvestment plan
DRIP Default risk premium
DRP Days sales outstanding
DSO Effective annual rate, EFF%
EAR Earnings before interest and taxes; net operating income
EBIT Earnings before interest, taxes, depreciation, and amortization
EBITDA Earnings per share
EPS Economic value added
EVA (1) Fixed operating costs
F (2) Flotation cost
Free cash flow
FCF Future value for Year N
FVN Future value of an annuity for N years
FVAN Growth rate in earnings, dividends, and stock prices
Interest rate; also referred to as r
g Interest rate key on some calculators
I Interest payment in dollars
I/YR Inflation premium
INT Initial public offering
IP Internal rate of return
IPO Liquidity premium
IRR Maturity value of a bond
LP Market-to-book ratio
M Modified internal rate of return
M/B Maturity risk premium
MIRR Market value added
MRP Calculator key denoting number of periods
MVA Represents area under a standard normal distribution function
N Net operating profit after taxes
N(di) Net operating working capital
NOPAT Net present value
NOWC (1) Price of a share of stock in Period t; P0 = price of the stock today
NPV (2) Sales price per unit of product sold
P

Pc Conversion price
Pf Price of good in foreign country
Ph Price of good in home country
P/E Price/earnings ratio
PMT Payment of an annuity
PPP Purchasing power parity
PV Present value
PVAN Present value of an annuity for N years
Q Quantity produced or sold
QBE Breakeven quantity
r (1) A percentage discount rate, or cost of capital; also referred to

r- as I
rˆ (2) Nominal risk-adjusted required rate of return
r* “r bar,” historic, or realized, rate of return
rd “r hat,” an expected rate of return
re Real risk-free rate of return
rf Before-tax cost of debt
rh Cost of new common stock (outside equity)
ri Interest rate in foreign country
rM Interest rate in home country
rNOM Required return for an individual firm or security
rp Return for “the market,” or an “average” stock
Nominal rate of interest; also referred to as INOM
rPER (1) Cost of preferred stock
rRF (2) Portfolio’s return
Periodic rate of return
rs Rate of return on a risk-free security
(1) Cost of retained earnings
␳ (2) Required return on common stock
ROA Correlation coefficient; also denoted as R when using historical data
ROE Return on assets
Return on equity
RP Risk premium
RPM Market risk premium
Retention rate
RR (1) Sales
S (2) Estimated standard deviation for sample data
Security Market Line
SML Summation sign
⌺ Standard deviation
␴ Variance
␴2 Time period
t Marginal income tax rate
T A stock’s horizon, or terminal, value
Times interest earned
TVN Variable cost per unit
TIE Bond value
Value of preferred stock
V
VB Total variable costs
Vp Weighted averaged cost of capital
VC Exercise price of option
WACC Yield to call
X Yield to maturity
YTC
YTM