Some Solutions for Concise 5Th Edition

Some solutions for concise 5th edition

2-9a.01

||$500(1.06) = $530.00.

-500FV = ?

Using a financial calculator, enter N = 1, I/YR = 6, PV = -500, PMT = 0, and FV = ? Solve for FV = $530.00.

b.012

|||$500(1.06)2 = $561.80.

-500FV = ?

Using a financial calculator, enter N = 2, I/YR = 6, PV = -500, PMT = 0, and FV = ? Solve for FV = $561.80.

c.01

||$500(1/1.06) = $471.70.

PV = ?500

Using a financial calculator, enter N = 1, I/YR = 6, PMT = 0, and FV = 500, and PV = ? Solve for PV = $471.70.

d.012

|||$500(1/1.06)2 = $445.00.

PV = ?500

Using a financial calculator, enter N = 2, I/YR = 6, PMT = 0, FV = 500, and PV = ? Solve for PV = $445.00.

2-10a.012345678910

|||||||||||$500(1.06)10 = $895.42.

-500FV = ?

Using a financial calculator, enter N = 10, I/YR = 6, PV = -500, PMT = 0, and FV = ? Solve for FV = $895.42.

b.012345678910

|||||||||||$500(1.12)10 = $1,552.92.

-500FV = ?

Using a financial calculator, enter N = 10, I/YR = 12, PV = -500, PMT = 0, and FV = ? Solve for FV = $1,552.92.

c.012345678910

|||||||||||$500/(1.06)10 = $279.20.

PV = ?500

Using a financial calculator, enter N = 10, I/YR = 6, PMT = 0, FV = 500, and PV = ? Solve for PV = $279.20.

d.012345678910

|||||||||||

PV = ?1,552.90

$1,552.90/(1.12)10 = $499.99.

Using a financial calculator, enter N = 10, I/YR = 12, PMT = 0, FV = 1552.90, and PV = ? Solve for PV = $499.99.

$1,552.90/(1.06)10 = $867.13.

Using a financial calculator, enter N = 10, I/YR = 6, PMT = 0, FV = 1552.90, and PV = ? Solve for PV = $867.13.

e.The present value is the value today of a sum of money to be received in the future. For example, the value today of $1,552.90 to be received 10 years in the future is about $500 at an interest rate of 12%, but it is approximately $867 if the interest rate is 6%. Therefore, if you had $500 today and invested it at 12%, you would end up with $1,552.90 in 10 years. The present value depends on the interest rate because the interest rate determines the amount of interest you forgo by not having the money today.

2-11a.200020012002200320042005

||||||

-612 (in millions)

With a calculator, enter N = 5, PV = -6, PMT = 0, FV = 12, and then solve for I/YR = 14.87%.

b.The calculation described in the quotation fails to consider the compounding effect. It can be demonstrated to be incorrect as follows:

$6,000,000(1.20)5 = $6,000,000(2.48832) = $14,929,920,

which is greater than $12 million. Thus, the annual growth rate is less than 20%; in fact, it is about 15%, as shown in part a.

2-12These problems can all be solved using a financial calculator by entering the known values shown on the time lines and then pressing the I/YR button.

a.01

||

+700-749

With a financial calculator, enter: N = 1, PV = 700, PMT = 0, and FV = -749. I/YR = 7%.

b.01

||

-700+749

With a financial calculator, enter: N = 1, PV = -700, PMT = 0, and FV = 749. I/YR = 7%.

c.010

||

+85,000-201,229

With a financial calculator, enter: N = 10, PV = 85000, PMT = 0, and FV = -201229. I/YR = 9%.

d.012345

||||||

+9,000-2,684.80-2,684.80-2,684.80-2,684.80-2,684.80

With a financial calculator, enter: N = 5, PV = 9000, PMT = -2684.80, and FV = 0. I/YR = 15%.

2-13a.?

||

-200400

With a financial calculator, enter I/YR = 7, PV = -200, PMT = 0, and FV = 400. Then press the N key to find N = 10.24. Override I/YR with the other values to find N = 7.27, 4.19, and 1.00.

b.?

||Enter: I/YR = 10, PV = -200, PMT = 0, and FV = 400.

-200400N = 7.27.

c.?

||Enter: I/YR = 18, PV = -200, PMT = 0, and FV = 400.

-200400N = 4.19.

d.?

||Enter: I/YR = 100, PV = -200, PMT = 0, and FV = 400.

-200 400N = 1.00.

2-14a.012345678910

|||||||||||

400400400400400400400400400400

FV = ?

With a financial calculator, enter N = 10, I/YR = 10, PV = 0, and PMT = -400. Then press the FV key to find FV = $6,374.97.

b.012345

||||||

200200200200200

FV = ?

With a financial calculator, enter N = 5, I/YR = 5, PV = 0, and PMT = -200. Then press the FV key to find FV = $1,105.13.

c.012345

||||||

400400400400400

FV = ?

With a financial calculator, enter N = 5, I/YR = 0, PV = 0, and PMT = -400. Then press the FV key to find FV = $2,000.

d.To solve part d using a financial calculator, repeat the procedures discussed in parts a, b, and c, but first switch the calculator to “BEG” mode. Make sure you switch the calculator back to “END” mode after working the problem.

1.012345678910

|||||||||||

400400400400400400400400400400FV = ?

With a financial calculator on BEG, enter: N = 10, I/YR = 10, PV = 0, and PMT = -400. FV = $7,012.47.

2.012345

||||||

200200200200200FV = ?

With a financial calculator on BEG, enter: N = 5, I/YR = 5, PV = 0, and PMT = -200. FV = $1,160.38.

3.012345

||||||

400400400400400FV = ?

With a financial calculator on BEG, enter: N = 5, I/YR = 0, PV = 0, and PMT = -400. FV = $2,000.

2-15a.012345678910

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PV = ?400400400400400400400400400400

With a financial calculator, simply enter the known values and then press the key for the unknown. Enter: N = 10, I/YR = 10, PMT = -400, and FV = 0. PV = $2,457.83.

b.012345

||||||

PV = ?200200200200200

With a financial calculator, enter: N = 5, I/YR = 5, PMT = -200, and FV = 0. PV = $865.90.

c.012345

||||||

PV = ?400400400400400

With a financial calculator, enter: N = 5, I/YR = 0, PMT = -400, and FV = 0. PV = $2,000.00.

d.1.012345678910

|||||||||||

400400400400400400400400400400

PV = ?

With a financial calculator on BEG, enter: N = 10, I/YR = 10, PMT = -400, and FV = 0. PV = $2,703.61.

2.012345

||||||

200200200200200

PV = ?

With a financial calculator on BEG, enter: N = 5, I/YR = 5, PMT = -200, and FV = 0. PV = $909.19.

3.012345

||||||

400400400400400

PV = ?

With a financial calculator on BEG, enter: N = 5, I/YR = 0, PMT = -400, and FV = 0. PV = $2,000.00.

2-20Contract 1: PV=

= $2,727,272.73+$2,479,338.84+$2,253,944.40 + $2,049,040.37

= $9,509,596.34.

Using your financial calculator, enter the following data: CF0 = 0; CF1-4 = 3000000; I/YR = 10; NPV = ? Solve for NPV = $9,509,596.34.

Contract 2: PV=

= $1,818,181.82 + $2,479,338.84 + $3,005,259.20 + $3,415,067.28

= $10,717,847.14.

Alternatively, using your financial calculator, enter the following data: CF0 = 0; CF1 = 2000000; CF2 = 3000000; CF3 = 4000000; CF4 = 5000000; I/YR = 10; NPV = ? Solve for NPV = $10,717,847.14.

Contract 3: PV=

= $6,363,636.36 + $826,446.28 + $751,314.80 + $683,013.46

= $8,624,410.90.

Alternatively, using your financial calculator, enter the following data: CF0 = 0; CF1 = 7000000; CF2 = 1000000; CF3 = 1000000; CF4 = 1000000; I/YR = 10; NPV = ? Solve for NPV = $8,624,410.90.

Contract 2 gives the quarterback the highest present value; therefore, he should accept Contract 2.

3-5Statements b and d will decrease the amount of cash on a company’s balance sheet. Statement a will increase cash through the sale of common stock. This is a source of cash through financing activities. On one hand, Statement c would decrease cash; however, it is also possible that Statement c would increase cash, if the firm receives a tax refund.

3-6 Ending R/E= Beg. R/E  Net income  Dividends

$278,900,000= $212,300,000  Net income  $22,500,000

$278,900,000= $189,800,000  Net income

Net income= $89,100,000.

3-7a.From the statement of cash flows the change in cash must equal cash flow from operating activities plus long-term investing activities plus financing activities. First, we must identify the change in cash as follows:

Cash at the end of the year$25,000

– Cash at the beginning of the year– 55,000

Change in cash-$30,000

The sum of cash flows generated from operations, investment, and financing must equal a negative $30,000. Therefore, we can calculate the cash flow from operations as follows:

CF from operations  CF from investing  CF from financing =  in cash

CF from operations  $250,000  $170,000 = -$30,000

CF from operations= $50,000.

b.To determine the firm’s net income for the current year, you must realize that cash flow from operations is determined by adding sources of cash (such as depreciation and amortization and increases in accrued liabilities) and subtracting uses of cash (such as increases in accounts receivable and inventories) from net income. Since we determined that the firm’s cash flow from operations totaled $50,000 in part a of this problem, we can now calculate the firm’s net income as follows:

NI =

NI + $10,000 + $25,000 – $100,000= $50,000

NI – $65,000= $50,000

NI= $115,000.

3-8EBIT = $750,000; DEP = $200,000; AMORT = 0; 100% Equity; T = 40%; NI = ?; NCF = ?; OCF = ?

First, determine net income by setting up an income statement:

EBIT$750,000

Interest 0

EBT$750,000

Taxes (40%) 300,000

NI$450,000

NCF = NI + DEP and AMORT = $450,000 + $200,000 = $650,000.

OCF = EBIT(1 – T) + DEP and AMORT = $750,000(0.6) + $200,000 = $650,000.

Note that NCF = OCF because the firm is 100% equity financed.

3-9 MVA= (P0 Number of common shares)  BV of equity

$130,000,000= $60X  $500,000,000

$630,000,000= $60X

X= 10,500,000 common shares.

3-10a.NOPAT= EBIT(1 – T)

= $4,000,000,000(0.6)

= $2,400,000,000.

b.NCF= NI + DEP and AMORT

= $1,500,000,000 + $3,000,000,000

= $4,500,000,000.

c.OCF= NOPAT + DEP and AMORT

= $2,400,000,000 + $3,000,000,000

= $5,400,000,000.

d.FCF= NOPAT – Net Investment in Operating Capital

= $2,400,000,000 – $1,300,000,000

= $1,100,000,000.

3-11Working up the income statement you can calculate the new sales level would be $12,681,482.

Sales$12,681,482$5,706,667/(1  0.55)

Operating costs (excl. D&A) 6,974,815$12,681,482  0.55

EBITDA$ 5,706,667$4,826,667 + $880,000

Depr. & amort. 880,000$800,000  1.10

EBIT$ 4,826,667$4,166,667 + $660,000

Interest 660,000$600,000  1.10

EBT$ 4,166,667$2,500,000/(1  0.4)

Taxes (40%) 1,666,667$4,166,667  0.40

Net income$ 2,500,000

4-7Step 1:Calculate total assets from information given.

Sales = $6 million.

3.2= Sales/TA

3.2=

Assets= $1,875,000.

Step 2:Calculate net income.

There is 50% debt and 50% equity, so Equity = $1,875,000  0.5 = $937,500.

ROE= NI/S  S/TA  TA/E

0.12= NI/$6,000,000  3.2  $1,875,000/$937,500

0.12=

$720,000= 6.4NI

$112,500= NI.

4-10We are given ROA = 3% and Sales/Total assets = 1.5.

From the basic Du Pont equation: ROA= Profit margin  Total assets turnover

3%= Profit margin(1.5)

Profit margin= 3%/1.5 = 2%.

We can also calculate the company’s debt ratio in a similar manner, given the facts of the problem. We are given ROA(NI/A) and ROE(NI/E); if we use the reciprocal of ROE we have the following equation:

Alternatively, using the extended Du Pont equation:

ROE= ROA  EM

5%= 3%  EM

EM= 5%/3% = 5/3 = TA/E.

Take reciprocal: E/TA = 3/5 = 60%;therefore, D/A = 1 – 0.60 = 0.40 = 40%.

Thus, the firm’s profit margin = 2% and its debt ratio = 40%.

4-17Statement a is correct. Refer to the solution setup for Problem 4-16 and think about it this way: (1) Adding assets will not affect common equity if the assets are financed with debt. (2) Adding assets will cause expected EBIT to increase by the amount EBIT = BEP(added assets). (3) Interest expense will increase by the amount Int. rate(added assets). (4) Pre-tax income will rise by the amount (added assets)(BEP – Int. rate). Assuming BEP > Int. rate, if pre-tax income increases so will net income. (5) If expected net income increases but common equity is held constant, then the expected ROE will also increase. Note that if Int. rate > BEP, then adding assets financed by debt would lower net income and thus the ROE. Therefore, Statement a is true—if assets financed by debt are added, and if the expected BEP on those assets exceeds the interest rate on debt, then the firm’s ROE will increase.

Statements b, c, and d are false, because the BEP ratio uses EBIT, which is calculated before the effects of taxes or interest charges are felt. Of course, Statement e is also false.

4-18TA = $5,000,000,000; T = 40%; EBIT/TA = 10%; ROA = 5%; TIE ?

Now use the income statement format to determine interest so you can calculate the firm’s TIE ratio.

EBIT$500,000,000See above.

INT 83,333,333

EBT$416,666,667EBT = $250,000,000/0.6

Taxes (40%) 166,666,667

NI$250,000,000See above.

TIE= EBIT/INT

= $500,000,000/$83,333,333

= 6.0.

4-19Present current ratio = = 2.5.

Minimum current ratio = = 2.0.

$1,312,500 + NP= $1,050,000 + 2NP

NP= $262,500.

Short-term debt can increase by a maximum of $262,500 without violating a 2 to 1 current ratio, assuming that the entire increase in notes payable is used to increase current assets. Since we assumed that the additional funds would be used to increase inventory, the inventory account will increase to $637,500 and current assets will total $1,575,000, and current liabilities will total $787,500.

4-20Step 1:Solve for current annual sales using the DSO equation:

55= $750,000/(Sales/365)

55Sales= $273,750,000

Sales= $4,977,272.73.

Step 2:If sales fall by 15%, the new sales level will be $4,977,272.73(0.85) = $4,230,681.82. Again, using the DSO equation, solve for the new accounts receivable figure as follows:

35= AR/($4,230,681.82/365)

35= AR/$11,590.91

AR= $405,681.82  $405,682.

4-21The current EPS is $2,000,000/500,000 shares or $4.00. The current P/E ratio is then $40/$4 = 10.00. The new number of shares outstanding will be 650,000. Thus, the new EPS = $3,250,000/650,000 = $5.00. If the shares are selling for 10 times EPS, then they must be selling for $5.00(10) = $50.

7-1With your financial calculator, enter the following:

N = 10; I/YR = YTM = 9%; PMT = 0.08  1,000 = 80; FV = 1000; PV = VB = ?

PV = $935.82.

7-2VB = $985; M = $1,000; Int = 0.07  $1,000 = $70.

a.Current yield= Annual interest/Current price of bond

= $70/$985.00

= 7.11%.

b.N = 10; PV = -985; PMT = 70; FV = 1000; YTM = ?

Solve for I/YR = YTM = 7.2157%  7.22%.

c.N = 7; I/YR = 7.2157; PMT = 70; FV = 1000; PV = ?

Solve for VB = PV = $988.46.

7-3The problem asks you to find the price of a bond, given the following facts: N = 2  8 = 16; I/YR = 8.5/2 = 4.25; PMT = 45; FV = 1000.

With a financial calculator, solve for PV = $1,028.60.

7-4With your financial calculator, enter the following to find YTM:

N = 10  2 = 20; PV = -1100; PMT = 0.08/2  1,000 = 40; FV = 1000; I/YR = YTM = ?

YTM = 3.31%  2 = 6.62%.

With your financial calculator, enter the following to find YTC:

N = 5  2 = 10; PV = -1100; PMT = 0.08/2  1,000 = 40; FV = 1050; I/YR = YTC = ?

YTC = 3.24%  2 = 6.49%.

Since the YTC is less than the YTM, investors would expect the bonds to be called and to earn the YTC.

7-5a.1.5%:Bond L:Input N = 15, I/YR = 5, PMT = 100, FV = 1000, PV = ?, PV = $1,518.98.

Bond S:Change N = 1, PV = ? PV = $1,047.62.

2.8%:Bond L:From Bond S inputs, change N = 15 and I/YR = 8, PV = ?, PV = $1,171.19.

Bond S:Change N = 1, PV = ? PV = $1,018.52.

3.12%:Bond L:From Bond S inputs, change N = 15 and I/YR = 12, PV = ?, PV = $863.78.

Bond S:Change N = 1, PV = ? PV = $982.14.

b.Think about a bond that matures in one month. Its present value is influenced primarily by the maturity value, which will be received in only one month. Even if interest rates double, the price of the bond will still be close to $1,000. A 1-year bond’s value would fluctuate more than the one-month bond’s value because of the difference in the timing of receipts. However, its value would still be fairly close to $1,000 even if interest rates doubled. A long-term bond paying semiannual coupons, on the other hand, will be dominated by distant receipts, receipts that are multiplied by 1/(1 + rd/2)t, and if rd increases, these multipliers will decrease significantly. Another way to view this problem is from an opportunity point of view. A 1month bond can be reinvested at the new rate very quickly, and hence the opportunity to invest at this new rate is not lost; however, the long-term bond locks in subnormal returns for a long period of time.

7-7Percentage

Price at 8%Price at 7% Change

10-year, 10% annual coupon $1,134.20 $1,210.71 6.75%

10-year zero 463.19 508.35 9.75

5-year zero 680.58 712.99 4.76

30-year zero 99.38 131.37 32.19

$100 perpetuity 1,250.00 1,428.57 14.29

7-20a.Find the YTM as follows:

N = 10, PV = -1175, PMT = 110, FV = 1000

I/YR = YTM = 8.35%.

b.Find the YTC, if called in Year 5 as follows:

N = 5, PV = -1175, PMT = 110, FV = 1090

I/YR = YTC = 8.13%.

c.The bonds are selling at a premium which indicates that interest rates have fallen since the bonds were originally issued. Assuming that interest rates do not change from the present level, investors would expect to earn the yield to call. (Note that the YTC is less than the YTM.)

d.Similarly from above, YTC can be found, if called in each subsequent year.

If called in Year 6:

N = 6, PV = -1175, PMT = 110, FV = 1080

I/YR = YTC = 8.27%.

If called in Year 7:

N = 7, PV = -1175, PMT = 110, FV = 1070

I/YR = YTC = 8.37%.

If called in Year 8:

N = 8, PV = -1175, PMT = 110, FV = 1060

I/YR = YTC = 8.46%.

If called in Year 9:

N = 9, PV = -1175, PMT = 110, FV = 1050

I/YR = YTC = 8.53%.

According to these calculations, the latest investors might expect a call of the bonds is in Year 6. This is the last year that the expected YTC will be less than the expected YTM. At this time, the firm still finds an advantage to calling the bonds, rather than seeing them to maturity.

8-1= (0.1)(-50%) + (0.2)(-5%) + (0.4)(16%) + (0.2)(25%) + (0.1)(60%)

= 11.40%.

2 = (-50% – 11.40%)2(0.1) + (-5% – 11.40%)2(0.2) + (16% – 11.40%)2(0.4)

+ (25% – 11.40%)2(0.2) + (60% – 11.40%)2(0.1)

2 = 712.44;  = 26.69%.

CV = = 2.34.

8-2InvestmentBeta

$35,000 0.8

40,000 1.4

Total$75,000

bp = ($35,000/$75,000)(0.8) + ($40,000/$75,000)(1.4) = 1.12.

8-3rRF = 6%; rM = 13%; b = 0.7; r = ?

r= rRF + (rM – rRF)b

= 6% + (13% – 6%)0.7

= 10.9%.

8-4rRF = 5%; RPM = 6%; rM = ?

rM = 5% + (6%)1 = 11%.

r when b = 1.2 = ?

r = 5% + 6%(1.2) = 12.2%.

8-5a.r = 11%; rRF = 7%; RPM = 4%.

r= rRF + (rM – rRF)b

11%= 7% + 4%b

4%= 4%b

b= 1.

b.rRF = 7%; RPM = 6%; b = 1.

r= rRF + (rM – rRF)b

= 7% + (6%)1

= 13%.

8-6a..

= 0.1(-35%) + 0.2(0%) + 0.4(20%) + 0.2(25%) + 0.1(45%)

= 14% versus 12% for X.

b. = .

= (-10% – 12%)2(0.1) + (2% – 12%)2(0.2) + (12% – 12%)2(0.4)

+ (20% – 12%)2(0.2) + (38% – 12%)2(0.1) = 148.8%.

X = 12.20% versus 20.35% for Y.

CVX = X/X = 12.20%/12% = 1.02, while

CVY = 20.35%/14% = 1.45.

If Stock Y is less highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.

8-7Portfolio beta= (1.50) + (-0.50) + (1.25) + (0.75)

bp= (0.1)(1.5) + (0.15)(-0.50) + (0.25)(1.25) + (0.5)(0.75)

= 0.15 – 0.075 + 0.3125 + 0.375 = 0.7625.

rp= rRF + (rM – rRF)(bp) = 6% + (14% – 6%)(0.7625) = 12.1%.

Alternative solution: First, calculate the return for each stock using the CAPM equation
[rRF + (rM – rRF)b], and then calculate the weighted average of these returns.

rRF = 6% and (rM – rRF) = 8%.

StockInvestmentBetar = rRF + (rM – rRF)bWeight

A $ 400,000 1.50 18% 0.10

B 600,000 (0.50) 2 0.15

C 1,000,000 1.25 16 0.25

D 2,000,000 0.75 12 0.50

Total $4,000,000 1.00

rp = 18%(0.10) + 2%(0.15) + 16%(0.25) + 12%(0.50) = 12.1%.

8-12Using Stock X (or any stock):

9%= rRF + (rM – rRF)bX

9%= 5.5% + (rM – rRF)0.8

(rM – rRF)= 4.375%.

8-17After additional investments are made, for the entire fund to have an expected return of 13%, the portfolio must have a beta of 1.5455 as shown below:

13%= 4.5% + (5.5%)b

b= 1.5455.

Since the fund’s beta is a weighted average of the betas of all the individual investments, we can calculate the required beta on the additional investment as follows:

1.5455= +

1.5455= 1.2 + 0.2X

0.3455= 0.2X

X= 1.7275.

8-21a. = 0.1(7%) + 0.2(9%) + 0.4(11%) + 0.2(13%) + 0.1(15%) = 11%.

rRF = 6%. (given)

Therefore, the SML equation is:

ri = rRF + (rM – rRF)bi = 6% + (11% – 6%)bi = 6% + (5%)bi.

b.First, determine the fund’s beta, bF. The weights are the percentage of funds invested in each stock:

A = $160/$500 = 0.32.

B = $120/$500 = 0.24.

C = $80/$500 = 0.16.

D = $80/$500 = 0.16.

E = $60/$500 = 0.12.

bF= 0.32(0.5) + 0.24(2.0) + 0.16(4.0) + 0.16(1.0) + 0.12(3.0)

= 0.16 + 0.48 + 0.64 + 0.16 + 0.36 = 1.8.

Next, use bF = 1.8 in the SML determined in Part a:

= 6% + (11% – 6%)1.8 = 6% + 9% = 15%.

c.rN = Required rate of return on new stock = 6% + (5%)2.0 = 16%.

An expected return of 15% on the new stock is below the 16% required rate of return on an investment with a risk of b = 2.0. Since rN = 16% > = 15%, the new stock should not be purchased. The expected rate of return that would make the fund indifferent to purchasing the stock is 16%.

9-1D0 = $1.50; g1-3 = 7%; gn = 5%; D1 through D5 = ?

D1 = D0(1 + g1) = $1.50(1.07) = $1.6050.

D2 = D0(1 + g1)(1 + g2) = $1.50(1.07)2 = $1.7174.

D3 = D0(1 + g1)(1 + g2)(1 + g3) = $1.50(1.07)3 = $1.8376.

D4 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn) = $1.50(1.07)3(1.05) = $1.9294.

D5 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn)2 = $1.50(1.07)3(1.05)2 = $2.0259.

9-2D1 = $0.50; g = 7%; rs = 15%;= ?

9-3P0 = $20; D0 = $1.00; g = 6%; = ?; rs = ?

= P0(1 + g) = $20(1.06) = $21.20.

= + g = + 0.06

= + 0.06 = 11.30%. rs = 11.30%.

9-4a.The terminal, or horizon, date is the date when the growth rate becomes constant. This occurs at the end of Year 2.

b.0123

||||

1.251.501.801.89

37.80 =

The horizon, or terminal, value is the value at the horizon date of all dividends expected thereafter. In this problem it is calculated as follows:

c.The firm’s intrinsic value is calculated as the sum of the present value of all dividends during the supernormal growth period plus the present value of the terminal value. Using your financial calculator, enter the following inputs: CF0 = 0, CF1 = 1.50, CF2 = 1.80 + 37.80 = 39.60, I/YR = 10, and then solve for NPV = $34.09.

9-5The firm’s free cash flow is expected to grow at a constant rate, hence we can apply a constant growth formula to determine the total value of the firm.

Firm value= FCF1/(WACC – g)

= $150,000,000/(0.10 – 0.05)

= $3,000,000,000.

To find the value of an equity claim upon the company (share of stock), we must subtract out the market value of debt and preferred stock. This firm happens to be entirely equity funded, and this step is unnecessary. Hence, to find the value of a share of stock, we divide equity value (or in this case, firm value) by the number of shares outstanding.

Equity value per share= Equity value/Shares outstanding

= $3,000,000,000/50,000,000

= $60.

Each share of common stock is worth $60, according to the corporate valuation model.

9-8a.

b.

9-11First, solve for the current price.

= D1/(rs – g)

= $0.50/(0.12 – 0.07)

= $10.00.

If the stock is in a constant growth state, the constant dividend growth rate is also the capital gains yield for the stock and the stock price growth rate. Hence, to find the price of the stock four years from today:

= P0(1 + g)4

= $10.00(1.07)4

= $13.10796 ≈ $13.11.

10-1rd(1 – T) = 0.12(0.65) = 7.80%.

10-2Pp = $47.50; Dp = $3.80; rp = ?

rp= = = 8%.

10-340% Debt; 60% Common equity; rd = 9%; T = 40%; WACC = 9.96%; rs = ?

WACC= (wd)(rd)(1 – T) + (wc)(rs)

0.0996= (0.4)(0.09)(1 – 0.4) + (0.6)rs

0.0996= 0.0216 + 0.6rs

0.078= 0.6rs

rs= 13%.

10-8Debt = 40%, Common equity = 60%.

P0 = $22.50, D0 = $2.00, D1 = $2.00(1.07) = $2.14, g = 7%.

rs = + g = + 7% = 16.51%.

WACC= (0.4)(0.12)(1 – 0.4) + (0.6)(0.1651)

= 0.0288 + 0.0991 = 12.79%.

10-17a.rs= + g

0.09= + g

0.09= 0.06 + g

g= 3%.

b.Current EPS $5.400

Less: Dividends per share 3.600

Retained earnings per share $1.800

Rate of return  0.090

Increase in EPS $0.162

Plus: Current EPS 5.400

Next year’s EPS $5.562

Alternatively, EPS1 = EPS0(1 + g) = $5.40(1.03) = $5.562.

11-1Financial calculator solution: Input CF0 = -52125, CF1-8 = 12000, I/YR = 12, and then solve for NPV = $7,486.68.

11-2Financial calculator solution: Input CF0 = -52125, CF1-8 = 12000, and then solve for IRR = 16%.

11-4Since the cash flows are a constant $12,000, calculate the payback period as: $52,125/$12,000 = 4.3438, so the payback is about 4 years.

11-6a.Project A: Using a financial calculator, enter the following:

CF0 = -25, CF1 = 5, CF2 = 10, CF3 = 17, I/YR = 5; NPV = $3.52.

Change I/YR = 5 to I/YR = 10; NPV = $0.58.

Change I/YR = 10 to I/YR = 15; NPV = -$1.91.

Project B: Using a financial calculator, enter the following:

CF0 = -20, CF1 = 10, CF2 = 9, CF3 = 6, I/YR = 5; NPV = $2.87.

Change I/YR = 5 to I/YR = 10; NPV = $1.04.

Change I/YR = 10 to I/YR = 15; NPV = -$0.55.

b.Using the data for Project A, enter the cash flows into a financial calculator and solve for IRRA = 11.10%. The IRR is independent of the WACC, so it doesn’t change when the WACC changes.

Using the data for Project B, enter the cash flows into a financial calculator and solve for IRRB = 13.18%. Again, the IRR is independent of the WACC, so it doesn’t change when the WACC changes.

c.At a WACC = 5%, NPVA> NPVB so choose Project A.

At a WACC = 10%, NPVB > NPVA so choose Project B.

At a WACC = 15%, both NPVs are less than zero, so neither project would be chosen.

12-12a.WACC1 = 12%; WACC2 = 12.5% after $3,250,000 of new capital is raised.

Since each project is independent and of average risk, all projects whose IRR > WACC2 will be accepted. Consequently, Projects A, B, C, D, and E will be accepted and the optimal capital budget is $5,250,000.

13-2The optimal capital structure is that capital structure where WACC is minimized and stock price is maximized. Because Jackson’s stock price is maximized at a 30% debt ratio, the firm’s optimal capital structure is 30% debt and 70% equity. This is also the debt level where the firm’s WACC is minimized.