罗斯《公司理财》第9版精要版英文原书课后部分章节答案

CH5 11，13，18，19，20

11. To find the PV of a lump sum, we use:

PV = FV / (1 + r)t

PV = $1,000,000 / (1.10)80 = $488.19

13. To answer this question, we can use either the FV or the PV formula. Both will give the same

answer since they are the inverse of each other. We will use the FV formula, that is:

FV = PV(1 + r)t

Solving for r, we get:

r = (FV / PV)1 / t – 1

r = ($1,260,000 / $150)1/112 – 1 = .0840 or 8.40%

To find the FV of the first prize, we use:

FV = PV(1 + r)t

FV = $1,260,000(1.0840)33 = $18,056,409.94

18. To find the FV of a lump sum, we use:

FV = PV(1 + r)t

FV = $4,000(1.11)45 = $438,120.97

FV = $4,000(1.11)35 = $154,299.40

Better start early!

19. We need to find the FV of a lump sum. However, the money will only be invested for six years,

so the number of periods is six.

FV = PV(1 + r)t

FV = $20,000(1.084)6 = $32,449.33

20. To answer this question, we can use either the FV or the PV formula. Both will give the same

answer since they are the inverse of each other. We will use the FV formula, that is:

FV = PV(1 + r)t

Solving for t, we get:

t = ln(FV / PV) / ln(1 + r)

t = ln($75,000 / $10,000) / ln(1.11) = 19.31

So, the money must be invested for 19.31 years. However, you will not receive the money for

another two years. From now, you’ll wait:

2 years + 19.31 years = 21.31 years

CH6 16，24，27，42，58

16. For this problem, we simply need to find the FV of a lump sum using the equation:

FV = PV(1 + r)t

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24.

27.

It is important to note that compounding occurs semiannually. To account for this, we will divide

the interest rate by two (the number of compounding periods in a year), and multiply the number

of periods by two. Doing so, we get:

FV = $2,100[1 + (.084/2)]34 = $8,505.93

This problem requires us to find the FVA. The equation to find the FVA is:

FVA = C{[(1 + r)t – 1] / r}

FVA = $300[{[1 + (.10/12) ]360

– 1} / (.10/12)] = $678,146.38

The cash flows are annual and the compounding period is quarterly, so we need to calculate the

EAR to make the interest rate comparable with the timing of the cash flows. Using the equation

for the EAR, we get:

EAR = [1 + (APR / m)]m – 1

EAR = [1 + (.11/4)]4 – 1 = .1146 or 11.46%

And now we use the EAR to find the PV of each cash flow as a lump sum and add them together:

PV = $725 / 1.1146 + $980 / 1.11462 + $1,360 / 1.11464 = $2,320.36

42. The amount of principal paid on the loan is the PV of the monthly payments you make. So, the

present value of the $1,150 monthly payments is:

PVA = $1,150[(1 – {1 / [1 + (.0635/12)]}360) / (.0635/12)] = $184,817.42

The monthly payments of $1,150 will amount to a principal payment of $184,817.42. The

amount of principal you will still owe is:

$240,000 – 184,817.42 = $55,182.58

This remaining principal amount will increase at the interest rate on the loan until the end of the

loan period. So the balloon payment in 30 years, which is the FV of the remaining principal will

be:

Balloon payment = $55,182.58[1 + (.0635/12)]360 = $368,936.54

58. To answer this question, we should find the PV of both options, and compare them. Since we are

purchasing the car, the lowest PV is the best option. The PV of the leasing is simply the PV of

the lease payments, plus the $99. The interest rate we would use for the leasing option is the

same as the interest rate of the loan. The PV of leasing is:

PV = $99 + $450{1 – [1 / (1 + .07/12)12(3)]} / (.07/12) = $14,672.91

The PV of purchasing the car is the current price of the car minus the PV of the resale price. The

PV of the resale price is:

PV = $23,000 / [1 + (.07/12)]12(3) = $18,654.82

The PV of the decision to purchase is:

$32,000 – 18,654.82 = $13,345.18

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In this case, it is cheaper to buy the car than leasing it since the PV of the purchase cash flows is

lower. To find the breakeven resale price, we need to find the resale price that makes the PV of

the two options the same. In other words, the PV of the decision to buy should be:

$32,000 – PV of resale price = $14,672.91

PV of resale price = $17,327.09

The resale price that would make the PV of the lease versus buy decision is the FV of this value,

so:

Breakeven resale price = $17,327.09[1 + (.07/12)]12(3) = $21,363.01

CH7 3，18，21，22，31

3. The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this

problem assumes an annual coupon. The price of the bond will be:

P = $75({1 – [1/(1 + .0875)]10 } / .0875) + $1,000[1 / (1 + .0875)10] = $918.89

We would like to introduce shorthand notation here. Rather than write (or type, as the case may

be) the entire equation for the PV of a lump sum, or the PVA equation, it is common to

abbreviate the equations as:

PVIFR,t = 1 / (1 + r)t

which stands for Present Value Interest Factor

PVIFAR,t

= ({1 – [1/(1 + r)]t } / r )

which stands for Present Value Interest Factor of an Annuity

These abbreviations are short hand notation for the equations in which the interest rate and the

number of periods are substituted into the equation and solved. We will use this shorthand

notation in remainder of the solutions key.

18. The bond price equation for this bond is:

P0 = $1,068 = $46(PVIFAR%,18) + $1,000(PVIFR%,18)

Using a spreadsheet, financial calculator, or trial and error we find:

R = 4.06%

This is the semiannual interest rate, so the YTM is:

YTM = 2  4.06% = 8.12%

The current yield is:

Current yield = Annual coupon payment / Price = $92 / $1,068 = .0861 or 8.61%

The effective annual yield is the same as the EAR, so using the EAR equation from the previous

chapter:

Effective annual yield = (1 + 0.0406)2

– 1 = .0829 or 8.29%

20. Accrued interest is the coupon payment for the period times the fraction of the period that has

passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon

payment per six months is one-half of the annual coupon payment. There are four months until

the next coupon payment, so two months have passed since the last coupon payment. The

accrued interest for the bond is:

Accrued interest = $74/2 × 2/6 = $12.33

And we calculate the clean price as:

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Clean price = Dirty price – Accrued interest = $968 – 12.33 = $955.67

21. Accrued interest is the coupon payment for the period times the fraction of the period that has

passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon

payment per six months is one-half of the annual coupon payment. There are two months until

the next coupon payment, so four months have passed since the last coupon payment. The

accrued interest for the bond is:

Accrued interest = $68/2 × 4/6 = $22.67

And we calculate the dirty price as:

Dirty price = Clean price + Accrued interest = $1,073 + 22.67 = $1,095.67

22. To find the number of years to maturity for the bond, we need to find the price of the bond. Since

we already have the coupon rate, we can use the bond price equation, and solve for the number

of years to maturity. We are given the current yield of the bond, so we can calculate the price as:

Current yield = .0755 = $80/P0

P0 = $80/.0755 = $1,059.60

Now that we have the price of the bond, the bond price equation is:

P = $1,059.60 = $80[(1 – (1/1.072)t ) / .072 ] + $1,000/1.072t

We can solve this equation for t as follows:

$1,059.60(1.072)t = $1,111.11(1.072)t – 1,111.11 + 1,000

111.11 = 51.51(1.072)t

2.1570 = 1.072t

t = log 2.1570 / log 1.072 = 11.06  11 years

The bond has 11 years to maturity.

31. The price of any bond (or financial instrument) is the PV of the future cash flows. Even though

Bond M makes different coupons payments, to find the price of the bond, we just find the PV of

the cash flows. The PV of the cash flows for Bond M is:

PM = $1,100(PVIFA3.5%,16)(PVIF3.5%,12) + $1,400(PVIFA3.5%,12)(PVIF3.5%,28) +

$20,000(PVIF3.5%,40)

PM = $19,018.78

Notice that for the coupon payments of $1,400, we found the PVA for the coupon payments, and

then discounted the lump sum back to today.

Bond N is a zero coupon bond with a $20,000 par value, therefore, the price of the bond is the

PV of the par, or:

PN = $20,000(PVIF3.5%,40) = $5,051.45

CH8 4，18，20，22，24

4. Using the constant growth model, we find the price of the stock today is:

P0 = D1

/ (R – g) = $3.04 / (.11 – .038) = $42.22

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18. The price of a share of preferred stock is the dividend payment divided by the required return.

We know the dividend payment in Year 20, so we can find the price of the stock in Year 19, one

year before the first dividend payment. Doing so, we get:

P19 = $20.00 / .064

P19 = $312.50

The price of the stock today is the PV of the stock price in the future, so the price today will be:

P0 = $312.50 / (1.064)19

P0 = $96.15

20. We can use the two-stage dividend growth model for this problem, which is:

P0 = [D0(1 + g1)/(R – g1)]{1 – [(1 + g1)/(1 + R)]T}+ [(1 + g1)/(1 + R)]T[D0(1 + g2)/(R – g2)]

P0 = [$1.25(1.28)/(.13 – .28)][1 – (1.28/1.13)8] + [(1.28)/(1.13)]8[$1.25(1.06)/(.13 – .06)]

P0 = $69.55

22. We are asked to find the dividend yield and capital gains yield for each of the stocks. All of the

stocks have a 15 percent required return, which is the sum of the dividend yield and the capital

gains yield. To find the components of the total return, we need to find the stock price for each

stock. Using this stock price and the dividend, we can calculate the dividend yield. The capital

gains yield for the stock will be the total return (required return) minus the dividend yield.

W: P0 = D0(1 + g) / (R – g) = $4.50(1.10)/(.19 – .10) = $55.00

Dividend yield = D1/P0 = $4.50(1.10)/$55.00 = .09 or 9%

Capital gains yield = .19 – .09 = .10 or 10%

X: P0 = D0(1 + g) / (R – g) = $4.50/(.19 – 0) = $23.68

Dividend yield = D1/P0 = $4.50/$23.68 = .19 or 19%

Capital gains yield = .19 – .19 = 0%

Y: P0 = D0(1 + g) / (R – g) = $4.50(1 – .05)/(.19 + .05) = $17.81

Dividend yield = D1/P0 = $4.50(0.95)/$17.81 = .24 or 24%

Capital gains yield = .19 – .24 = –.05 or –5%

Z: P2 = D2(1 + g) / (R – g) = D0(1 + g1)2(1 + g2)/(R – g2) = $4.50(1.20)2(1.12)/(.19 – .12) =

$103.68

P0 = $4.50 (1.20) / (1.19) + $4.50 (1.20)2

/ (1.19)2 + $103.68 / (1.19)2 = $82.33

Dividend yield = D1/P0 = $4.50(1.20)/$82.33 = .066 or 6.6%

Capital gains yield = .19 – .066 = .124 or 12.4%

In all cases, the required return is 19%, but the return is distributed differently between

current income and capital gains. High growth stocks have an appreciable capital gains

component but a relatively small current income yield; conversely, mature, negative-growth

stocks provide a high current income but also price depreciation over time.

24. Here we have a stock with supernormal growth, but the dividend growth changes every year for

the first four years. We can find the price of the stock in Year 3 since the dividend growth rate is

constant after the third dividend. The price of the stock in Year 3 will be the dividend in Year 4,

divided by the required return minus the constant dividend growth rate. So, the price in Year 3

will be:

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CH9 3，4，6，9，15

3. Project A has cash flows of $19,000 in Year 1, so the cash flows are short by $21,000 of

recapturing the initial investment, so the payback for Project A is:

Payback = 1 + ($21,000 / $25,000) = 1.84 years

Project B has cash flows of:

Cash flows = $14,000 + 17,000 + 24,000 = $55,000

during this first three years. The cash flows are still short by $5,000 of recapturing the initial

investment, so the payback for Project B is:

B: Payback = 3 + ($5,000 / $270,000) = 3.019 years

Using the payback criterion and a cutoff of 3 years, accept project A and reject project B.

4. When we use discounted payback, we need to find the value of all cash flows today. The value

today of the project cash flows for the first four years is:

Value today of Year 1 cash flow = $4,200/1.14 = $3,684.21

Value today of Year 2 cash flow = $5,300/1.142 = $4,078.18

Value today of Year 3 cash flow = $6,100/1.143 = $4,117.33

Value today of Year 4 cash flow = $7,400/1.144 = $4,381.39

To find the discounted payback, we use these values to find the payback period. The discounted

first year cash flow is $3,684.21, so the discounted payback for a $7,000 initial cost is:

Discounted payback = 1 + ($7,000 – 3,684.21)/$4,078.18 = 1.81 years

For an initial cost of $10,000, the discounted payback is:

Discounted payback = 2 + ($10,000 – 3,684.21 – 4,078.18)/$4,117.33 = 2.54 years

Notice the calculation of discounted payback. We know the payback period is between two and

three years, so we subtract the discounted values of the Year 1 and Year 2 cash flows from the

initial cost. This is the numerator, which is the discounted amount we still need to make to

recover our initial investment. We divide this amount by the discounted amount we will earn in

Year 3 to get the fractional portion of the discounted payback.

If the initial cost is $13,000, the discounted payback is:

Discounted payback = 3 + ($13,000 – 3,684.21 – 4,078.18 – 4,117.33) / $4,381.39 = 3.26 years

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P3 = $2.45(1.20)(1.15)(1.10)(1.05) / (.11 – .05) = $65.08

The price of the stock today will be the PV of the first three dividends, plus the PV of the stock

price in Year 3, so:

P0 = $2.45(1.20)/(1.11) + $2.45(1.20)(1.15)/1.112 + $2.45(1.20)(1.15)(1.10)/1.113 + $65.08/1.113

P0 = $55.70

6. Our definition of AAR is the average net income divided by the average book value. The average

net income for this project is:

Average net income = ($1,938,200 + 2,201,600 + 1,876,000 + 1,329,500) / 4 = $1,836,325

And the average book value is:

Average book value = ($15,000,000 + 0) / 2 = $7,500,000

So, the AAR for this project is:

AAR = Average net income / Average book value = $1,836,325 / $7,500,000 = .2448 or 24.48%

9. The NPV of a project is the PV of the outflows minus the PV of the inflows. Since the cash

inflows are an annuity, the equation for the NPV of this project at an 8 percent required return is:

NPV = –$138,000 + $28,500(PVIFA8%, 9) = $40,036.31

At an 8 percent required return, the NPV is positive, so we would accept the project.

The equation for the NPV of the project at a 20 percent required return is:

NPV = –$138,000 + $28,500(PVIFA20%, 9) = –$23,117.45

At a 20 percent required return, the NPV is negative, so we would reject the project.

We would be indifferent to the project if the required return was equal to the IRR of the project,

since at that required return the NPV is zero. The IRR of the project is:

0 = –$138,000 + $28,500(PVIFAIRR, 9)

IRR = 14.59%

15. The profitability index is defined as the PV of the cash inflows divided by the PV of the cash

outflows. The equation for the profitability index at a required return of 10 percent is:

PI = [$7,300/1.1 + $6,900/1.12 + $5,700/1.13] / $14,000 = 1.187

The equation for the profitability index at a required return of 15 percent is:

PI = [$7,300/1.15 + $6,900/1.152 + $5,700/1.153] / $14,000 = 1.094

The equation for the profitability index at a required return of 22 percent is:

PI = [$7,300/1.22 + $6,900/1.222 + $5,700/1.223] / $14,000 = 0.983

7 / 17

We would accept the project if the required return were 10 percent or 15 percent since the PI is

greater than one. We would reject the project if the required return were 22 percent since the PI

is less than one.

CH10 9，13，14，17，18

9. Using the tax shield approach to calculating OCF (Remember the approach is irrelevant; the final

answer will be the same no matter which of the four methods you use.), we get:

OCF = (Sales – Costs)(1 – tC) + tCDepreciation

OCF = ($2,650,000 – 840,000)(1 – 0.35) + 0.35($3,900,000/3)

OCF = $1,631,500

13. First we will calculate the annual depreciation of the new equipment. It will be:

Annual depreciation = $560,000/5

Annual depreciation = $112,000

Now, we calculate the aftertax salvage value. The aftertax salvage value is the market price

minus (or plus) the taxes on the sale of the equipment, so:

Aftertax salvage value = MV + (BV – MV)tc

Very often the book value of the equipment is zero as it is in this case. If the book value is zero,

the equation for the aftertax salvage value becomes:

Aftertax salvage value = MV + (0 – MV)tc

Aftertax salvage value = MV(1 – tc)

We will use this equation to find the aftertax salvage value since we know the book value is zero.

So, the aftertax salvage value is:

Aftertax salvage value = $85,000(1 – 0.34)

Aftertax salvage value = $56,100

Using the tax shield approach, we find the OCF for the project is:

OCF = $165,000(1 – 0.34) + 0.34($112,000)

OCF = $146,980

Now we can find the project NPV. Notice we include the NWC in the initial cash outlay. The

recovery of the NWC occurs in Year 5, along with the aftertax salvage value.

NPV = –$560,000 – 29,000 + $146,980(PVIFA10%,5) + [($56,100 + 29,000) / 1.105]

8 / 17

14.

NPV = $21,010.24

First we will calculate the annual depreciation of the new equipment. It will be:

Annual depreciation charge = $720,000/5

Annual depreciation charge = $144,000

The aftertax salvage value of the equipment is:

Aftertax salvage value = $75,000(1 – 0.35)

Aftertax salvage value = $48,750

Using the tax shield approach, the OCF is:

OCF = $260,000(1 – 0.35) + 0.35($144,000)

OCF = $219,400

Now we can find the project IRR. There is an unusual feature that is a part of this project.

Accepting this project means that we will reduce NWC. This reduction in NWC is a cash inflow

at Year 0. This reduction in NWC implies that when the project ends, we will have to increase

NWC. So, at the end of the project, we will have a cash outflow to restore the NWC to its level

before the project. We also must include the aftertax salvage value at the end of the project. The

IRR of the project is:

NPV = 0 = –$720,000 + 110,000 + $219,400(PVIFAIRR%,5) + [($48,750 – 110,000) / (1+IRR)5]

IRR = 21.65%

17. We will need the aftertax salvage value of the equipment to compute the EAC. Even though the

equipment for each product has a different initial cost, both have the same salvage value. The

aftertax salvage value for both is:

Both cases: aftertax salvage value = $40,000(1 – 0.35) = $26,000

To calculate the EAC, we first need the OCF and NPV of each option. The OCF and NPV for

Techron I is:

OCF = –$67,000(1 – 0.35) + 0.35($290,000/3) = –9,716.67

NPV = –$290,000 – $9,716.67(PVIFA10%,3) + ($26,000/1.103) = –$294,629.73

EAC = –$294,629.73 / (PVIFA10%,3) = –$118,474.97

And the OCF and NPV for Techron II is:

9 / 17

OCF = –$35,000(1 – 0.35) + 0.35($510,000/5) = $12,950

NPV = –$510,000 + $12,950(PVIFA10%,5) + ($26,000/1.105) = –$444,765.36

EAC = –$444,765.36 / (PVIFA10%,5) = –$117,327.98

The two milling machines have unequal lives, so they can only be compared by expressing both

on an equivalent annual basis, which is what the EAC method does. Thus, you prefer the

Techron II because it has the lower (less negative) annual cost.

18. To find the bid price, we need to calculate all other cash flows for the project, and then solve for

the bid price. The aftertax salvage value of the equipment is:

Aftertax salvage value = $70,000(1 – 0.35) = $45,500

Now we can solve for the necessary OCF that will give the project a zero NPV. The equation for

the NPV of the project is:

NPV = 0 = –$940,000 – 75,000 + OCF(PVIFA12%,5) + [($75,000 + 45,500) / 1.125]

Solving for the OCF, we find the OCF that makes the project NPV equal to zero is:

OCF = $946,625.06 / PVIFA12%,5 = $262,603.01

The easiest way to calculate the bid price is the tax shield approach, so:

OCF = $262,603.01 = [(P – v)Q – FC ](1 – tc) + tcD

$262,603.01 = [(P – $9.25)(185,000) – $305,000 ](1 – 0.35) + 0.35($940,000/5)

P = $12.54

CH14 6、9、20、23、24

6. The pretax cost of debt is the YTM of the company’s bonds, so:

P0 = $1,070 = $35(PVIFAR%,30) + $1,000(PVIFR%,30)

R = 3.137%

YTM = 2 × 3.137% = 6.27%

And the aftertax cost of debt is:

RD = .0627(1 – .35) = .0408 or 4.08%

9. a. Using the equation to calculate the WACC, we find:

10 / 17

20.

b.

WACC = .60(.14) + .05(.06) + .35(.08)(1 – .35) = .1052 or 10.52%

Since interest is tax deductible and dividends are not, we must look at the after-tax cost of

debt, which is:

.08(1 – .35) = .0520 or 5.20%

Hence, on an after-tax basis, debt is cheaper than the preferred stock.

Using the debt-equity ratio to calculate the WACC, we find:

WACC = (.90/1.90)(.048) + (1/1.90)(.13) = .0912 or 9.12%

Since the project is riskier than the company, we need to adjust the project discount rate for the

additional risk. Using the subjective risk factor given, we find:

Project discount rate = 9.12% + 2.00% = 11.12%

We would accept the project if the NPV is positive. The NPV is the PV of the cash outflows plus

the PV of the cash inflows. Since we have the costs, we just need to find the PV of inflows. The

cash inflows are a growing perpetuity. If you remember, the equation for the PV of a growing

perpetuity is the same as the dividend growth equation, so:

PV of future CF = $2,700,000/(.1112 – .04) = $37,943,787

The project should only be undertaken if its cost is less than $37,943,787 since costs less than

this amount will result in a positive NPV.

a.

b.

c.

Using the dividend discount model, the cost of equity is:

RE = [(0.80)(1.05)/$61] + .05

RE = .0638 or 6.38%

Using the CAPM, the cost of equity is:

RE = .055 + 1.50(.1200 – .0550)

RE = .1525 or 15.25%

When using the dividend growth model or the CAPM, you must remember that both are

estimates for the cost of equity. Additionally, and perhaps more importantly, each method

of estimating the cost of equity depends upon different assumptions.

Challenge

23.

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24. We can use the debt-equity ratio to calculate the weights of equity and debt. The debt of the

company has a weight for long-term debt and a weight for accounts payable. We can use the

weight given for accounts payable to calculate the weight of accounts payable and the weight of

long-term debt. The weight of each will be:

Accounts payable weight = .20/1.20 = .17

Long-term debt weight = 1/1.20 = .83

Since the accounts payable has the same cost as the overall WACC, we can write the equation

for the WACC as:

WACC = (1/1.7)(.14) + (0.7/1.7)[(.20/1.2)WACC + (1/1.2)(.08)(1 – .35)]

Solving for WACC, we find:

WACC = .0824 + .4118[(.20/1.2)WACC + .0433]

WACC = .0824 + (.0686)WACC + .0178

(.9314)WACC = .1002

WACC = .1076 or 10.76%

We will use basically the same equation to calculate the weighted average flotation cost, except

we will use the flotation cost for each form of financing. Doing so, we get:

Flotation costs = (1/1.7)(.08) + (0.7/1.7)[(.20/1.2)(0) + (1/1.2)(.04)] = .0608 or 6.08%

The total amount we need to raise to fund the new equipment will be:

Amount raised cost = $45,000,000/(1 – .0608)

Amount raised = $47,912,317

Since the cash flows go to perpetuity, we can calculate the present value using the equation for

the PV of a perpetuity. The NPV is:

NPV = –$47,912,317 + ($6,200,000/.1076)

NPV = $9,719,777

CH16 1，4，12，14，17

1. a. A table outlining the income statement for the three possible states of the economy is

shown below. The EPS is the net income divided by the 5,000 shares outstanding. The last

row shows the percentage change in EPS the company will experience in a recession or an

expansion economy.

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b.

EBIT

Interest

NI

EPS

%EPS

Recession

$14,000

0

$14,000

$ 2.80

–50

Normal

$28,000

0

$28,000

$ 5.60

–––

Expansion

$36,400

0

$36,400

$ 7.28

+30

If the company undergoes the proposed recapitalization, it will repurchase:

Share price = Equity / Shares outstanding

Share price = $250,000/5,000

Share price = $50

Shares repurchased = Debt issued / Share price

Shares repurchased =$90,000/$50

Shares repurchased = 1,800

The interest payment each year under all three scenarios will be:

Interest payment = $90,000(.07) = $6,300

The last row shows the percentage change in EPS the company will experience in a

recession or an expansion economy under the proposed recapitalization.

Recession Normal Expansion

EBIT $14,000 $28,000 $36,400

Interest 6,300 6,300 6,300

NI $7,700 $21,700 $30,100

EPS $2.41 $ 6.78 $9.41

–64.52 ––– +38.71

%EPS

4. a. Under Plan I, the unlevered company, net income is the same as EBIT with no corporate tax.

The EPS under this capitalization will be:

EPS = $350,000/160,000 shares

EPS = $2.19

Under Plan II, the levered company, EBIT will be reduced by the interest payment. The

interest payment is the amount of debt times the interest rate, so:

NI = $500,000 – .08($2,800,000)

NI = $126,000

And the EPS will be:

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b.

c.

EPS = $126,000/80,000 shares

EPS = $1.58

Plan I has the higher EPS when EBIT is $350,000.

Under Plan I, the net income is $500,000 and the EPS is:

EPS = $500,000/160,000 shares

EPS = $3.13

Under Plan II, the net income is:

NI = $500,000 – .08($2,800,000)

NI = $276,000

And the EPS is:

EPS = $276,000/80,000 shares

EPS = $3.45

Plan II has the higher EPS when EBIT is $500,000.

To find the breakeven EBIT for two different capital structures, we simply set the equations

for EPS equal to each other and solve for EBIT. The breakeven EBIT is:

EBIT/160,000 = [EBIT – .08($2,800,000)]/80,000

EBIT = $448,000

With the information provided, we can use the equation for calculating WACC to find the

cost of equity. The equation for WACC is:

WACC = (E/V)RE + (D/V)RD(1 – tC)

The company has a debt-equity ratio of 1.5, which implies the weight of debt is 1.5/2.5, and

the weight of equity is 1/2.5, so

WACC = .10 = (1/2.5)RE + (1.5/2.5)(.07)(1 – .35)

RE = .1818 or 18.18%

To find the unlevered cost of equity we need to use M&M Proposition II with taxes, so:

RE = RU + (RU – RD)(D/E)(1 – tC)

.1818 = RU + (RU – .07)(1.5)(1 – .35)

RU = .1266 or 12.66%

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12. a.

b.

14.

17.

c. To find the cost of equity under different capital structures, we can again use M&M

Proposition II with taxes. With a debt-equity ratio of 2, the cost of equity is:

RE = RU + (RU – RD)(D/E)(1 – tC)

RE = .1266 + (.1266 – .07)(2)(1 – .35)

RE = .2001 or 20.01%

With a debt-equity ratio of 1.0, the cost of equity is:

RE = .1266 + (.1266 – .07)(1)(1 – .35)

RE = .1634 or 16.34%

And with a debt-equity ratio of 0, the cost of equity is:

RE = .1266 + (.1266 – .07)(0)(1 – .35)

RE = RU = .1266 or 12.66%

The value of the unlevered firm is:

VU = EBIT(1 – tC)/RU

VU = $92,000(1 – .35)/.15

VU = $398,666.67

The value of the levered firm is:

VU = VU + tCD

VU = $398,666.67 + .35($60,000)

VU = $419,666.67

a.

b.

With no debt, we are finding the value of an unlevered firm, so:

VU = EBIT(1 – tC)/RU

VU = $14,000(1 – .35)/.16

VU = $56,875

With debt, we simply need to use the equation for the value of a levered firm. With 50 percent

debt, one-half of the firm value is debt, so the value of the levered firm is:

VL

= VU

+ tC(D/V)VU

VL = $56,875 + .35(.50)($56,875)

VL = $66,828.13

And with 100 percent debt, the value of the firm is:

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VL

= VU

+ tC(D/V)VU

VL = $56,875 + .35(1.0)($56,875)

VL = $76,781.25

c. The net cash flows is the present value of the average daily collections times the daily

interest rate, minus the transaction cost per day, so:

Net cash flow per day = $1,276,275(.0002) – $0.50(385)

Net cash flow per day = $62.76

The net cash flow per check is the net cash flow per day divided by the number of checks

received per day, or:

Net cash flow per check = $62.76/385

Net cash flow per check = $0.16

Alternatively, we could find the net cash flow per check as the number of days the system

reduces collection time times the average check amount times the daily interest rate, minus

the transaction cost per check. Doing so, we confirm our previous answer as:

Net cash flow per check = 3($1,105)(.0002) – $0.50

Net cash flow per check = $0.16 per check

This makes the total costs:

Total costs = $18,900,000 + 56,320,000 = $75,220,000

The flotation costs as a percentage of the amount raised is the total cost divided by the amount

raised, so:

Flotation cost percentage = $75,220,000/$180,780,000 = .4161 or 41.61%

8. The number of rights needed per new share is:

Number of rights needed = 120,000 old shares/25,000 new shares = 4.8 rights per new share.

Using PRO as the rights-on price, and PS as the subscription price, we can express the price per

share of the stock ex-rights as:

PX = [NPRO + PS]/(N + 1)

a. PX = [4.8($94) + $94]/(4.80 + 1) = $94.00; No change.

b. PX = [4.8($94) + $90]/(4.80 + 1) = $93.31; Price drops by $0.69 per share.

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c. PX = [4.8($94) + $85]/(4.80 + 1) = $92.45; Price drops by $1.55 per share.

To get EBITD (earnings before interest, taxes, and depreciation), the numerator in the cash

coverage

ratio, add depreciation to EBIT:

EBITD = EBIT + Depreciation = $23,556.52 + 2,382 = $25,938.52

Now, simply plug the numbers into the cash coverage ratio and calculate:

Cash coverage ratio = EBITD / Interest = $25,938.52 / $3,605 = 7.20 times

24. The only ratio given which includes cost of goods sold is the inventory turnover ratio, so it is the

last ratio used. Since current liabilities is given, we start with the current ratio:

Current ratio = 1.40 = CA / CL = CA / $365,000

CA = $511,000

Using the quick ratio, we solve for inventory:

Quick ratio = 0.85 = (CA – Inventory) / CL = ($511,000 – Inventory) / $365,000

Inventory = CA – (Quick ratio × CL)

Inventory = $511,000 – (0.85 × $365,000)

Inventory = $200,750

Inventory turnover = 5.82 = COGS / Inventory = COGS / $200,750

COGS = $1,164,350

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