2024年5月15日发(作者：ie8卸载工具)

CHAPTER 3 B-1

Chapter3

ating financial the following financial ratios for Smolira Golf Corp.(use

year-end figures rather than average values where appropriate.)

SMOLIRA GOLF CORP

2004 and 2005 balanced sheets

Assets

Current assets

Cash

Accounts recievable

inventary

Total

Fixed assets

Net plant and equipment

Total assets

SMOLIRA GOLF CORP.

2005 Income Statement

Sales

Cost of goods sold

Depreciation

Earnings before interest and taxes

Interest paid

Taxable income

Taxes(35%)

Net income

Dividends

Addition to retained earning

$4,000

3,842

$33,500

18,970

1,980

12,550

486

$12,064

4,222

7,842

2004

$815

2,405

4,608

$7,828

$15,164

$22,992

2005

Liabilities and Owners' Equity

Current liabilities

$906 Accounts payable

2,510 Notes payable

4,906 Other

$8,322 Long-term debt

Owners' equity

$19,167 Common stock

paid-in surplus

Retained earnings

Total

$27,489 Total

and

2004

$983

720

105

$1,808

$4,817

$10,000

6,367

$16,367

$22,992

2005

$1,292

840

188

2,320

4,960

$10,000

10,209

$20,209

$27,489

答案：

Short-term solvency ratios:

Current ratio = Current assets / Current liabilities

Current ratio 2004 = $7,828 / $1,808 = 4.33 times

Current ratio 2005 = $8,322 / $2,320 = 3.59 times

Quick ratio = (Current assets – Inventory) / Current liabilities

Quick ratio 2004 = ($7,828 – 4,608) / $1,808 = 1.78 times

Quick ratio 2005 = ($8,322 – 4,906) / $2,320 = 1.47 times

Cash ratio = Cash / Current liabilities

CHAPTER 3 B-2

Cash ratio 2004 = $815 / $1,808 = 0.45 times

Cash ratio 2005 = $906 / $2,320 = 0.39 times

Asset utilization ratios:

Total asset turnover = Sales / Total assets

Total asset turnover = $33,500 / $27,489 = 1.22 times

Inventory turnover = Cost of goods sold / Inventory

Inventory turnover = $18,970 / $4,906 = 3.87 times

Receivables turnover = Sales / Accounts receivable

Receivables turnover = $33,500 / $2,510 = 13.35 times

Long-term solvency ratios:

Total debt ratio = (Total assets – Total equity) / Total assets

Total debt ratio 2004 = ($22,992 – 16,367) / $22,992 = 0.29

Total debt ratio 2005 = ($27,489 – 20,209) / $27,489 = 0.26

Debt-equity ratio = Total debt / Total equity

Debt-equity ratio 2004 = ($1,808 + 4,817) / $16,367 = 0.40

Debt-equity ratio 2005 = ($2,320 + 4,960) / $20,209 = 0.36

Equity multiplier = 1 + D/E

Equity multiplier 2004 = 1 + 0.40 = 1.40

Equity multiplier 2005 = 1 + 0.36 = 1.36

Times interest earned = EBIT / Interest

Times interest earned = $12,550 / $486 = 25.82 times

Cash coverage ratio = (EBIT + Depreciation) / Interest

Cash coverage ratio = ($12,550 + 1,980) / $486 = 29.90 times

Profitability ratios:

Profit margin = Net income / Sales

Profit margin = $7,842 / $33,500 = 23.41%

Return on assets = Net income / Total assets

Return on assets = $7,842 / $27,489 = 28.53%

Return on equity = Net income / Total equity

Return on equity = $7,842 / $20,209 = 38.80%

Pont uct the Du Pont Identity for the Smolira Golf Corp.

答案：The DuPont identity is:

ROE = (PM)(TAT)(EM)

CHAPTER 3 B-3

ROE = (0.2341)(1.22)(1.36) = 0.3880 or 38.80%

ent of cash e the 2005 statement of cash flows for Smolira Golf Corp.

答案：

Statement of Cash Flows For 2005

Cash, beginning of the year

$ 815

Operating activities

Net income $ 7,842

Plus:

Depreciation $ 1,980

Increase in accounts payable 309

Increase in other current liabilities 83

Less:

Increase in accounts receivable $ (105)

Increase in inventory (298)

Net cash from operating activities

Investment activities

Fixed asset acquisition

Net cash from investment activities

Financing activities

Increase in notes payable

Dividends paid

Decrease in long-term debt

$ 9,811

$ (5,983)

$ (5,983)

$ 120

(4,000)

143

$ (3,737)

$ 91

$ 906

Net cash from financing activities

Net increase in cash

Cash, end of year

Value a Golf 2500 shares of common stock outstanding,and the

market price for a share of stock at the end of 2005 was $ is the price-earning ratio?What

are the dividends per share？What is the market-to-book ratio at the end of 2005?

答案：

Earnings per share = Net income / Shares

Earnings per share = $7,842 / 2,500 = $3.14 per share

P/E ratio = Shares price / Earnings per share

P/E ratio = $67 / $3.14 = 21.36 times

Dividends per share = Dividends / Shares

Dividends per share = $4,000 / 2,500 = $1.60 per share

CHAPTER 3 B-4

Book value per share = Total equity / Shares

Book value per share = $20,209 / 2,500 shares = $8.08 per share

Market-to-book ratio = Share price / Book value per share

Market-to-book ratio = $67.00 / $8.08 = 8.29 times

Chapter4

ating most recent financial statements for Moose Tours,Inc.. for

2005 are projected to grow by 20%.Interest expense will remain constant ;the taxes rate and the

dividend payout rate will also remain ,other expenses,current assets,and accounts

payable increase spontaneously with the firm is operating at full capacity and no new debt

or equity is issued,what is the external financial needed to support the 20% growth rate in sales？

MOOSE TOURS,INC

2004 Income Statement

Sales

Costs

Other expenses

Earnings before interest and taxes

Interest paid

Taxable income

Taxes (35%)

Net income

Dividends

Addition to retained earnings

MOOSE TOURS,INC

Balance Sheet as of December 31,2004

Assets

Current assets

Cash

Accounts recievable

Inventory

Total

Fixed assets

Net plant and equipment

Total assets

Liabilities and owners'equity

Current liabilities

$25,000 Accounts payable

43,000 Notes payable

76,000 Total

$144,000 Long-term debt

Owners'equity

$364,000 Common stock and paid-in

surplus

Retained earnings

Total

$508,000 Total liabilities and owners'equity

$65,000

9,000

$74,000

$156,000

$21,000

257,000

$278,000

$508,000

$42,458

63,687

$905,000

710,000

12,000

$183,000

19,700

$163,300

57,155

$106,145

CHAPTER 3 B-5

答案：Assuming costs vary with sales and a 20 percent increase in sales, the pro forma income

statement will look like this:

MOOSE TOURS INC.

Pro Forma Income Statement

Sales $ 1,086,000

Costs 852,000

Other expenses 14,400

EBIT $ 219,600

Interest 19,700

Taxable income $ 199,900

Taxes(35%) 69,965

Net income $ 129,935

The payout ratio is constant, so the dividends paid this year is the payout ratio from last year

times net income, or:

Dividends = ($42,458/$106,145)($129,935)

Dividends = $51,974

And the addition to retained earnings will be:

Addition to retained earnings = $129,935 – 51,974

Addition to retained earnings = $77,961

The new addition to retained earnings on the pro forma balance sheet will be:

New addition to retained earnings = $257,000 + 77,961

New addition to retained earnings = $334,961

The pro forma balance sheet will look like this:

MOOSE TOURS INC.

Pro Forma Balance Sheet

Assets Liabilities and Owners’ Equity

Current assets

Cash

Accounts receivable

Inventory

Total

Fixed assets

Net plant and

equipment

$

$

30,000

51,600

91,200

172,800

436,800

Current liabilities

Accounts payable

Notes payable

Total

Long-term debt

Owners’ equity

Common stock and

paid-in surplus

Retained earnings

$

$

78,000

9,000

87,000

156,000

$

21,000

334,961

CHAPTER 3 B-6

Total $ 355,961

Total liabilities and owners’

Total assets $ 609,600 equity $ 598,961

So the EFN is:

EFN = Total assets – Total liabilities and equity

EFN = $609,600 – 598,961

EFN = $10,639

ty Usage and the previous problem,suppose the firm was operating at only

80% capacity in is EFN now?

答案：First, we need to calculate full capacity sales, which is:

Full capacity sales = $905,000 / .80

Full capacity sales = $1,131,250

The capital intensity ratio at full capacity sales is:

Capital intensity ratio = Fixed assets / Full capacity sales

Capital intensity ratio = $364,000 / $1,131,250

Capital intensity ratio = .32177

The fixed assets required at full capacity sales is the capital intensity ratio times the projected

sales level:

Total fixed assets = .32177($1,086,000) = $349,440

So, EFN is：

EFN = ($172,800 + 349,440) – $598,961 = –$76,721

Note that this solution assumes that fixed assets are decreased (sold) so the company has a

100 percent fixed asset utilization. If we assume fixed assets are not sold, the answer

becomes:

EFN = ($172,800 + 364,000) – $598,961 = –$62,161

ating Problem 25,suppose the firm wishes to keep its debt-equity ratio

is EFN now?

答案：The D/E ratio of the company is:

D/E = ($156,000 + 74,000) / $278,000

D/E = .82734

So the new total debt amount will be:

New total debt = .82734($355,961)

New total debt = $294,500.11

CHAPTER 3 B-7

So the EFN is:

EFN = $609,600 – ($294,500.11 + 355,961) = –$40,861.11

An interpretation of the answer is not that the company has a negative EFN. Looking back at

Problem 25, we see that for the same sales growth, the EFN is $10,639. The negative number

in this case means the company has too much capital. There are two possible solutions. First,

the company can put the excess funds in cash, which has the effect of changing the current

asset growth rate. Second, the company can use the excess funds to repurchase debt and

equity. To maintain the current capital structure, the repurchase must be in the same

proportion as the current capital structure.

and Internal Growth. Redo Problem 27 using sales growth rates of 15% and 25% in

addition to 20%.Illustrate graphically the relationship between EFN and the growth rate,and use

this graph to determine the relationship between them .At what growth rate is the EFN equal to

zero? Why is this internal growth rate different from that found by using the equation in the text?

答案：The pro forma income statements for all three growth rates will be:

MOOSE TOURS INC.

Pro Forma Income Statement

15 % Sales 20% Sales 25% Sales

Growth Growth Growth

Sales $1,040,750 $1,086,000 $1,131,250

Costs 816,500 852,000 887,500

Other expenses 13,800 14,400 15,000

EBIT $ 210,450 $ 219,600 $ 228,750

Interest 19,700 19,700 19,700

Taxable income $ 190,750 $ 199,900 $ 209,050

Taxes (35%) 66,763 69,965 73,168

Net income $ 123,988 $ 129,935 $ 135,883

Dividends $ 49,595 $ 51,974 $ 54,353

Add to RE 74,393 77,961 81,530

We will calculate the EFN for the 15 percent growth rate first. Assuming the payout ratio is

constant, the dividends paid will be:

Dividends = ($42,458/$106,145)($123,988)

Dividends = $49,595

And the addition to retained earnings will be:

Addition to retained earnings = $123,988 – 49,595

Addition to retained earnings = $74,393

The new addition to retained earnings on the pro forma balance sheet will be:

CHAPTER 3 B-8

New addition to retained earnings = $257,000 + 74,393

New addition to retained earnings = $331,393

The pro forma balance sheet will look like this:

15% Sales Growth:

MOOSE TOURS INC.

Pro Forma Balance Sheet

Assets Liabilities and Owners’ Equity

74,750

9,000

83,750

156,000

Current assets Current liabilities

Cash $ 28,750 Accounts payable $

Accounts receivable 49,450 Notes payable

Inventory 87,400 Total $

Total $ 165,600 Long-term debt

Fixed assets

Net plant and Owners’ equity

equipment 418,600 Common stock and

paid-in surplus $

Retained earnings

Total $

Total liabilities and owners’

Total assets $ 584,200 equity $

So the EFN is:

EFN = Total assets – Total liabilities and equity

EFN = $584,200 – 592,143

EFN = –$7,943

At a 20 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be:

Dividends = ($42,458/$106,145)($129,935)

Dividends = $51,974

And the addition to retained earnings will be:

Addition to retained earnings = $129,935 – 51,974

Addition to retained earnings = $77,961

The new addition to retained earnings on the pro forma balance sheet will be:

New addition to retained earnings = $257,000 + 77,961

New addition to retained earnings = $334,961

The pro forma balance sheet will look like this:

20% Sales Growth:

21,000

331,393

352,393

592,143

CHAPTER 3 B-9

MOOSE TOURS INC.

Pro Forma Balance Sheet

Liabilities and Owners’ Equity

78,000

9,000

87,000

156,000

Assets

Current assets Current liabilities

Cash $ 30,000 Accounts payable $

Accounts receivable 51,600 Notes payable

Inventory 91,200 Total $

Total $ 172,800 Long-term debt

Fixed assets

Net plant and Owners’ equity

equipment 436,800 Common stock and

paid-in surplus $

Retained earnings

Total $

Total liabilities and owners’

Total assets $ 609,600 equity $

So the EFN is:

EFN = Total assets – Total liabilities and equity

EFN = $609,600 – 598,961

EFN = $10,639

At a 25 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be:

Dividends = ($42,458/$106,145)($135,883)

Dividends = $54,353

And the addition to retained earnings will be:

Addition to retained earnings = $135,883 – 54,353

Addition to retained earnings = $81,530

The new addition to retained earnings on the pro forma balance sheet will be:

New addition to retained earnings = $257,000 + 81,530

New addition to retained earnings = $338,530

The pro forma balance sheet will look like this:

25% Sales Growth:

MOOSE TOURS INC.

Pro Forma Balance Sheet

Assets Liabilities and Owners’ Equity

21,000

334,961

355,961

598,961

CHAPTER 3 B-10

81,250

9,000

90,250

156,000

Current assets Current liabilities

Cash $ 31,250 Accounts payable $

Accounts receivable 53,750 Notes payable

Inventory 95,000 Total $

Total $ 180,000 Long-term debt

Fixed assets

Net plant and Owners’ equity

equipment 455,000 Common stock and

paid-in surplus $

Retained earnings

Total $

Total liabilities and owners’

Total assets $ 635,000 equity $

So the EFN is:

EFN = Total assets – Total liabilities and equity

EFN = $635,000 – 605,780

EFN = $29,221

aints on Recording,Inc.,wish to maintain a growth rate of 14% per year

and a debt-equity ratio of margin is 6.2 %,and the ratio of total assets to sales is

constant at this growth rate possible? To answer ,determine what the dividend payout ratio

must be .How do you interpret the result?

答案：We must need the ROE to calculate the sustainable growth rate. The ROE is:

ROE = (PM)(TAT)(EM)

ROE = (.062)(1 / 1.55)(1 + 0.3)

ROE = .0520 or 5.20%

Now we can use the sustainable growth rate equation to find the retention ratio as:

Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]

Sustainable growth rate = .14 = [.0520(b)] / [1 – .0520(b)

b = 2.36

This implies the payout ratio is:

Payout ratio = 1 – b

Payout ratio = 1 – 2.36

Payout ratio = –1.36

This is a negative dividend payout ratio of 136 percent, which is impossible. The growth rate

is not consistent with the other constraints. The lowest possible payout rate is 0, which

corresponds to retention ratio of 1, or total earnings retention.

21,000

338,530

359,530

605,780

CHAPTER 3 B-11

The maximum sustainable growth rate for this company is:

Maximum sustainable growth rate = (ROE × b) / [1 – (ROE × b)]

Maximum sustainable growth rate = [.0520(1)] / [1 – .0520(1)]

Maximum sustainable growth rate = .0549 or 5.49%

d the following:

S=Previous year's sales

A=Total assets

D=Total debt

E=Total equity

g=Projected growth in sales

PM=Profit margin

b=Retention(plowback)ratio

Show that EFN can be written as：EFN=-PM(S)b+(A-PM(S)b)*g

答案：We know that EFN is:

EFN = Increase in assets – Addition to retained earnings

The increase in assets is the beginning assets times the growth rate, so:

Increase in assets = A  g

The addition to retained earnings next year is the current net income times the retention ratio,

times one plus the growth rate, so:

Addition to retained earnings = (NI  b)(1 + g)

And rearranging the profit margin to solve for net income, we get:

NI = PM(S)

Substituting the last three equations into the EFN equation we started with and rearranging,

we get:

EFN = A(g) – PM(S)b(1 + g)

EFN = A(g) – PM(S)b – [PM(S)b]g

EFN = – PM(S)b + [A – PM(S)b]g

Chapter6

nt Interest question illustrate what is known as discount e

you are discussing a loan with a somewhat unscrupulous lender .You want to borrow $20,000 for

one interest rate is 12%,you and the lender agree that the interest on the loan will be

0.12*$20,000=$2,400 ,so the lender deducts this interest amount from the loan up front and give

you $17,600 .In this case,we say that the discount is $24,'s wrong here?

答案： To find the APR and EAR, we need to use the actual cash flows of the loan. In other words,

the interest rate quoted in the problem is only relevant to determine the total interest under

the terms given. The cash flows of the loan are the $20,000 you must repay in one year, and

the $17,600 you borrow today. The interest rate of the loan is:

$20,000 = $17,600(1 + r)

CHAPTER 3 B-12

r = ($20,000 – 17,600) – 1 = 13.64%

Because of the discount, you only get the use of $17,600, and the interest you pay on that

amount is 13.64%, not 12%.

ating EAR with Add-On problem illustrates a deceptive way of quoting

interest rate called add-on e that you see an advertisement for Crazy Judy's

Stereo City that reads something like this :"$1,000 Instant Credit! 15% Simple Interest !

Three Years To Pay !Low,Low Monthly payments !" You're not exactly sure what all this

means and somebody has spilled ink over the APR on the loan contract, so you ask the

manager for clarification.

Judy explains that if you borrow $1,000 for three years at 15% interest, in three years

you will owe: $1,000 * 1.15

3

= $1,000 * 1.52088=$1,520.88.

Now, Judy recognizes that coming up with $1,520.88 all at once might be a strain, so she

lets you make "Low,Low Monthly payments" of $1,520.88 / 36 =$42.25 per month, even though

this is extra bookkeeping work for her.

Is that a 15% loan? Why or why not? What is the APR on this loan? What is the EAR? Why

do you think this is called add-on interest?

答案：Be careful of interest rate quotations. The actual interest rate of a loan is determined by the

cash flows. Here, we are told that the PV of the loan is $1,000, and the payments are $42.25

per month for three years, so the interest rate on the loan is:

PVA = $1,000 = $42.25[ {1 – [1 / (1 + r)]

36

} / r ]

Solving for r with a spreadsheet, on a financial calculator, or by trial and error, gives:

r = 2.47% per month

APR = 12(2.47%) = 29.63%

EAR = (1 + .0247)

12

– 1 = 34.00%

It’s called add-on interest because the interest amount of the loan is added to the principal

amount of the loan before the loan payments are calculated.

ating Annuity is a classic retirement problem.A time line will help in

solving it. Your friend is celebrating her 35th birthday today and wants to start saving for

her anticipated retirement at age wants to be able to withdraw $90,000 from her

savings account on each birthday for 15 years following her retirement. The first withdraw

will be on her 66th birthday. Your friend intends to invest her money inn the local credit

union, which offers 8% per year. She wants to make equal annual payments on each birthday

into the account established at the credit union for her retirement fund.

A. If she start making these deposits on her 36th birthday and continues to make deposits until she

is 65 (the last deposits will be on her 65th birthday ), what account she will deposit annually to be

able to make the desired withdrawals at retirement?

B. Suppose your friend has just inherited a large sum of money . Rather than making equal annual

payments,she has decided to make one lump-sum payment on her 35th birthday to cover her

retirement amount does she have to deposit?

CHAPTER 3 B-13

C. Suppose your friend's employer will contribute $1,500 to the account every year as part of the

company 's profit-sharing plan. In addition, your friend expects a $25,000 distribution from a

family trust fund on her 55th birthday, which she will also put into her retirement account. What

amount must she deposit annually noe to be able to make the desired withdrawals at retirement?

答案：Here we are solving a two-step time value of money problem. Each question asks for a

different possible cash flow to fund the same retirement plan. Each savings possibility has

the same FV, that is, the PV of the retirement spending when your friend is ready to retire.

The amount needed when your friend is ready to retire is:

PVA = $90,000{[1 – (1/1.08)

15

] / .08} = $770,353.08

This amount is the same for all three parts of this question.

a. If your friend makes equal annual deposits into the account, this is an annuity with the

FVA equal to the amount needed in retirement. The required savings each year will be:

FVA = $770,353.08 = C[(1.08

30

– 1) / .08]

C = $6,800.24

b. Here we need to find a lump sum savings amount. Using the FV for a lump sum

equation, we get:

FV = $770,353.08 = PV(1.08)

30

PV = $76,555.63

c. In this problem, we have a lump sum savings in addition to an annual deposit. Since we

already

know the value needed at retirement, we can subtract the value of the lump sum savings

at retirement to find out how much your friend is short. Doing so gives us:

FV of trust fund deposit = $25,000(1.08)

10

= $53,973.12

So, the amount your friend still needs at retirement is:

FV = $770,353.08 – 53,973.12 = $716,379.96

Using the FVA equation, and solving for the payment, we get:

$716,379.96 = C[(1.08

30

– 1) / .08]

C = $6,323.80

This is the total annual contribution, but your friend’s employer will contribute $1,500 per

year, so your friend must contribute:

Friend's contribution = $6,323.80 – 1,500 = $4,823.80

75. Calculating EAR. A check-cashing store is in the business of making personal loans to

walk-up customers. The store makes only one-week loans at 10% interest per week.

A. What APR must the store report to its customers? What is the EAR that the customers are

actually paying?

B. Now suppose the store makes one-week loans at 10% discount interest per week (see question

60). What is the APR now? The EAR?

CHAPTER 3 B-14

C. The check-cashing store also makes one month add-on interest loans at 9% discount interest

per week. Thus ,is you borrow $100 for one month(four weeks),the interest will be ($100*1.09

4

) -

100= $41.16. Because this is discount interest , your net loan proceeds today will be $58.84. You

must then repay the store $100 at the end of the month. To help you out, though, the store lets you

pay off this $100 in installments of $25 per week. What is the APR of this loan? What is the EAR?

答案： a. The APR is the interest rate per week times 52 weeks in a year, so:

APR = 52(10%) = 520%

EAR = (1 + .10)

52

– 1 = 14,104.29%

b. In a discount loan, the amount you receive is lowered by the discount, and you repay

the full principal. With a 10 percent discount, you would receive $9 for every $10 in

principal, so the weekly interest rate would be:

$10 = $9(1 + r)

r = ($10 / $9) – 1 = 11.11%

Note the dollar amount we use is irrelevant. In other words, we could use $0.90 and $1,

$90 and $100, or any other combination and we would get the same interest rate. Now we

can find the APR and the EAR:

APR = 52(11.11%) = 577.78%

EAR = (1 + .1111)

52

– 1 = 23,854.63%

c. Using the cash flows from the loan, we have the PVA and the annuity payments and

need to find the interest rate, so:

PVA = $58.84 = $25[{1 – [1 / (1 + r)]

4

}/ r ]

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

r = 25.18% per week

APR = 52(25.18%) = 1,309.92%

EAR = 1.2518

52

– 1 = 11,851,501.94%

Chapter7

21. Accrued interest. You purchase a bond with a coupon rate of 6.5%, and a clean price of

$865. If the next semiannual coupon payment is due inn three months, what is the invoice price?

答案：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 three

months until the next coupon payment, so three months have passed since the last coupon

payment. The accrued interest for the bond is:

Accrued interest = $65/2 × 3/6 = $16.25

And we calculate the dirty price as:

Dirty price = Clean price + Accrued interest = $865 + 16.25 = $881.25

24. Bond prices versus yields.

A. What is the relationship between the price of a bond and its YTM?

CHAPTER 3 B-15

B. Explain why some bonds sell at a premium over par value while other bonds sell at a discount.

What do you know about the relationship between the coupon rate and YTM for premium bonds?

What about for discount bonds? For bonds selling at par value?

C. What is the relationship between the current yield and YTM for premium bonds? For discount

bonds? For bonds selling at par value ?

答案： a. The bond price is the present value of the cash flows from a bond. The YTM is the

interest rate used in valuing the cash flows from a bond.

B. If the coupon rate is higher than the required return on a bond, the bond will sell at a

premium, since it provides periodic income in the form of coupon payments in excess

of that required by investors on other similar bonds. If the coupon rate is lower than the

required return on a bond, the bond will sell at a discount since it provides insufficient

coupon payments compared to that required by investors on other similar bonds. For

premium bonds, the coupon rate exceeds the YTM; for discount bonds, the YTM

exceeds the coupon rate, and for bonds selling at par, the YTM is equal to the coupon

rate.

C. Current yield is defined as the annual coupon payment divided by the current bond price.

For

premium bonds, the current yield exceeds the YTM, for discount bonds the current

yield is less than the YTM, and for bonds selling at par value, the current yield is equal

to the YTM. In all cases, the current yield plus the expected one-period capital gains

yield of the bond must be equal to the required return.

g bonds. The Mallory Corporation has two different bonds currently outstanding. Bond

M has a face value of $20,000 and matures in 20 years. The bond makes no payment for the first

six years, the pays $1,200 every six months over the subsequent eight years, and finally pays

$1,500 every six months the last six years. Bond N also has a face value of $20,000 and a maturity

of 20 years;it makes no coupon payments over the life of the bond. If the required return on both

these bonds is 10% compounded semiannually,what is the current price of Bond M? Of Bond N?

答案：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:

P

M

= $1,200(PVIFA

5%,16

)(PVIF

5%,12

) + $1,500(PVIFA

5%,12

)(PVIF

5%,28

) +

$20,000(PVIF

5%,40

)

P

M

= $13,474.20

Notice that for the coupon payments of $1,500, 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:

P

N

= $20,000(PVIF

5%,40

) = $2,840.91

Chapter8

20. Stock valuation. Most corporations pay quarterly dividends on their common stock rather

CHAPTER 3 B-16

than annual dividends. Barring any unusual circumstances during the year, the board raises,lowers

or maintains the current dividend once a year and then pays this dividend out in equal quarterly

installments to its shareholders.

A. Suppose a company currently pays a $3.00 annual dividend on its common stock in a single

annual installment ,and management plans on raising this dividend by 6% per year, indefinitely. If

the required return on this stock is 14%,what is the current share price?

B. Now suppose that the company in a actually pays its annual dividend in equal quarterly

installment ;thus, this company has just paid a $0.75 dividend per share,as it has for the previous

three quarters. What is your value for the current share price now?(Hint:find the equivalent annual

end-of-year dividend for each year).comment on whether or not you think that this model of stock

valuation is appropriate.

答案： a. Using the constant growth model, the price of the stock paying annual dividends will

be:

P

0

= D

0

(1 + g) / (R – g) = $3.00(1.06)/(.14 – .06) = $39.75

b. If the company pays quarterly dividends instead of annual dividends, the quarterly

dividend will be one-fourth of annual dividend, or:

Quarterly dividend: $3.00(1.06)/4 = $0.795

To find the equivalent annual dividend, we must assume that the quarterly dividends are

reinvested at the required return. We can then use this interest rate to find the equivalent

annual dividend. In other words, when we receive the quarterly dividend, we reinvest it

at the required return on the stock. So, the effective quarterly rate is:

Effective quarterly rate: 1.14

.25

– 1 = .0333

The effective annual dividend will be the FVA of the quarterly dividend payments at the

effective quarterly required return. In this case, the effective annual dividend will be:

Effective D

1

= $0.795(FVIFA

3.33%,4

) = $3.34

Now, we can use the constant growth model to find the current stock price as:

P

0

= $3.34/(.14 – .06) = $41.78

Note that we can not simply find the quarterly effective required return and growth rate

to find the value of the stock. This would assume the dividends increased each quarter,

not each year.

21. Nonconstant growth. Storico Co. Just paid a dividend of $3.50 per share. The company will

increase its dividend by 20% next year and will then reduce its dividend growth rate by 5% points

per year until it reaches the industry average of 5% dividend growth, after which the company will

keep a constant growth rate,forever. If the required return on Storico stock is 13%,what will a

share of stock sell for today?

答案：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

CHAPTER 3 B-17

in Year 4, divided by the required return minus the constant dividend growth rate. So, the

price in Year 3 will be:

P

3

= $3.50(1.20)(1.15)(1.10)(1.05) / (.13 – .05) = $69.73

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:

P

0

= $3.50(1.20)/(1.13) + $3.50(1.20)(1.15)/1.13

2

+ $3.50(1.20)(1.15)(1.10)/1.13

3

+

$69.73/1.13

3

P

0

= $59.51

22. Nonconstant growth. This one's a little harder. Suppose the current share price for the firm in

the previous problem is $98.65 and all the dividend information remains the same. What required

return must investors be demanding on Storio stock?(hint:set up the valuation formula with all the

relevant cash flows,and use trial and error to find the unknown rate of return.)

答案:Here we want to find the required return that makes the PV of the dividends equal to the

current stock price. The equation for the stock price is:

P = $3.50(1.20)/(1 + R) + $3.50(1.20)(1.15)/(1 + R)

2

+ $3.50(1.20)(1.15)(1.10)/(1 + R)

3

+ [$3.50(1.20)(1.15)(1.10)(1.05)/(R – .05)]/(1 + R)

3

= $98.65

We need to find the roots of this equation. Using spreadsheet, trial and error, or a calculator

with a root solving function, we find that:

R = 9.85%

Chapter 9

22. Multiple IRRs. Consider the following cash flows. How many different IRRs are there?

When should we take this project?

Year

0

1

2

3

4

Cash flow

-$504

2,862

-6,070

5,700

-2,000

答案：The equation for the IRR of the project is:

0 = –$504 + $2,862/(1 + IRR) – $6,070/(1 + IRR)

2

+ $5,700/(1 + IRR)

3

– $2,000/(1 + IRR)

4

Using Descartes rule of signs, from looking at the cash flows we know there are four IRRs

for this project. Even with most computer spreadsheets, we have to do some trial and error.

From trial and error, IRRs of 25%, 33.33%, 42.86%, and 66.67% are found.

We would accept the project when the NPV is greater than zero. See for yourself if that NPV

is greater than zero for required returns between 25% and 33.33% or between 42.86% and

66.67%.

23. NPV Valuation. The Yurdone Corporation wants to set up a private cemetery business.

According to the CFO, Barry M. Deep , business is "looking up". As a result, the cemetery project

CHAPTER 3 B-18

will provide a net cash inflow of $50,000 for the firm during the first year,and the cash flows are

projected to grow at a rate of 6% per year forever. The project requires an initial investment of

$780,000.

A. If Yurdone requires a 13% return on such undertakings,should he cemetery business be

started?

B. The company is somewhat unsure about the assumption of a 6% growth rate on its cash flows.

At what constant growth rate would the company just break even if it still required a 13% return

on investment?

答案：a. Here the cash inflows of the project go on forever, which is a perpetuity. Unlike

ordinary perpetuity cash flows, the cash flows here grow at a constant rate forever,

which is a growing perpetuity. If you remember back to the chapter on stock valuation,

we presented a formula for valuing a stock with constant growth in dividends. This

formula is actually the formula for a growing perpetuity, so we can use it here. The PV

of the future cash flows from the project is:

PV of cash inflows = C

1

/(R – g)

PV of cash inflows = $50,000/(.13 – .06) = $714,285.71

NPV is the PV of the outflows minus by the PV of the inflows, so the NPV is:

NPV of the project = –$780,000 + 714,285.71 = –$65,714.29

The NPV is negative, so we would reject the project.

b. Here we want to know the minimum growth rate in cash flows necessary to accept the

project. The minimum growth rate is the growth rate at which we would have a zero

NPV. The equation for a zero NPV, using the equation for the PV of a growing

perpetuity is:

0 = – $780,000 + $50,000/(.13 – g)

Solving for g, we get:

g = 6.59%

Chapter10

14. Project evaluation. Your firm is contemplating the purchase of a new $925,000

computer-based order entry system. The system will be depreciated straight-line to zero over its

five-year life. It will be worth $90,000 at the end of that time. You will save $360,000 before taxes

per year in order processing costs and you will be able to reduce working capital by $125,000 (this

is a one-time reduction). If the taxes rate is 35%, what is the IRR for this project?

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

Annual depreciation charge = $925,000/5

Annual depreciation charge = $185,000

The aftertax salvage value of the equipment is:

Aftertax salvage value = $90,000(1 – 0.35)

Aftertax salvage value = $58,500

CHAPTER 3 B-19

Using the tax shield approach, the OCF is:

OCF = $360,000(1 – 0.35) + 0.35($185,000)

OCF = $298,750

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 = –$925,000 + 125,000 + $298,750(PVIFA

IRR%,5

) + [($58,500 – 125,000) /

(1+IRR)

5

]

IRR = 23.85%

15. Project evaluation. In the previous problem, suppose your required return on the project is

20% and you pretax cost savings are $400,000 per year. Will you accept the project? What if the

pretax cost savings are $300,000 per year? At what level of pretax cost savings would you be

indifferent between accepting the project and not accepting it ?

答案：To evaluate the project with a $400,000 cost savings, we need the OCF to compute the NPV.

Using the tax shield approach, the OCF is:

OCF = $400,000(1 – 0.35) + 0.35($185,000) = $324,750

NPV = – $925,000 + 125,000 + $324,750(PVIFA

20%,5

) + [($58,500 – 125,000) / (1.20)

5

]

NPV = $144,476.43

The NPV with a $300,000 cost savings is:

OCF = $300,000(1 – 0.35) + 0.35($185,000)

OCF = $259,750

NPV = – $925,000 + 125,000 + $259,750(PVIFA

20%,5

) + [($58,500 – 125,000) / (1.20)

5

]

NPV = – $49,913.36

We would accept the project if cost savings were $400,000, and reject the project if the cost

savings were $300,000. The required pretax cost savings that would make us indifferent

about the project is the cost savings that results in a zero NPV. The NPV of the project is:

NPV = 0 = – $925,000 + $125,000 + OCF(PVIFA

20%,5

) + [($58,500 – 125,000) / (1.20)

5

]

Solving for the OCF, we find the necessary OCF for zero NPV is:

OCF = $276,440.01

Using the tax shield approach to calculating OCF, we get:

OCF = $276,440.01 = (S – C)(1 – 0.35) + 0.35($185K)

(S – C) = $325,676.94

The cost savings that will make us indifferent is $325,676.94.

18. Calculating a Bid Price. Guthrie Enterprises needs someone to supply it with 150,000 cartons

of machine screws per year to support its manufacturing needs over the next five years, and you've

CHAPTER 3 B-20

decided to bid on the contract. It will cost you $780,000 to install the equipment necessary to start

production;you'll depreciate this cost straight-line to zero over the project's life. You estimate that

in five years,this equipment can be salvaged for $50,000. Your fixed production costs will be

$240,000 per year, and your variable production costs should be $8.50 per carton. You also need

an initial investment in net working capital of $75,000. If your tax rate is 35% and you require a

16% return on your investment, what bid price should you submit?

答案：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 = $50,000(1 – 0.35) = $32,500

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 = – $780,000 – 75,000 + OCF(PVIFA

16%,5

) + [($75,000 + 32,500) / 1.16

5

]

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

OCF = $803,817.85 / PVIFA

16%,5

= $245,493.51

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

OCF = $245,493.51 = [(P – v)Q – FC ](1 – t

c

) + t

c

D

$245,493.51 = [(P – $8.50)(150,000) – $240,000 ](1 – 0.35) + 0.35($780,000/5)

P = $12.06

22. Calculating a bid price. Consider a project to supply 80 million postage stamps per year to

the U.S. Postal Service for the next five years. You have an idle parcel of land available that cost

$1,000,000 five years ago;if the land were sold today, it would net you $1,200,000, after-tax. You

will need to install $3.1 million in new manufacturing plant and equipment to actually produce the

stamps; the plant and equipment will be depreciated straight-line to zero over the project's

five-year life. The equipment can be sold for $600,000 at the end of the project. You will also need

$600,000 in initial net working capital for the project, and an additional investment of $50,000 in

every year thereafter. Your production costs are 0.5 cents per stamp, and you have fixed costs of

$800,000 per year. If your tax rate is 34%and your required return on this project is 15%, what

bid price should you submit on the contract?

答案：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:

After-tax salvage value = $600,000(1 – 0.34)

After-tax salvage value = $396,000

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 = – $3,100,000 – 1,200,000 – 600,000 + OCF (PVIFA

15%,5

) – $50,000(PVIFA

15%,4

)

+ {($396,000 + 600,000 + 4(50,000)] / 1.15

5

}

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

OCF = $4,448,125.54 / PVIFA

15%,5

OCF = $1,326,945.03

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

CHAPTER 3 B-21

OCF = $1,326,945.03 = [(P – v)Q – FC ](1 – t

C

) + t

c

D

$1,326,945.03 = [(P – $0.005)(80,000,000) – $800,000](1 – 0.34) + 0.34($3,100,000/5)

P = $0.03614

27. Financial break-even analysis. To solve the bid price problem presented in the text,we set the

project NPV equal to zero and found the required price using the definition of OCF. Thus the bid

price represents a financial break-even level for the project . This type of analysis can be extended

to many other types of problem.

A. In problem 18, assume that the price per carton is $13 and find the project NPV. What does

your answer tell you about your bid price? What do you know about the number of cartons you

can sell and still break even? How about your level of costs?

B. Solve problem 18 again with the price of $13 but find the quantity of cartons per year that you

can supply and still break even. Hint:it's less than 150,000.

C. Repeat (b) with a price of $13 and a quantity of 150,000 cartons per year, and find the highest

level of fixed costs you could afford and still break even .hint: it's more than $240,000.

答案：a. This problem is basically the same as Problem 18, except we are given a sales price. The

cash flow at Time 0 for all three parts of this question will be:

Capital spending –$780,000

Change in NWC –75,000

Total cash flow –$855,000

We will use the initial cash flow and the salvage value we already found in that problem.

Using the bottom up approach to calculating the OCF, we get:

Assume price per unit = $13 and units/year = 150,000

Year 1 2 3 4 5

Sales $1,950,000 $1,950,000 $1,950,000 $1,950,000 $1,950,000

Variable costs 1,275,000 1,275,000 1,275,000 1,275,000 1,275,000

Fixed costs 240,000 240,000 240,000 240,000 240,000

Depreciation 156,000 156,000 156,000 156,000 156,000

EBIT

Taxes (35%)

Net Income

Depreciation

Operating CF

Year

Operating CF

Change in NWC

Capital spending

Total CF

279,000

97,650

181,350

156,000

$337,350

1

$337,350

0

0

$337,350

279,000

97,650

181,350

156,000

$337,350

2

$337,350

0

0

$337,350

279,000

97,650

181,350

156,000

$337,350

3

$337,350

0

0

$337,350

279,000

97,650

181,350

156,000

$337,350

4

$337,350

0

0

$337,350

279,000

97,650

181,350

156,000

$337,350

5

$337,350

75,000

32,500

$444,850

CHAPTER 3 B-22

With these cash flows, the NPV of the project is:

NPV = – $780,000 – 75,000 + $337,350(PVIFA

16%,5

) + [($75,000 + 32,500) / 1.16

5

]

NPV = $300,765.11

If the actual price is above the bid price that results in a zero NPV, the project will have a

positive NPV. As for the cartons sold, if the number of cartons sold increases, the NPV will

increase, and if the costs increase, the NPV will decrease.

b. To find the minimum number of cartons sold to still breakeven, we need to use the tax shield

approach to calculating OCF, and solve the problem similar to finding a bid price. Using the initial

cash flow and salvage value we already calculated, the equation for a zero NPV of the project is:

NPV = 0 = – $780,000 – 75,000 + OCF(PVIFA

16%,5

) + [($75,000 + 32,500) / 1.16

5

]

So, the necessary OCF for a zero NPV is:

OCF = $803,817.85 / PVIFA

16%,5

= $245,493.51

Now we can use the tax shield approach to solve for the minimum quantity as follows:

OCF = $245,493.51 = [(P – v)Q – FC ](1 – t

c

) + t

c

D

$245,493.51 = [($13.00 – 8.50)Q – 240,000 ](1 – 0.35) + 0.35($780,000/5)

Q = 118,596

As a check, we can calculate the NPV of the project with this quantity. The calculations are:

Year

Sales

Variable costs

Fixed costs

Depreciation

EBIT

Taxes (35%)

Net Income

Depreciation

Operating CF

Year

Operating CF

Change in NWC

Capital spending

Total CF

NPV = – $780,000 – 75,000 + $245,493(PVIFA

16%,5

) + [($75,000 + 32,500) / 1.16

5

]  $0

1

$1,541,748

1,008,066

240,000

156,000

137,682

48,189

89,493

156,000

$245,493

1

$245,493

0

0

$245,493

2

$1,541,748

1,008,066

240,000

156,000

137,682

48,189

89,493

156,000

$245,493

2

$245,493

0

0

$245,493

3

$1,541,748

1,008,066

240,000

156,000

137,682

48,189

89,493

156,000

$245,493

3

$245,493

0

0

$245,493

4

$1,541,748

1,008,066

240,000

156,000

137,682

48,189

89,493

156,000

$245,493

4

$245,493

0

0

$245,493

5

$1,541,748

1,008,066

240,000

156,000

137,682

48,189

89,493

156,000

$245,493

5

$245,493

75,000

32,500

$352,993

CHAPTER 3 B-23

Note, the NPV is not exactly equal to zero because we had to round the number of cartons

sold, you cannot sell one-half of a carton.

c. To find the highest level of fixed costs and still breakeven, we need to use the tax shield

approach to calculating OCF, and solve the problem similar to finding a bid price. Using the

initial cash flow and salvage value we already calculated, the equation for a zero NPV of the

project is:

NPV = 0 = – $780,000 – 75,000 + OCF(PVIFA

16%,5

) + [($75,000 + 32,500) / 1.16

5

]

OCF = $803,817.85 / PVIFA

16%,5

= $245,493.51

Notice this is the same OCF we calculated in part b. Now we can use the tax shield approach to

solve for the maximum level of fixed costs as follows:

OCF = $245,493.51 = [(P–v)Q – FC ](1 – t

C

) + t

C

D

$245,493.51 = [($13.00 – $8.50)(150,000) – FC](1 – 0.35) + 0.35($780,000/5)

FC = $381,317.67

As a check, we can calculate the NPV of the project with this quantity. The calculations are:

Year 1 2 3 4 5

Sales $1,950,000 $1,950,000 $1,950,000 $1,950,000 $1,950,000

Variable costs 1,275,000 1,275,000 1,275,000 1,275,000 1,275,000

Fixed costs 381,318 381,318 381,318 381,318 381,318

Depreciation 156,000 156,000 156,000 156,000 156,000

EBIT

Taxes (35%)

Net Income

Depreciation

Operating CF

Year

Operating CF

Change in NWC

Capital spending

Total CF

NPV = – $780,000 – 75,000 + $245,493(PVIFA

16%,5

) + [($75,000 + 32,500) / 1.16

5

]  $0

28. Calculating a bid price. Your company has been approached to bid on a contract to sell

10,000 voice recognition computer keyboards a year for four years. Due to technological

improvements, beyond that time they will be outdated and no sales will be possible. The

equipment necessary for the production will cost $2.4 million and will be depreciated on a

137,682

48,189

89,494

156,000

$245,494

1

$245,494

0

0

$245,494

137,682

48,189

89,494

156,000

$245,494

2

$245,494

0

0

$245,494

137,682

48,189

89,494

156,000

$245,494

3

$245,494

0

0

$245,494

137,682

48,189

89,494

156,000

$245,494

4

$245,494

0

0

$245,494

137,682

48,189

89,494

156,000

$245,494

5

$245,494

75,000

32,500

$352,994

CHAPTER 3 B-24

straight-line basis to a zero salvage value. Production will require an investment in the net

working capital of $75,000 to be returned at the end of the project and the equipment can be sold

for $200,000 at the end of production. Fixed costs are $500,000 per year ,and variable costs are

$165 per unit. In addition to the contract, you feel your company can sell 3,000, 6,000, 8,000, and

5,000 additional units to companies in other countries over the next four years, respectively, at a

price of $275. This price is fixed . The tax rate is 40%, and the required return is 13%.

Additionally, the president of the company will only undertake the project if it has an NPV of

$100,000. What bid price should you set for the contract?

答案： We need to find the bid price for a project, but the project has extra cash flows. Since we

don’t already produce the keyboard, the sales of the keyboard outside the contract are

relevant cash flows. Since we know the extra sales number and price, we can calculate the

cash flows generated by these sales. The cash flow generated from the sale of the keyboard

outside the contract is:

1 2 3 4

Sales $825,000 $1,650,000 $2,200,000 $1,375,000

Variable costs 495,000 990,000 1,320,000 825,000

EBT

Tax

Net income (and OCF)

$330,000

132,000

$198,000

$660,000

264,000

$396,000

$880,000

352,000

$528,000

$550,000

220,000

$330,000

So, the addition to NPV of these market sales is:

NPV of market sales = $198,000/1.13 + $396,000/1.13

2

+ $528,000/1.13

3

+ $330,000/1.13

4

NPV of market sales = $1,053,672.99

You may have noticed that we did not include the initial cash outlay, depreciation or fixed costs in

the calculation of cash flows from the market sales. The reason is that it is irrelevant whether

or not we include these here. Remember, we are not only trying to determine the bid price,

but we are also determining whether or not the project is feasible. In other words, we are

trying to calculate the NPV of the project, not just the NPV of the bid price. We will include

these cash flows in the bid price calculation. The reason we stated earlier that whether we

included these costs in this initial calculation was irrelevant is that you will come up with the

same bid price if you include these costs in this calculation, or if you include them in the bid

price calculation.

Next, we need to calculate the aftertax salvage value, which is:

Aftertax salvage value = $200,000(1 – .40) = $120,000

Instead of solving for a zero NPV as is usual in setting a bid price, the company president requires

an NPV of $100,000, so we will solve for a NPV of that amount. The NPV equation for this

project is (remember to include the NWC cash flow at the beginning of the project, and the

NWC recovery at the end):

NPV = $100,000 = –$2,400,000 – 75,000 + 1,053,672.99 + OCF (PVIFA

13%,4

) + [($120,000

+ 75,000) / 1.13

4

]

CHAPTER 3 B-25

Solving for the OCF, we get:

OCF = $1,401,729.86 / PVIFA

13%,4

= $471,253.44

Now we can solve for the bid price as follows:

OCF = $471,253.44 = [(P – v)Q – FC ](1 – t

C

) + t

C

D

$471,253.44 = [(P – $165)(10,000) – $500,000](1 – 0.40) + 0.40($2,400,000/4)

P = $253.54

Chapter11

19. Project analysis. You are considering anew product launch . The project will cost $720,000,

have a four-year life, and have no salvage value;depreciation is straight-line to zero . Sales are

projected at 190 units per year; price per unit will be $21,000, variable cost per unit will be

$15,000, and fixed costs will be $225,000 per year. The required return on the project is 15%, and

the relevant tax rate is 35%.

A. based on your experience, you think the unit sales, variable cost, and fixed cost projections

given here are probably accurate to +

/- 10%. What are the upper and lower bounds for these

projections? What is the base-case NPV? What are the best-case and worst-case scenarios?

B. Evaluating the sensitivity of your base-case NPV to changes in fixed costs.

C. What is the cash break-even level of output for this project (ignoring taxes)？

D. What is the accounting break-even level of output for this project? What is the degree of

operating leverage at the accounting break-even point? How do you interpret this number?

答案：a. The base-case, best-case, and worst-case values are shown below. Remember that in the

best-case, sales and price increase, while costs decrease. In the worst-case, sales and

price decrease, and costs increase.

Scenario Unit sales Variable cost Fixed costs

Base 190 $15,000 $225,000

Best 209 $13,500 $202,500

Worst 171 $16,500 $247,500

Using the tax shield approach, the OCF and NPV for the base case estimate is:

OCF

base

= [($21,000 – 15,000)(190) – $225,000](0.65) + 0.35($720,000/4)

OCF

base

= $657,750

NPV

base

= –$720,000 + $657,750(PVIFA

15%,4

)

NPV

base

= $1,157,862.02

The OCF and NPV for the worst case estimate are:

OCF

worst

= [($21,000 – 16,500)(171) – $247,500](0.65) + 0.35($720,000/4)

OCF

worst

= $402,300

NPV

worst

= –$720,000 + $402,300(PVIFA

15%,4

)

NPV

worst

= +$428,557.80

CHAPTER 3 B-26

b.

And the OCF and NPV for the best case estimate are:

OCF

best

= [($21,000 – 13,500)(209) – $202,500](0.65) + 0.35($720,000/4)

OCF

best

= $950,250

NPV

best

= –$720,000 + $950,250(PVIFA

15%,4

)

NPV

best

= $1,992,943.19

To calculate the sensitivity of the NPV to changes in fixed costs we choose another

level of fixed costs. We will use fixed costs of $230,000. The OCF using this level of

fixed costs and the other base case values with the tax shield approach, we get:

OCF = [($21,000 – 15,000)(190) – $230,000](0.65) + 0.35($720,000/4)

OCF = $654,500

And the NPV is:

NPV = –$720,000 + $654,500(PVIFA

15%,4

)

NPV = $1,148,583.34

The sensitivity of NPV to changes in fixed costs is:

c.

NPV/FC = ($1,157,862.02 – 1,148,583.34)/($225,000 – 230,000)

NPV/FC = –$1.856

For every dollar FC increase, NPV falls by $1.86.

The cash breakeven is:

Q

C

= FC/(P – v)

Q

C

= $225,000/($21,000 – 15,000)

d.

Q

C

= 38

The accounting breakeven is:

Q

A

= (FC + D)/(P – v)

Q

A

= [$225,000 + ($720,000/4)]/($21,000 – 15,000)

Q

A

= 68

At the accounting breakeven, the DOL is:

DOL = 1 + FC/OCF

DOL = 1 + ($225,000/$180,000) = 2.2500

For each 1% increase in unit sales, OCF will increase by 2.2500%.

20. Project analysis. McGilla Golf has decided to sell a new line of golf clubs. The clubs will sell

for $700 per set and have a variable cost of $320 per set. The company has spent $150,000 for a

marketing study that determined the company will sell 55,000 sets per year for seven years. The

marketing study also determined that the company will lose sales of $13,000 sets of its high-priced

clubs. The high-priced clubs sell at $1,100 and have variable costs of $600. The company will also

increase sales of its cheap clubs by 10,000 sets. The cheap clubs sell for $400 and have variable

costs of $180 per set. The fixed costs each year will be $7,500,000. The company has also spent

CHAPTER 3 B-27

$1,000,000 on research and development for the new clubs. The plant and equipment required will

cost $18,200,000 and will be depreciated in a straight-line basis. The new clubs will also require

an increase in net working capital of $950,000 that will be returned at the end of the project. The

tax rate is 40%, and the cost of capital is 14% . Calculate the payback period, the NPV, and the

IRR.

答案：The marketing study and the research and development are both sunk costs and should be

ignored. We will calculate the sales and variable costs first. Since we will lose sales of the

expensive clubs and gain sales of the cheap clubs, these must be accounted for as erosion.

The total sales for the new project will be:

Sales

New clubs

$700  55,000 = $38,500,000

Exp. clubs

$1,100  (–13,000) = –14,300,000

Cheap clubs

$400  10,000 = 4,000,000

$28,200,000

For the variable costs, we must include the units gained or lost from the existing clubs. Note

that the variable costs of the expensive clubs are an inflow. If we are not producing the sets

anymore, we will save these variable costs, which is an inflow. So:

Var. costs

New clubs

–$320  55,000 = –$17,600,000

Exp. clubs

–$600  (–13,000) =

7,800,000

Cheap clubs

–$180  10,000 = –1,800,000

–$11,600,000

The pro forma income statement will be:

Sales $28,200,000

Variable costs 11,600,000

Costs 7,500,000

Depreciation 2,600,000

EBT 6,500,000

Taxes 2,600,000

Net income $ 3,900,000

Using the bottom up OCF calculation, we get:

OCF = NI + Depreciation = $3,900,000 + 2,600,000

OCF = $6,500,000

So, the payback period is:

Payback period = 2 + $6.15M/$6.5M

Payback period = 2.946 years

The NPV is:

NPV = –$18.2M – .95M + $6.5M(PVIFA

14%,7

) + $0.95M/1.14

7

CHAPTER 3 B-28

NPV = $9,103,636.91

And the IRR is:

IRR = –$18.2M – .95M + $6.5M(PVIFA

IRR%,7

) + $0.95M/IRR

7

IRR = 28.24%

23. Break-even and taxes. This problem concerns the effect of taxes on the various break-even

measures.

A. Show that ,when we consider taxes,the general relationship between operating cash flow ,

OCF ,and sales volume, Q, can be written as :

OCF - T*D

+FC

1-T

P-v

B. Use the expression in part a to find the cash, accounting, and financial break-even points

for the Wettway sailboat example in the chapter. Assume a 38% tax rate.

C. In part b, the accounting break-even should be the same as before. Why？ Verify this

algebraically.

答案：a. The tax shield definition of OCF is:

OCF = [(P – v)Q – FC ](1 – t

C

) + t

C

D

Rearranging and solving for Q, we find:

(OCF – t

C

D)/(1 – t

C

) = (P – v)Q – FC

Q = {FC + [(OCF – t

C

D)/(1 – t

C

)]}/(P – v)

b. The cash breakeven is:

Q

C

= $500,000/($40,000 – 20,000)

Q

C

= 25

And the accounting breakeven is:

Q

A

= {$500,000 + [($700,000 – $700,000(0.38))/0.62]}/($40,000 – 20,000)

Q

A

= 60

The financial breakeven is the point at which the NPV is zero, so:

OCF

F

= $3,500,000/PVIFA

20%,5

OCF

F

= $1,170,328.96

So:

Q

F

= [FC + (OCF – t

C

× D)]/(P – v)

Q

F

= {$500,000 + [$1,170,328.96 – .35($700,000)]}/($40,000 – 20,000)

c.

Q

F

= 97.93  98

At the accounting break-even point, the net income is zero. This using the bottom up

definition of OCF:

OCF = NI + D

We can see that OCF must be equal to depreciation. So, the accounting breakeven is:

Q

A

= {FC + [(D – t

C

D)/(1 – t)]}/(P – v)

CHAPTER 3 B-29

Q

A

= (FC + D)/(P – v)

Q

A

= (FC + OCF)/(P – v)

The tax rate has cancelled out in this case.

25. Scenario analysis. Consider a project to supply Detroit with 40,000 tons of machine

screws annually for automobile production. You will need an initial $1,700,000 investment in

threading equipment to get the project started ;the project will last for five years. The accounting

department estimates that annual fixed costs will be $450,000 and that variable costs should be

$210 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over

the five-year project life. It also estimate a salvage value of $500,000 after dismantling costs. The

marketing department estimates that the automakers will let the contract at a selling price of $230

per ton. The engineering department estimates you will need an initial net working capital

investment of $450,000. You require a 13% return an d face a marginal tax rate of 38% on this

project.

A. What is the estimated OCF foe the project? The NPV? Should you pursue this project?

B. Suppose you believe that the accounting department's initial cost and salvage value projections

are accurate only to within +/- 15%;the marketing department's price estimate is accurate only to

within +/- 10%; and the engineering department's net working capital estimate is accurate only to

within +/- 5%. What is your worst-case scenario for this project? Your best-case scenario? Do you

still want to pursue the project ?

答案：

a. Using the tax shield approach, the OCF is:

OCF = [($230 – 210)(40,000) – $450,000](0.62) + 0.38($1,700,000/5)

OCF = $346,200

And the NPV is:

NPV = –$1.7M – 450K + $346,200(PVIFA

13%,5

) + [$450K + $500K(1 – .38)]/1.13

5

NPV = –$519,836.99

b. In the worst-case, the OCF is:

OCF

worst

= {[($230)(0.9) – 210](40,000) – $450,000}(0.62) + 0.38($1,955,000/5)

OCF

worst

= –$204,820

And the worst-case NPV is:

NPV

worst

= –$1,955,000 – $450,000(1.05) + –$204,820(PVIFA

13%,5

) +

[$450,000(1.05) + $500,000(0.85)(1 – .38)]/1.13

5

NPV

worst

= –$2,748,427.99

The best-case OCF is:

OCF

best

= {[$230(1.1) – 210](40,000) – $450,000}(0.62) + 0.38($1,445,000/5)

OCF

best

= $897,220

And the best-case NPV is:

NPV

best

= – $1,445,000 – $450,000(0.95) + $897,220(PVIFA

13%,5

) +

[$450,000(0.95) + $500,000(1.15)(1 – .38)]/1.13

5

NPV

best

= $1,708,754.02

CHAPTER 3 B-30

Chapter14

8. Option pricing. Suppose a certain stock currently sells for $30 per share. If a put option and a

call option are available with $30 exercise price ,which do you think will sell for more, the put or

the call?

答案：The call option will sell for more since it provides an unlimited profit opportunity, while the

potential profit from the put is limited (the stock price cannot fall below zero).

5. Calculating option value. The price of Tara,Inc., stock will be either $60 or $80 at the end of

the year. Call options are available with one year to expiration. T-bills currently yield 5%.

A. Suppose the current price of Tara stock is $70. What is the value of the call option if the

exercise price is $45 per share?

B. Suppose the exercise price is $70 in part a. What is the value of the call option now?

答案：a. The value of the call is the stock price minus the present value of the exercise price, so:

C

0

= $70 – $45/1.05

C

0

= $27.14

b. Using the equation presented in the text to prevent arbitrage, we find the value of the

call is:

$70 = 2C

0

+ $60/1.05

C

0

= $6.43

7. Equity as an option. Rackin Pinion Corporation's assets are currently worth $1,050. In one

year, they will be worth either $1,000 or $1,400. The risk-free interest rate is 5%. Suppose Rackin

Pinion has an outstanding debt issue with a face value of $1,000.

A. What is the value of the equity?

B. What is the value of the debt? The interest rate on the debt?

C. Would the value of the equity go up or down if the risk-free were 20%? Why? What does your

answer illustrate?

答案：a. The equity can be valued as a call option on the firm with an exercise price equal to the

value of the debt, so:

E

0

= $1,050 – [$1,000/1.05]

E

0

= $97.62

b. The current value of debt is the value of the firm’s assets minus the value of the equity, so:

D

0

= $1,050 – 97.62

D

0

= $952.38

We can use the face value of the debt and the current market value of the debt to find

the interest rate, so:

Interest rate = [$1,000/$952.38] – 1

Interest rate = .05 or 5%

c. The value of the equity will increase. The debt then requires a higher return; therefore the

present value of the debt is less while the value of the firm does not change.

9. Calculating conversion value. A $1,000 par convertible debenture has a conversion price for

common stock of $80 per share. With the common stock selling at $90, what is the conversion

value of the bond?

答案：The conversion ratio is the par value divided by the conversion price, so:

CHAPTER 3 B-31

Conversion ratio = $1,000/$80

Conversion ratio = 12.50

The conversion value is the conversion ratio times the stock price, so:

Conversion value = 12.5($90)

Conversion value = $1,125.00

13. Option to wait. Your company is deciding whether to invest in a new machine. The new

machine will increase cash flow by $280,000 per year. You believe the technology used in the

machine has a 10-year life; in other words, no matter when you purchase the machine , it will be

obsolete 10 years from today. The machine is currently priced at $1,500,000. The cost of the

machine will decline by $125,000 per year until it reaches $1,000,000, where it will remain. If you

required return is 12%, should you purchase the machine? If so, when should you purchase it ?

答案：If we purchase the machine today, the NPV is the cost plus the present value of the increased

cash flows, so:

NPV

0

= –$1,500,000 + $280,000(PVIFA

12%,10

)

NPV

0

= $82,062.45

We should not purchase the machine today. We would want to purchase the machine when the

NPV is the highest. So, we need to calculate the NPV each year. The NPV each year will be

the cost plus the present value of the increased cash savings. We must be careful however. In

order to make the correct decision, the NPV for each year must be taken to a common date.

We will discount all of the NPVs to today. Doing so, we get:

Year 1: NPV

1

= [–$1,375,000 + $280,000(PVIFA

12%,9

)] / 1.12

NPV

1

= $104,383.88

Year 2: NPV

2

= [–$1,250,000 + $280,000(PVIFA

12%,8

)] / 1.12

2

NPV

2

= $112,355.82

Year 3: NPV

3

= [–$1,125,000 + $280,000(PVIFA

12%,7

)] / 1.12

3

NPV

3

= $108,796.91

Year 4: NPV

4

= [–$1,000,000 + $280,000(PVIFA

12%,6

)] / 1.12

4

NPV

4

= $96,086.55

Year 5: NPV

5

= [–$1,000,000 + $280,000(PVIFA

12%,5

)] / 1.12

5

NPV

5

= $5,298.26

Year 6: NPV

6

= [–$1,000,000 + $280,000(PVIFA

12%,4

)] / 1.12

6

NPV

6

= –$75,762.72

The company should purchase the machine two years from now when the NPV is the highest.

17. Intuition and option value. Suppose a share of stock sells for $65. The risk-free rate is 5%,

and the stock price in one year will be either $75 or $85.

A. What is the value of a call option with a $75 exercise price?

B. What is wrong here? What would you do?

答案:a. The value of the call is the maximum of the stock price minus the present value of the

exercise price, or zero, so:

C

0

= Max[$65 – ($75/1.05),0]

C

0

= $0

The option isn’t worth anything.

CHAPTER 3 B-32

b.

Chapter15

15. Finding the WACC. Given the following information for Huntington Power Co., find the

WACC. Assume the company's tax rate is 35%.

Debt: 4,000 7% coupon bonds outstanding, $1,000 par value, 20 years to maturity, selling for

103% of par; the bonds make semiannual payments.

Common stock: 90,000 shares outstanding ,selling for $57 per share ; the beta is 1.10.

Preferred stock: 13,000 shares of 6% preferred stock outstanding, currently selling for $104 per

share.

Market: 8% market risk premium and 6% risk-free rate.

答案：We will begin by finding the market value of each type of financing. We find:

MV

D

= 4,000($1,000)(1.03) = $4.12M

MV

E

= 90,000($57) = $5.13M

MV

P

= 13,000($104) = $1.352M

And the total market value of the firm is: V = $4.12M + 5.13M + 1.352M = $10.602M

Now, we can find the cost of equity using the CAPM. The cost of equity is:

R

E

= .06 + 1.10(.08) = .1480 or 14.80%

The cost of debt is the YTM of the bonds, so: P

0

= $1,030 = $35(PVIFA

R%,40

) +

$1,000(PVIF

R%,40

)

R = 3.36%

YTM = 3.36% × 2 = 6.72%

And the aftertax cost of debt is: R

D

= (1 – .35)(.0672) = .0437 or 4.37%

The cost of preferred stock is: R

P

= $6/$104 = .0577 or 5.77%

Now we have all of the components to calculate the WACC. The WACC is:

WACC = .0437(4.12/10.602) + .1480(5.13/10.602) + .0577(1.352/10.602) = 9.60%

Notice that we didn’t include the (1 – t

C

) term in the WACC equation. We simply used the

aftertax cost of debt in the equation, so the term is not needed here.

and WACC. An all-equity firm is considering the following projects:

Project

W

X

Y

Z

Beta

0.60

0.90

1.20

1.70

Expected return

11%

13

14

16

The stock price is too low for the option to finish in the money. The minimum return on the

stock required to get the option in the money is:

Minimum stock return = ($75 – 65)/$65

Minimum stock return = .1538 or 15.38%

which is much higher than the risk-free rate of interest.

The T-bill rate is 5%, and the expected return on the market is 12%.

A. Which project have a higher expected return than the firm's 12% cost of capital?

B. Which project should be accepted?

CHAPTER 3 B-33

C. Which projects would be incorrectly accepted or rejected if the firm's overall cost of capital

were used as a hurdle rate?

答案：a. Projects X, Y and Z.

b. Using the CAPM to consider the projects, we need to calculate the expected return of

the project given its level of risk. This expected return should then be compared to the

expected return of the project. If the return calculated using the CAPM is higher than

the project expected return, we should accept the project, if not, we reject the project.

After considering risk via the CAPM:

E[W] = .05 + .60(.12 – .05) = .0920 < .11, so accept W

E[X] = .05 + .90(.12 – .05) = .1130 < .13, so accept X

E[Y] = .05 + 1.20(.12 – .05) = .1340 < .14, so accept Y

E[Z] = .05 + 1.70(.12 – .05) = .1690 > .16, so reject Z

Project W would be incorrectly rejected; Project Z would be incorrectly accepted.

20. WACC and NPV. Och,Inc., is considering a project that will result in initial aftertax cash

savings of $3.5 million at the end of the first year, and these savings will grow at a rate of 5%

per year indefinitely. The firm has a target debt-equity ratio of 0.65, a cost of equity of 15%, and

an aftertax cost of debt of 5.5%. The cost-saving proposal is somewhat riskier than the usual

project the firm undertakes; management uses the subjective approach and applies an adjustment

factor of +2% to the cost of capital for such risky project. Under what circumstances should Och

take on the project?

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

WACC = (.65/1.65)(.055) + (1/1.65)(.15) = .1126 or 11.26%

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 = 11.26% + 2.00% = 13.26%

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 = $3,500,000/(.1326 – .05) = $42,385,321

The project should only be undertaken if its cost is less than $42,385,321 since costs less

than this amount will result in a positive NPV.

Chapter17

14. M&M and taxes. Bruce & Co. expects its EBIT to be $95,000 every year forever. The firm

can borrow at 11%. Bruce currentlt has no debt, and its cost of equity is 22%. If the tax rate is

35%, what is the value of the firm? What will the value be if Bruce borrows $60,000 and uses the

proceeds to repurchase shares?

答案：a. The value of the unlevered firm is:

V = EBIT(1 – t

C

)/R

U

V = $95,000(1 – .35)/.22

V = $280,681.82

b. The value of the levered firm is:

CHAPTER 3 B-34

V = V

U

+ t

C

D

V = $280,681.82 + .35($60,000)

V = $301,681.82

15. M&M and taxes. In problem 14, what is the cost of equity after recapitalization? What is

WACC? What are the implications for the firm's capital structure decision?

答案：We can find the cost of equity using M&M Proposition II with taxes. Doing so, we find:

R

E

= R

U

+ (R

U

– R

D

)(D/E)(1 – t)

R

E

= .22 + (.22 – .11)($60,000/$241,681.82)(1 – .35)

R

E

= .2378 or 23.78%

Using this cost of equity, the WACC for the firm after recapitalization is:

WACC = (E/V)R

E

+ (D/V)R

D

(1 – t

C

)

WACC = .2378($241,681.82/$301,681.82) + .11(1 – .35)($60,000/$301,681.82)

WACC = .2047 or 20.47%

When there are corporate taxes, the overall cost of capital for the firm declines the more

highly leveraged is the firm’s capital structure. This is M&M Proposition I with taxes.

16. M &M. Tool Manufacturing has an expected EBIT of $35,000 in perpetuity and a tax rate of

35%. The firm has $70,000 in outstanding debt at an interest rate of 9%, and its unlevered

cost of capital is 14%. What is the value of the firm according to M&M Proposition I with

taxes? Should Tool change its debt-equity ratio if the goal is to maximize the value of the

value of the firm? Explain.

答案：To find the value of the levered firm we first need to find the value of an unlevered firm. So,

the value of the unlevered firm is:

V

U

= EBIT(1 – t

C

)/R

U

V

U

= ($35,000)(1 – .35)/.14

V

U

= $162,500

Now we can find the value of the levered firm as:

V

L

= V

U

+ t

C

D

V

L

= $162,500 + .35($70,000)

V

L

= $187,000

Applying M&M Proposition I with taxes, the firm has increased its value by issuing debt. As

long as M&M Proposition I holds, that is, there are no bankruptcy costs and so forth, then the

company should continue to increase its debt/equity ratio to maximize the value of the firm.

17. Firm value. Old school corporation expects an EBIT of $9,000 every year forever. Old school

currently has no debt, and its cost of equity is 17%. The firm can borrow at 10%. If the

corporation tax rate is 35%, what is the value of the firm? What will the value be if Old

school converts to 50 % debt? To 100% debt?

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

V = EBIT(1 – t

C

)/R

U

V = $9,000(1 – .35)/.17

V = $34,411.76

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

CHAPTER 3 B-35

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

V

= V

U

+ t

C

D

V = $34,411.76 + .35($34,411.76/2)

V = $40,433.82

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

V

= V

U

+ t

C

D

V = $34,411.76 + .35($34,411.76)

V = $46,455.88

Chapter18

10. Residual dividend policy. Soprano, Inc., a litter recycling company, uses a residual

dividend policy. A debt-equity ratio of 0.80 is considered optimal. Earnings for the period

just ended were $1,200, and a dividend of $480 was declared. How much in new debt was

borrowed? What were total capital outlays?

答案：The equity portion of capital outlays is the retained earnings. Subtracting dividends from net

income, we get:

Equity portion of capital outlays = $1,200 – 480 = $720

Since the debt-equity ratio is .80, we can find the new borrowings for the company by

multiplying the equity investment by the debt-equity ratio, so:

New borrowings = .80($720) = $576

And the total capital outlay will be the sum of the new equity and the new debt, which is:

Total capital outlays = $720 + 576 =$1,296.

Chapter19

9. Calculating payment. The Thunder Dan Corporation 's purchase from suppliers in a quarter

are equal to 75 % of the next quarter's forecasted sales. The payables period is 60 days. Wages,

taxes, and other expenses are 20% of sales, and interest and dividends are $60 per quarter. No

capital expenditures are planned.

Projected quarterly sales are:

Sales

Q1

$750

Q2

$920

Q3

$890

Q5

$790

Sales foe the first quarter of the following year are projected at $970. Calculate Thunder's cash

outlays by completing the following:

Payment of accounts

Wages, taxes,

expenses

Total

and

Q1

other

Q2

Q3

Q4

Long-term financing expenses

答案：Since the payables period is 60 days, the payables in each period will be:

Payables each period = 2/3 of last quarter’s orders + 1/3 of this quarter’s orders

Payables each period = 2/3(.75) times current sales + 1/3(.75) next period sales

CHAPTER 3 B-36

Payment of accounts

Wages, taxes, other expenses

Long-term financing expenses

Total

Q1

$605.00

150.00

60.00

$815.00

Q2

$682.50

184.00

60.00

$926.50

Q3

$642.50

178.00

60.00

$880.50

Q4

$637.50

158.00

60.00

$855.50

10. Calculating cash collections. The following is the sales budget for Duck-n-Run, Inc., for fist

quarter of 2004:

Sales budget

January

$150,000

February

$173,000

March

$194,000

Credit sales are collected as follow:

65% in the month of the sale

20% in the month after the sale

15% in the second month after the sale

The accounts receivable balance at the end of the previous quarter was $57,000 ($41,000 of which

was uncollected December sales ).

A. Computer the sales for November.

B. Computer the sales for December.

C. Computer the cash collections from sales for each month from January through March.

答案：a. The November sales must have been the total uncollected sales minus the uncollected

sales from December, divided by the collection rate two months after the sale, so:

November sales = ($57,000 – 41,000)/0.15

November sales = $106,666.67

b. The December sales are the uncollected sales from December divided by the collection

rate of the previous months’ sales, so:

December sales = $41,000/0.35

December sales = $117,142.86

c. The collections each month for this company are:

Collections = .15(Sales from 2 months ago) + .20(Last months sales) + .65 (Current

sales)

January collections = .15($106,666.67) + .20($117,142.86) + .65($150,000)

January collections = $136,928.57

February collections = .15($117,142.86) + .20($150,000) + .65($173,000)

February collections = $160,021.43

March collections = .15($150,000) + .20($173,000) + .65($194,000)

March collections = $183,200.00