assignment12 fundamentals of corporate finance, 4th edition brealey

is considering purchasing two machines, A and B, which are expected to generate $36,000 and $40,000 respectively in cash flows per year for 5 years.. d Machine A comes with an optional m

Winter 2007 Question 1 (18 marks)

Blooper Technology Inc is considering purchasing two machines, A and B, which are expected to generate $36,000 and $40,000 respectively in cash flows per year for 5 years Although Machine B is more expensive than Machine A, its payback period (3.25 years) is shorter compared to that of Machine A (3.5 years) Blooper’s opportunity cost of capital is 10%

(a) Which machine would you take if the machines were mutually exclusive and if shareholder maximization were your basis for decision? Explain (5 Marks)

Answer

COST OF MACHINE A=3.50×36,000=$126,000

COST OF MACHINE B=3.25×40,000=$130,000

NPVA=-126,000+36,000(PVIFA5,10%)= $10,468.32

NPVB=-130,000+40,000(PVIFA5,10%)= $21,631.47

MACHINE B SINCE IT HAS A GREATER NPV

(b) If the company is willing to accept any project with a discounted payback period less than 4.25 years, would you recommend buying these

machines? Explain (4 Marks)

Answer

(CASH FLOWS IN THOUSANDS OF DOLLARS)

$32.73 $29.75 $27.05 $24.59 $22.35

DISCOUNTED PAYBACK A=4.53 YEARS REJECT BECAUSE DPB>4.25

$36.36 $33.06 $30.05 $27.32 $24.84

DISCOUNTED PAYBACK B=4.13 YEARS ACCEPT BECAUSE DPB<4.25

(c) Calculate the internal rate of return on each machine Would you buy

these machines based on IRR? Explain (3 Marks)

Answer

IRR OF MACHINE A:13.20% (PV=-126,PMT=36,FV=0,N=5,I=?)

IRR OF MACHINE B:16.32% (PV=-130,PMT=40,FV=0,N=5,I=?)

YES.BOTH IRRS ARE GREATER THAN THE COST OF CAPITAL

(d) Machine A comes with an optional module which extends its useful life 2 more years (with the same annual cash flows of$36,000)at an additional initial cost of $20,000 Which machine should you take after considering this option? ( 6 Marks)

Answer

THE PV OF THE CF STREAM FROM MACHINE A =-146+36 X (PVIFA7,10%)

=-146+36×4.8684 =$29,263.08

EQUIVALENT ANNUAL CF FROM A= $29,263.08/4.8684=$6,010.82

THE PV OF THE CF STREAM FROM MACHINE B=-130+40×(PVIFA5,10%)

=-130+40×3.7908

=$21,631.47

EQUIVALENT ANNUAL CF FROM B= $21,631.47/3.7908=$5,707.31

CHOSE MACHINE A

Question 2 (10 marks)

Calculate the NPV for the following capital budgeting proposal: $110,000 initial cost, to be depreciated straight-line over five years to an expected salvage value

of $5,000, 35 percent tax rate, $35,000 additional annual revenues, $5,000 additional annual expense, $7,000 additional investment in working capital today

to be recovered in year 5 Project has a 9 percent cost of capital Assume that the CCA is same as depreciation

Answer

(Cash flows are in dollars)

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Cost

(110,000) Change in

Working Capital

Revenues

35,000 35,000 35,000

35,000 35,000 less Expenses

5,000 5,000 5,000

5,000 5,000 less

Depreciation 21,000 21,000 21,000

21,000 21,000

= Net Inc

9,000 9,000 9,000

9,000 16,000 less Taxes

3,150 5,600 = NI After Tax

5,850 5,850 5,850

5,850 10,400 Salvage Value

5,000

(117,000) 26,850 26,850 26,850

26,850 36,400 NPV of Project = PV of Cash Flows - Initial Investment

NPV = $26,850 + - $117,000 = -$6,356.02

Given that the NPV is negative, you reject the project

Alternatively,

(Cash flows are in dollars)

Cost

(110,000) Change in

Working Capital

Revenues

35,000 35,000 35,000

35,000 35,000 less Expenses

5,000 5,000 5,000

5,000 5,000 less

Depreciation 21,000 21,000 21,000

21,000 21,000

= Net Inc

9,000 9,000 9,000

9,000 9,000

1 09

1 09(1.09)4









 $36,400(1.09)5

less Taxes

3,150 3,150 = NI After Tax

5,850 5,850 5,850

5,850 5,850 Salvage Value

5,000

(117,000) 26,850 26,850 26,850

26,850 38,850

NPV of Project = PV of Cash Flows - Initial Investment

NPV = $26,850 + - $117,000 = -$4,763.68

Given that the NPV is negative, you reject the project

Both answers will be considered as valid

Question 3 (14 marks)

The Atkinson College Entrepreneurship Team (ACET) is consulting to New Venture Skis Inc (NVS) who has designed a new top of the line ski The skis are expected to retail at $600 with a profit margin (PM) of 60%

The first round of consulting to NVS, concluded earlier in the year, had been billed to NVS for $150,000 The research indicated that NVS would sell

50,000 sets of the new skis per year for 7 years which will reduce 12,000 sets

of projected sales per year from the current high end line of skis These high end skis sell for $1,000 with a variable cost of $550 However sales of the firm’s least expensive $300 skis will increase annually by 10,000 sets at a 33.3% PM

Fixed costs are $7 million annually One million dollars has been spent on research and development of the new $600 skis New plant and equipment will cost $15,400,000 and has a 30% CCA rate and an expected salvage of

$2 million Net working capital will increase by $900,000 annually that will be returned at the end of the project NVS has a 40% tax rate and a 14% cost of capital The half-year rule applies Compute the following for NVS:

(a) Payback period (3 marks)

Answer

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

1 09

1 09(1.09)4









 $38,850(1.09)5

Sales

New skis $600 × 50,000 = $30,000,000

Expensive

skis $1,000 × (– 12,000) = –$12,000,000

Cheap skis $300 × 10,000 = $3,000,000

Total $21,000,000

Var costs

New skis $240 × 50,000 = $12,000,000

Expensive

skis $550 × (–12,000) = –$6,600,000

Cheap skis $200 × 10,000 = $2,000,000

Total $7,400,000

For the next 4 years:

Year 1 Year 2 Year 3 Year 4 Sales $21,000,000 $21,000,000 $21,000,000 $21,000,000

Variable costs 7,400,000 7,400,000 7,400,000 7,400,000

Fixed costs 7,000,000 7,000,000 7,000,000 7,000,000

CCA 2,310,000 3,927,000 2,748,900 1,924,230

EBIT 4,290,000 2,673,000 3,851,100 4,675,770

Taxes 1,716,000 1,069,200 1,540,440 1,805,462

Net income $ 2,574,000 $1,603,800 $2,310,660 2,805,462

The half-year rule has been incorporated into the calculation of the annual

CCA To accurately calculate the payback period, we need to estimate the operating cash flows in the first four years These can be determined

from the following relationship (for this part depreciation is assumed to be the same as the CCA) :

OCF1 = NI + D = $(2,574,000 + 2,310,000) = $4,884,000

OCF2 = NI + D = $(1,603,800 + 3,927,000) = $5,530,800

OCF3 = NI + D = $(2,310,660 + 2,748,900) = $5,059,560

OCF4 = NI + D = $(2,805,462 + 1,924,230) = $4,729,692

The initial cost is made up of the cost of the plant and equipment plus the increase in net working capital in Year 0:

= $15.4M + 0.9M = $16.3M

The sum of the OCFs in the first 3 years is: $ $15,474,360

So the payback period = 3 years + $(16,300,000 – 15,474,360) / $4,729,692

= 3.175 years

(b) NPV (6 marks)

Answer

To find the NPV and IRR we need the after-tax net revenue each year as

well as the present value of the CCA tax shield and the initial and ending cash flows

Initial cash flow = -$(15,400,000 + 900,000) = -$16,300,000

After-tax net revenue in Years 1-7 = (S – C)(1 – Tc)

= $(21,000,000 – 14,400,000)(1 – 0.4)

= $3,960,000

Ending cash flows (Year 7) = recovery of NWC + salvage value =

$900,000 + 2,000,000 = $2,900,000

PV of CCATS = 15,400,000(0.3)(0.4) x (1 + 0.5(0.14))

0.14 +0.3 1 +0.14

-2,000,000(0.3)(0.4) x 1 0.14 + 0.3 (1.14)7

= $3,724,121

NPV = –$16.3M + $3.96M (PVIFA14%,7) + $3,724,121 + $2.9M/1.147

= $5,307,458

Alternatively, the after-tax net revenue in Years 1-7 = $3,960,000 –

$900,000 (change in NWC annually) = $3,060,000

NPV = –$16.3M + $3.06M (PVIFA14%,7) + $3,724,121 + $2.9M/1.147

= $1,705,282

Both NPV figures are acceptable for this question

(c) IRR (5 marks)

Answer

To simplify the IRR calculation, it is assumed that CCA tax shield cash flows are as risky as the cash flows for the company’s overall operations Accordingly, the appropriate discount rate for the CCA tax shield is the company’s cost of capital The PV of CCATS is thus the same as for the NPV calculation

NPV = 0 = –$16.3M + $3.96M (PVIFAIRR%,7) + $3,724,121 + $2.9M/(1 + IRR)7 ⇒ IRR ≅ 26.6%

Alternatively,

NPV = 0 = –$16.3M + $3.06M (PVIFAIRR%,7) + $3,724,121 + $2.9M/(1 + IRR)7 ⇒ IRR ≅ 18%

Again both values of IRR are considered correct

Question 4 (17 marks)

Another consulting assignment on which the ACET is working is with Keep You Warm Corp (KYC), who has asked ACET for an evaluation of a six year

$924,000 project to sell hi-tech ski glove warmers There is a zero salvage value

on the project assets which use straight-line depreciation (to zero) Assume that the CCA is the same as depreciation The new hi-tech glove warmers will sell for

$34 with a variable cost of $19 Sales are expected to be 130,000 pairs of

gloves per year Fixed costs are $800,000 per year KYC has a 35% tax rate and a 15% cost of capital Consider this as the base case scenario

(a) Calculate the accounting breakeven and the degree of operating leverage

at that point (4 marks)

Answer

Depreciation = $924,000/6 = $154,000 per year

The profit margin = $(34-19)/$34 = $0.4412

Accounting break even sales = ($800,000 + $154,000)/($0.4412) = $2,162,285

The following two answers are both acceptable for the DOL:

1) at the accounting break even sales level, the net income is 0, so the operating cash flow (OCF) = 0 + depreciation (D) = $154,000

So DOL = 1 + FC/OCF = 1 + FC/D

= 1 + [$800,000+$154,000]/$154,000 = 7.195 Alternatively, 2)

DOL = 1 + FC/profits = ∞ since profits are zero

(b) What is the sensitivity of Operating Cash Flows to change in the variable

cost figure? What does your answer suggest about a $1 reduction in the variable costs? (5 marks)

Answer

VCnew = $18 (i.e $1 reduction)

OCFnew = [($34 – $18)(130,000) – $800,000](0.65) + 0.35($154,000) =

$885,900

OCFbase = [($34 – $19)(130,000) – $800,000](0.65) + 0.35($154,000) =

$801,400

∆OCF/∆VC = ($885,900 – $801,400) / ($18 – 19) = –$84,500

So if variable costs fell by $1, then the OCF would rise by $84,500

(c) Calculate the NPV for the base case (most likely scenario) and do a

sensitivity analysis by identifying the best case and worst case scenarios

by changes to the sales numbers Explain why you selected these

numbers and what the impacts may be on your decision as to whether or not to move forward with the project (8 marks)

Answer

NPVbase = –$924,000 + $801,400(PVIFA15%,6) = $2,108,884.43

Answers to the sensitivity analysis will vary

For example if sales rise by 5,000 units to 135,000 units:

OCFnew = [$(34 – 19)(135,000) – $800,000](0.65) + 0.35($154,000) =

$850,150

NPVnew = –$924,000 + $850,150(PVIFA15%,6) = $2,293,377.96

∆NPV/∆S = ($2,293,377.96 – $2,108,884.43)/($34 × (135,000 –

130,000)) = 1.0853%

In contrast, if sales were to drop by 5,000 units, then the OCF would drop to: [$(34 – 19)(125,000) – $800,000](0.65) + 0.35($154,000) =

$752,650

NPVnew = –$924,000 + $752,650(PVIFA15%,6) = $1,924,390.90

∆NPV/∆S = ($1,924,390.90 – $2,108,884.43)/($34 × (125,000 –

130,000)) = 1.0853%

Question 5 (10 marks)

Calculate the expected returns, variances, and standard deviations for stock C, for stock E, and for a portfolio of both stocks C (2/3 weight) and E (1/3 weight)

Answer

Stock C :

6.59%

or , 59 6 43.41 deviation

Standard

0.004341

or squared,

s percentage

41

.

3

7.7%) 4%

( 0.2 7.7%)

(8%

0.5 7.7%) -(15%

0.3

Variance

7.7%

4%) ( 0.2 8%

0.5

% 5 0.3 return

Expected

2 2

2

=

=

=

−

−

× +

−

× +

×

=

=

−

× +

× +

×

=

Stock E :

Scenario Probability

Return on

C

Return on

E

or , 41 5 29.25 deviation

Standard

0.002925

or squared,

s percentage

25

.

29

2.5%) 0%

1 ( 0.2 2.5%) (4%

0.5 2.5%) -(-5%

0.3

Variance

2.5%

% 10 0.2 4%

0.5

%) 5 ( 0.3 return

Expected

2 2

2

=

=

=

−

× +

−

× +

×

=

=

× +

× +

−

×

=

Portfolio :

2.74%

or , 74 2 7.5339 deviation

Standard

0.00075339

or squared,

s percentage

5339

.

7

5.97%) 67%

0 ( 0.2 5.97%) (6.67%

0.5 5.97%)

-(8.33%

0.3

Variance

% 97 5

%) 5 2 ( 3 / 1

%) 7 7 ( 3 / 2 return

Expected

2 2

2

=

=

=

−

× +

−

× +

×

=

=

× +

×

=

Note that the standard deviation of the portfolio is less than that of either stock C

or stock E because of diversification

Question 6 (12 marks)

Use the following to answer the questions below:

A market portfolio contains two stocks with the following returns: Aggressive

Stock A, and Defensive Stock D:

Rate of Return

Scenario Market Aggressive Stock A Defensive Stock D

(a) Find the beta of each stock In what way is stock D defensive? (5 marks)

Answer

Beta is the responsiveness of each stock's return to changes in the market

return

D is considered to be a more defensive stock than A because its return is

less sensitive to the return of the overall market In a recession, D will

usually outperform both stock A and the market portfolio

(b) If each scenario is equally likely, find the expected rate of return on the

market portfolio and on each stock (4 marks)

We take an average of returns in each scenario to obtain the expected return

rm = (32% – 8%)/2 = 12%

rA = (38% – 10%)/2 = 14%

rD = (24% – 6%)/2 = 9%

(c) If the Treasury bill rate is 4 percent, what does the CAPM say about the

fair expected rates of return on the two stocks? (3 marks)

According to the CAPM, the expected returns that investors will demand of each stock, given the stock betas and given the expected return on the market, are:

r = rf + β(rm – rf)

rA = 4% + 1.2(12% – 4%) = 13.6%

rD = 4% + 0.75(12% – 4%) = 10.0%

Question 7 (6 marks)

Calculate the nominal return, real return, and risk premium for the following

common stock investment:

Purchase price $60.00 per share

Dividend $3.50 per year

Sales price $73.00 per share

Treasury bill yield 8.5%

Inflation rate 7.5%

ANSWER

NOMINAL RETURN =(CAPITAL GAIN +DIVIDEND)/INITIAL SHARE PRICE

=(73-60+3.50)/60 =27.5%

REAL RETURN =(1+NOMINAL RATE)/(1+INFLATION RATE) -1

=(1.275/1.075)-1

=18.6%

RISK PREMIUM = NOMINAL RETURN LESS NOMINAL RETURN ON TREASURY BILLS

=27.5–8.5

=19% IN NOMINAL TERMS

Question 8 (13 marks)

A company issued $35,000,000 of 15-year, 7.5%, $1,000 par value debt at par three years ago Assume semi-annual coupon payments The yield to maturity

on comparable debt today is 9% The firm also has 6,000,000 common shares outstanding, which currently trade at $26.00 per share The firm’s β is 1.26, the T-bill rate is 3.5% and the market risk premium is 6.7% Due to the early stage in its corporate life cycle, the firm has significant tax-loss carry forwards, resulting in the firm not expecting to have to pay taxes in the foreseeable future

(a) Compute the firm’s weighted average cost of capital (WACC) (6 marks) Answer

The bond price today is:

28 891

$ 70 347

$ 4955 14 5

37

$

) 045 1 (

000 , 1 ] ) 045 1 ( 045 0

1 045

0

1 [ 5

37

= +

×

=

+

×

−

×

.

The market value of debts (D) = ($35,000,000/$1,000) × $891.28 =

$31,194,800

The market value of equity (E) = $26 × 6,000,000 = $156,000,000

The market value of the firm (V) = D + E = $31,194,800 + $156,000,000 =

= $187,194,800

The cost of equity (requity) is computed using the CAPM as:

requity = 3.5% + 1.26 × 6.7% = 11.94%

The cost of debt (rdebt) is the YTM on bond, which is 9%

So the WACC with no taxes is calculated as:

% 45 11

% 94 11 800 , 194 , 187

$

000 , 000 , 156

$

% 9 800 , 194 , 187

$

800 , 194 , 31

$

r V

E r

V

D

=

× +

×

=

× +

×

=

(b) If the firm were able to issue an additional $26,000,000 in debt ($1,000 par

value) at an 8.5% coupon rate (paid semi-annually) and use the proceeds

to retire 1,000,000 shares, what would be the firm’s WACC? (4 marks) Answer