assignment10 fundamentals of corporate finance, 4th edition brealey

b 9 marks The initial investment and expected profits cash from 2 mutually exclusive capital investments being considered by a firm are as follows: Initial Investment 70,000 65,000 Year

AK/ADMS3530 Summer 2007 Assignment #2 -SOLUTIONS Instructions:

(1) This assignment is to be done individually You must sign and submit the

standard cover page supplied as the last page of this assignment

(2) This assignment is due at the start of class, the week of July 23rd, 2007

(last class) This assignment can be typewritten or handwritten Work

that is too difficult to read due to messiness and poor handwriting will receive zero credit You must show your work to receive full credit

(3) This assignment is worth a total of 100 marks and represents 10% of your

overall grade

Question #1 (14 marks)

(a) (5 marks)

A capital investment requiring one initial cash outflow is forecast to operating profits (cash) as follows

Year 1 $74,000

Year 2 $84,000

Year 3 $96,000

Year 4 $70,000

The investment has an NPV of $20,850 based on a required rate of return of 12% Calculate the payback period of the investment

Solution

(a)Since the investment's NPV is $20,850, the initial investment is the value of Inv

satisfying

$20,850 =

12 1

000 74

,

$

1.12

$84,000

1.12

$96,000

1.12

$70,000

– Inv

= $66,071.4 + $66,964.3 + $68,330.9 + $44,486.3 – Inv

Inv = $225,003

Full payback on the project occurs sometime between years 2 and 3 to recover our initial investment of $225,003

Cumulative profit after 2 years = $74,000 + $84,000 = $158,000

Cumulative profit after 3 years = $158,000 + 96,000 = $254,000

Payback period = 2 +

$158,000

$254,000

$158,000

$225,003

−

−

= 2.7 yrs or 2 yrs 8 months

(b) (9 marks)

The initial investment and expected profits (cash) from 2 mutually exclusive capital investments being considered by a firm are as follows:

Initial Investment 70,000 65,000

Year 1 profit 30,000 50,000

Year 2 profit 80,000 50,000

Calculate the internal rate of return for each investment Which one would be selected based on an IRR ranking? (3 marks)

(i) Which investment should be chosen if the firm’s cost of capital is 14%

(support your answer)? (3 marks)

(ii) Which investment should be chosen if the firm’s cost of capital is 17%

(support your answer)? (3 marks)

Solution (b)

(i) The IRR on Investment A is the value of i satisfying

NPV = 0 =

i

+ 1

$30,000

+

( )1 2

$80,000

i

+ – $70,000

The solution is i = 30.5% = IRR on Investment A

The IRR on Investment B is the value of i satisfying

NPV = 0 =

i

+ 1

$50,000

+

( )1 2

$50,000

i

+ – $65,000

The solution is i = 34.2% = IRR on Investment B

Investment B would be selected on the basis on an IRR ranking

(ii) NPV(Investment A) =

14 1

000 30

,

$

1.14

$80,000

– $70,000 = $17,873

NPV(Investment B) =

14 1

000 50

,

$

1.14

$50,000

– $65,000 = $17,333 With the cost of capital at 14%, Investment A has the larger NPV and

should be chosen

(iii) Similarly, if you repeat part (ii) with the cost of capital of 17%, you would derive the following answers

NPV(Investment A) = $14,082 NPV(Investment B) = $14,261

Investment B now has the higher NPV and should be chosen

Question #2 (14 marks)

Allergy-free Corp is considering launching a “hay-fever” vaccine in Canada that will eliminate entirely the need for many Canadians to take seasonal allergy medication The vaccines will be sold to the medical community and government for $2.30 per vaccine Variable costs are $0.6440 per pill and fixed costs excluding depreciation are $3,500,000 per year The capital investment for the new manufacturing equipment will be $4,500,000 and will be depreciated straight-line over 8 years to a final value of zero Allergy-free Corp.’s cost of capital is 14% annually and it currently pays no taxes

(a) What is the accounting break-even level of sales for the new vaccine, in terms of number of vaccines that must be sold?

Solution

Variable cost = $0.644 / $2.30 = $0.28 per $1 of revenue

Additional profit per $1 of additional sales is therefore $0.72

Depreciation per year = $4,500,000 / 8 = $562,500 for 8 years

Accounting Break-even sales level

=

sales of dollar additional each

from profit Additional

on Depreciati including

Costs Fixed

= 3,500,000 + 562,500 = $5,642,361 sales revenue

0.72

# of pills that must be sold = $5,642,361/$2.30 per pill = 2,453,200 vaccines

(b) What is the NPV break-even level of sales, in terms of the number of vaccines that must be sold? (5 marks)

Solution

To find the NPV break-even sales, first calculate cash flows With no taxes,

CF = 72 × Sales – 3,500,000

The 14%, 8-year PV annuity factor is 4.6389

Therefore, if project NPV equals zero: PV(cash flows) – Investment = 0 4.6389 × (.72 × Sales – 3,500,000) – 4,500,000 = 0

3.3400 × Sales – 16,236,150 – 4,500,000 = 0

3.3400 × Sales – 20,736,150 = 0

Sales = 20,736,150/3.3400

NPV Break-even sales = $6,208,428.14 revenue

Number of pills that must be sold = $8,042,215.57/2.30 = 2,699,317

vaccines

(c) Why is your answer in (b) higher than your answer in (a)

Accounting break-even does not incorporate time-value of money

(d) If Allergy-free Corp is taxable at a 35% tax rate and its existing allergy medication generated annual pre-tax cash flows of $3,200,000 (which will

now disappear), what is the new NPV break-even level of sales, in terms of

the number of vaccines that must be sold? (4 marks)

Solution

To find the new NPV break-even sales, recalculate cash flows

With 35% tax rate,

CFop = (1–T) (Revenue – foregone CF - Fixed Expenses) + T × Depreciation = 65 (.72 × Sales – 3,200,000 – 3,500,000) + 35 × 562,500

= 0.468 Sales – 4,158,125

The PV annuity factor is 4.6389, so we find NPV as follows:

4.6389 (.468 × Sales – 4,158,125) – 4,500,000 = 0

2.171 x Sales – 19,289,126 – 4,500,000 = 0

2.171 x Sales = 23,789,126

Sales = $10,957,681

Number of vaccines that must be sold = $10,957,681/2.30 = 4,764,209

Question #3 (16 marks)

You are considering a new product launch The project will cost $680,000 and will have a four year life and have no salvage value; depreciation is straight line

to zero Sales are projected at 160 units per year; price per unit will be $19,000; variable cost per unit will be $14,000 and fixed costs will be $150,000 per year The required return on the project is 15% and the relevant tax rate is 35%

Assume all sales, VC and FC are cash costs

a Based on your experience you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within +- 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 NPV scenarios? (5 marks)

b Evaluate the sensitivity of your base case NPV to changes in fixed costs? (assume fixed costs increase to $160,000) (4 marks)

c What is the cash flow break-even level of output (units) for this project (ignore taxes)? (2 mark)

d What is the accounting break even level of output (units) for this

project? What is the degree operating leverage at the accounting

break-even point? How do you interpret this number? (5 marks)

Solution

a Sales = 160(1±0.10) = 176, 144; variable costs = $14,000(1±0.10) = $15,400,

$12,600

Fixed costs = $150,000(1±0.10) = $165,000, $135,000

Cash Flow (base) = [($19,000 – 14,000)(160) – $150,000](0.65) +

0.35($680,000/4) = $482,000

NPV(base) = –$680,000 + $482,000(PVIFA15%,4) = $696,099.57

Cash Flow (worst) = [($19,000 – 15,400)(144) – $165,000](0.65) +

0.35($680,000/4) = $289,210

NPV (worst) = –$680,000 + $289,210(PVIFA15%,4) = +$145,688.29

Cash Flow (best) = [($19,000 – 12,600)(176) – $135,000](0.65) +

0.35($680,000/4) = $703,910

NPV (best) = –$680,000 + $703,910(PVIFA15%,4) = $1,329,647.82

b If FC are $160,000:

Cash Flow = [($19,000 – 14,000)(160) – $160,000](0.65) + 0.35($680,000/4) =

$475,500

NPV = –$680,000 + $475,500(PVIFA15%,4) = $677,542.21

∆NPV/∆FC = ($677,542.21 – 696,099.57)/($160,000 – 150,000) = –1.856

For every dollar FC increase, NPV falls by $1.86

c Break Even Units (cash flow) = $150,000/($19,000 – 14,000) = 30

d Break Even Units (accounting) = [$150,000 + ($680,000/4)]/($19,000 – 14,000)

= 64

At this level of output, Degree of Operating Leverage = 1 +

($150,000/$170,000) = 1.8824 The interpretation is that for each 1% increase

in unit sales, Cash Flow will increase by 1.88%

Question #4 ( 10 marks)

Consider the following information on three stocks

State of economy Probability state of Rate of return

Stock A Stock B Stock C

(a) If your portfolio is invested 40% each in A and B and 20% in C, what is the portfolio expected return? The Variance? The Standard Deviation? (4 marks)

(b) If the expected T-Bill rate is 3.80%, what is the expected risk premium on the portfolio? (2 mark)

(c) If the expected inflation rate is 3.5%, what are the approximate and exact expected real returns on the portfolio? What are the approximate and exact expected real risk premiums on the portfolio? (4 marks)

solution

(a) Boom: E[R] = 4(.20) + 4(.35) + 2(.60) = 34

Normal: E[R] = 4(.15) + 4(.12) + 2(.05) = 118

Bust: E[R] = 4(.01) + 4(–.25) + 2(–.50) = –.196

E[R] = 2(.34) + 5(.118) + 3(–.196) = 0682

σ2

p = 2(.34 – 0682)2 + 5(.118 – 0682)2 + 3(–.196 – 0682)2 = 036956

σp = [.036956]1/2 = 1922

(b) Risk Premium = E[R] – Rf = 0682 – 038 = 0302

(c) Approximate expected real return = E[R] – inflation rate = 0682 – 035 = 0332

Exact expected real return E[Real] = (1 + E[R])/(1 + inflation rate]) - 1 ;

E[real] = [1.0682/1.035] – 1 = 0321

Approximate expected real risk premium = 0.0302 – 0.0350 = - 0.0048

Exact expected real risk premium = 1.0302 / 1.035 – 1 = - 0.0046

Question #5 (12 marks)

Assume that you wanted to invest your hard earned money , $1 million total, into stocks of three companies (Tangier Corp., Lofalo Inc & Yinta Ltd.) and in a risk free instrument such as a T-bill The 3 stocks together have the same level of risk as the average stock in the market place

(a) If you invest $200,000 in Tangier with a Beta of 0.8 and $400,000 in Lofalo

with a Beta of 1.2 and if Yinta has a Beta of 1.3 how much will you invest

in Yinta and in T-Bills? (4 marks)

(b) Assume that the stocks of the 3 companies are on the Security Market

Line The prevailing T-bill rate is 5% and the average market rate of

return is 8% What is the rate of return on each stock? (4 marks)

(c) If there was another stock selling at $25 (Beta of 2) with an expected

dividend of $2 and a growth rate of 6% Based on the CAPM, is this stock priced correctly? Explain your answer (4 marks)

Solution

(a) Portfolio Beta of 3 Stocks = 1 (same as the market risk)

923 , 276 000 , 000 , 1 2769 0

276923

0 1

1

=

×

=

=

−

−

=

= +

+

=

Y

Y

L L T T Y

Y Y L L T T

V

β

β ω β ω ω

β ω β ω β ω β

The amount to be invested in the risk-free rate asset is

1,000,000 – 200,000 – 400,000 – 276,923 = 123,077

(b) Using the CAPM equation of R(e) = Rf + Beta (Rm – Rf)

R(Tangier) = 0.05 + 0.8 (0.08 – 0.05) = 7.4%

R(Lofalo) = 0.05 + 1.2 (0.08 – 0.05) = 8.6%

R(Yinta) = 0.05 + 1.3 (0.08 – 0.05) = 8.9%

(c) The return implied by the stock price is 14%

0

1 + =

P

Div

implied by the CAPM is E(r)=r f +β(r m −r f)=11% Since the stock’s rate of return would be too high relative to the CAPM, its current price must be too low Therefore the stock is undervalued

Question #6 (14 marks)

Five years ago, Cocoa Corp issued $45,000,000 of 20-year 7% bonds The yield

to maturity on these debts today is 6% The face value per bond is $1,000 Coupons are paid semi-annually The firm also has 250,000 shares of 4.5% preferred stocks outstanding with a total par value of $7,500,000 The current yield on these preferred stocks is 5% today Finally, the firm has 3,000,000 shares of common stocks outstanding, which just paid $0.75 dividend per share The firm’s common stocks have a beta of 1.5 The annual sustainable growth rate of the firm’s earnings and dividends is 3% The risk-free rate is 3.5% and the rate of return on the market portfolio is 12% The firm pays taxes at a rate of 35% Compute Cocoa’s WACC

Solution

Bonds:

The market price of bond today is:

$1,098

) 03 0 1 (

000 , 1 ]

) 03 0 1 ( 03 0

1 03

0

1 [ 35

$

) r (1

Value Face ]

) 1 (

1 1

[

30 30

t debt debt

debt debt

=

+

+ +

−

×

=

+

+ +

−

×

B

r r

r C

P

The number of bonds issued = $45,000,000/$1,000 = 45,000

So the total market value of bonds is: D = 45,000 × $1,098 = $49,410,099.30

Preferred stocks:

The par value of each preferred stock = $7,500,000/250,000 = $30

The annual dividend paid on each preferred stock = $30 × 4.5% = $1.35

So the market price of preferred stock per share = $1.35/0.05 = $27, and the total market value of preferred stocks is: P = 250,000 × $27 = $6,750,000

Common stocks:

Using the CAPM, we can calculate the cost of common stocks as:

%

25 16

%) 5 3

% 12 ( 5 1

% 5 3 ) (

equity =r f + r m −r f = + × − =

Using the DDM, we can compute today’s common stock price as:

83 5

% 3

% 25 16

%) 3 1 ( 75 0 DIV

equity

1

−

+

×

=

−

=

g r

Therefore, the total market value of common stocks is:

E = 3,000,000 × $5.83 = $17,490,566.04

Cocoa Corp.’s total market value is:

V = D + P +E = $(49,410,099.30 + 6,750,000 + 17,490,566.04) = $73,650,665.34

The weights of each security are: D/V = 0.6709, P/V = 0.0916, and E/V = 0.2375

0693 0

] 1625 0 2375 0 [ ] 05 0 0916 0 [ ] 06 0 ) 35 0 1 ( 6709 0 [

] [

] [

] ) 1 ( [

=

× +

× +

×

−

×

=

× +

× +

−

×

V

E r

V

P r

T V

D

c

So Cocoa Corp.’s WACC is about 6.93%

Question #7 (20 marks)

To compete with Apple’s new i-Phone, Motorola is planning on unveiling its

M-phone, a smart phone that include voice, internet access, unlimited data and a

new feature that allows users to scroll through their voicemail in an inbox like

email

The Motorola marketing department estimates annual sales of 150,000, 250,000,

80,000 and 30,000 units for years one to four respectively and which time, the

life cycle will end Pricing will be aggressive Motorola will sell the M-phone at a

price of $490 in the first year and then reduce it by $70 a year to appeal to the

mass markets Fixed costs are $3.2 million annually and variable costs are

estimated at 35% of the selling price In addition, the Motorola accounting

department will allocate general overhead of $2 million annually

The manufacturing equipment will cost $30 million, $4 million to

transport and another $1 million to install and falls into the class 8 (CCA

rate = 20%) pool along with other equipment After Year 4 there will still be class

8 assets remaining in the pool and the half-year rule applies At the end of the

project, the equipment can be sold as salvage for $75,000 Initial net working

capital (NWC) investment is forecast to be $1.5 million (today) and is expected to

decrease by $200,000 in each year from year 1 to year 4 It is estimated that

there will be a complete recovery of net working capital in year 5

R&D for this machine has been steep costing $20 million over the past two years

and expected additional $5 million in R&D is expected to be incurred in year one

before launching the multi-language version outside of the USA The M-phone

will be manufactured in China in a manufacturing plant already owned by

Motorola and currently vacant The plant cost $4.0 million two years ago and has

a current market value of $12.5 million Unfortunately, as consumers buy the

M-phone, Motorola expects profits of existing products, will be reduced by $2.5

million annually during the M-phone product life cycle Motorola pays corporate

taxes at the marginal rate of 36% and the CFO requires that all projects

worldwide earn at least 7% above its weighted average cost of capital

In addition you are given the following financial information:

Motorola Balance Sheet ( Book Value in $millions)

Cash & short-term securities $10 Bonds 8% coupon (paid semi-annually),

Maturity = 10 years, current YTM = 9% $40

Accounts receivable 30 Preferred Stock (par value = $20/share) 20

Inventories 70 Common Stock 50

Plant & Equipment 110 Retained Earnings 110

Total Assets $220 Total liabilities & net worth $220