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A 5-year project will require an investment of $100 million. this comprises of plant andmachinery worth $80 million and a net working capital of $20 million. the entire outlay willbe incurred at the project’s commencement.financing for the project has been arranged as follows:80,000 new common shares are issued, the market price of which is $500 per share. theseshares will offer a dividend of $4 per share in year 1, which is expected to grow at a rate of 9%per year for an indefinite tenure.remaining funds are borrowed by issuing 5-year, 9% semi-annual bonds, each bond having aface value of $1,000. these bonds now have a market value of $1,150 each.at the end of 5 years, fixed assets will fetch a net salvage value of $30 million, whereas the networking capital will be liquidated at its book value.the project is expected to increase revenues of the firm by $120 million per year. expenses,other than depreciation, interest and tax, will amount to $80 million per year. the firm is subjectto a tax rate of 30%plant and machinery will be depreciated at the rate of 25% per year as per the written-downvalue method.you are required to:1. compute the cost of equity for this project (2 marks)2. compute the relevant cost of debt for this project. (2 marks)3. compute the wacc (4 marks)4. determine the initial cash flow for the project. (1 mark)5. determine the earnings before taxes for years 1 through 5 (2 marks)6. compute the ocf for years 1 through 5 (3 marks)

Sagot :

Answer:

1. The cost of equity can be derived from the share price, which is the present value of the expected dividend one year from now(using the present value of growing perpetuity) as shown below:

share price=D1/(r-g)

share price=$500

D1=expected dividend one year from now=$4

r=cost of equity=unknown

g=constant growth rate=9%

$500=$4/(r-9%)

$500*(r-9%)=$4

r-9%=$4/$500

r=($4/$500)+9%

r=9.8

the Cost of Equity for the project is 9.8%

2. Compute the relevant cost of debt for this project is 5.53%

Market Value= 1,150

Face Value= 1,000

Term= 5 years, 10 semi-annual periods

Coupon Rate= 9%, 4.5% semi-annual rate

Tax Rate= 30%

N=10(semiannual coupons in 5 years)

PMT=45(semiannual coupon=face value*coupon rate/2=$1000*9%/2=$45)

PV=-1150(current market price)

FV=1000(face value of the bond is $1,000)

CPT(press compute)

I/Y=2.762766%(semiannual yield)

annual yield=2.762766%*2

annual yield=5.53%

3. The weighted average cost of capital is the sum of equity and the after-tax cost of debt multiplied by their respective market value weights

WACC=(cost of equity*weight of equity)+(after-tax cost of debt*weight of debt)

cost of equity=9.80%

the market value of equity raised=shares issued*market price of the share

the market value of equity raised=80,000*$500

the market value of equity raised=$40 million

weight of equity=market value of equity/total amount raised

weight of equity=$40 million/$100 million

weight of equity=40.00%

weight of debt=1-weight of equity

weight of debt=1-40.00%

weight of debt=60.00%

after-tax cost of debt=bond yield*(1-tax rate)

the after-tax cost of debt=5.53%*(1-30% )

the after-tax cost of debt=3.87%

WACC=(9.80%*40.00%)+(3.87%*60.00%)

WACC= 6.2426% or 6.24%

Therefore the WACC is 6.2426% or 6.24% rounded off to 2decimal place

4. Determine the initial cash flow for the project =$100 million

The initial cash outlay is the sum of the plant and machinery and net working capital investment required to commence the project

Plant and machinery= $80 million

Networking capital = $20 million

Total Initial Cash Flow= $100 million

5. Determine the earnings before taxes for years 1 through 5

Year

1 2 3 4 5

Revenue

120,000,000 120,000,000 120,000,000 120,000,000 120,000,000

Expenses

(80,000,000) (80,000,000) (80,000,000) (80,000,000) (80,000,000)

Depreciation (20,000,000) (15,000,000) (11,250,000) (8,437,500) (6,328,125)

EBT

20,000,000 25,000,000 28,750,000 31,562,500 33,671,875

Step-by-step explanation:

5. Depreciation schedule:

Year 1 = 80 × 25% = 20

Year 2 = (80-20) × 25% = 15

Year 3 = (80-20-15) × 25% = 11.25

Year 4 = (80-20-15-11.25) × 25% = 8.4375

Year 5 = (80-20-15-11.25-8.4375) × 25% = 6.328125

EBT = revenue - Expenses - depreciation

Year 1 = 120 - 80 - 20 = 20 Million

Year 2 = 120-80- 15 = 25 Million

Year 3 = 120-80- 11.25 = 28.75 Million

Year 4 = 120-80- 8.4375 = 31.5625 Million

Year 5 = 120-80- 6.328125 = 33.671875Million

The cost of equity of the project through the use of Gordan's formula will be 9.87%.

How to compute the cost of equity?

It should be noted that the price of stock is computed thus:

= Previous dividend + Growth / Cost of equity - Growth

Po = Do + g/Ke - g

500 = 4 + 9%/Ke - 9%

500 = 4 + (0.09 × 4) / Ke - 9%

500 = 4.36/Ke - 9%

500(Ke - 9%) = 4.36

500Ke = 4.36 + 45

500Ke = 49.36

Ke = 49.36/500

Ke = 9.87%

The cost of debt will be:

= Interest rate (1 - Tax rate)

= 9% × (1 - 30%)

= 9% × 0.7

= 6.30%

The amount of the cost of debt will be:

= $1000 × 6.30%

= $63.00

Learn more about cost of equity on:

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