A corporation has $500,000 in bonds outstanding with a 5% annual coupon rate, 15

Question

A corporation has $500,000 in bonds outstanding with a 5% annual coupon rate, 15 years to maturity, a $1,000 face value, and a $890 market price. The company’s 5,000 shares of common stock sell for $20 per share and have a beta of 2.5. The risk free rate is 4%, and the market return is 12%. The company has a 35% tax rate. They are considering a project which will provide annual cash flows of $2,500 per year for 10 years, costs $20,000 and requires working capital of $3,000. What is the NPV for this project and should the company accept?

Select one:

a. NPV is 0 and the company should not accept

b. NPV is 4200 and the company should accept

c. NPV is -4200 and the company should not accept

d. NPV is -8200 and the company should not accept

e. NPV is -7200 and the company should not accept

Explanation / Answer

Calculating debt rate rd
Given coupon rate = 5% , PMT=50
Face value = $1000, FV=1000
Market Price = $890, PV=890
Time to maturity=15, T=15
Feeding these values in financial calculator and solving for I (interest rate), we get,
I= 6.14

Hence rd or debt rate in 6.14%.

Calculating debt rate re
Using CAPM Equation re = Risk free rate +beta*(market return - risk free rate)
= 4%+ 2.5(12%-4%)
= 24%

Calculating WACC
Total equity = No, of share* Market value of each share
= 5,000* $20
= $100,000
Weight of debt = Total debt/(Total debt + total equity)
= $500,000/($500,000+$100,000)
= 0.83
Weight of equity = Total equity / (Total debt+ total equity)
= $100,000/($500,000+$100,000)
= 0.17

WACC = weight of debt * rd * (1-Tax rate) + Weight of equity * re
= (0.83*6.14*(1-0.35) + 0.17 * 24)%
= 7.3%

Calculating NPV
CF0 = Initial cost + Working Capital
= -(20000+3000)
= -23000
CF1 to CF9 = 2500
CF10 = Cash flow provided by project+ return of working capital
= 2500+3000
=5500
Interest rate to be used for discounting = WACC = 7.3
Feeding these values in financial calculator we and solving for NPV, we get
NPV = -4200 and the company should not accept the project
Hence the correct answer is (c).

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