Consider the following projects. Project CO C1 C2 СЗ C4 C5 A -1,000 +1,000 0 0 0 10 B -2,000 |+1,000 |+1,000 +4,000 +1,000 +1,000 C -3,000 |+1,000 |+1,000 0 +1,000 +1,000 Assume that this firm's beta= 1.5 The expected market return is 12%. The risk free rate is 2.5%. This company can borrow debt at 5.2%. The firm has $5 billion in debt. It has 6 billion shares outstanding at $3 price/shr. The corporate tax rate (Tc) = 21% Question: What is the NPV of project B?a) $3,458 b) -$128
c) -$122
d) $2,158

a) $3,458

Explanation:

The net present value is the present value of future cash flows discounted at the firm's weighted average cost of capital(which is the appropriate discount rate in this case) minus the initial investment outlay

cost of equity=risk-free rate+beta*(expected market return-risk free rate)

cost of equity=2.5%+1.5*(12%-2.5%)

cost of equity=16.75%

after-tax cost of debt=5.2%*(1-21%)

after-tax cost of debt=4.11%

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

weight of equity=value of equity/(value of equity+value of debt)

value of equity=6 billion*$3=$18 billion

value of debt=$5 billion

weight of equity=$18 billion/($18 billion+$5 billion)

weight of equity=78.26%

weight of debt=1-78.26%

weight of debt=21.74%

WACC=(78.26%*16.75%)+(21.74%*4.11%)

WACC=14.00%

present value of a future cash flow=future cash flow/(1+WACC)^n

n is the year in which the cash flow is expected, it is 1 for year 1 cash flow, 2 for year 2 cash flow ,and so on

NPV of project B=1000/(1+14%)^1+1000/(1+14%)^2++4000/(1+14%)^3+1000/(1+14%)^4+1000/(1+14%)^5-2000

NPV of project B=$ 3,458.00  

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