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Assume the following information for firm Omega: Bonds = €30 million with yield to maturity = 8%; Stocks = €100 million; covariance of the stock returns with the market = 0

Finance Aug 12, 2020

Assume the following information for firm Omega: Bonds = €30 million with yield to maturity = 8%; Stocks = €100 million; covariance of the stock returns with the market = 0.048; standard deviation of the market = 0.20; market risk premium = 0.075; risk free return = 0.06; corporate tax rate = 0.28. Omega plans to buy a new machine that costs €40 million. The machine will lead to annual cash flows of €6 million per year for 20 years. The purchase of machine will not change the risk level of the firm. Should Omega buy the machine?

Expert Solution

Capital Amount (in EUR mn) Weightage (A) After-Tax Cost of Capital (B) Weighted Average Cost [A * B]
Bonds 30 0.230769230769231 5.76% 1.329230769231
Stocks 100 0.769230769231 15% 11.538461538462
Total 130 1   12.86769230769

Beta = Covariance of stock returns with market / (Std dev of market)2
= 0.048 / 0.04
= 1.2

Cost of Equity = Risk-Free Rate + Beta * (Market Risk Premium)
= 6% + 1.2 * 7.5%
= 6% + 9%
Cost of Equity = 15%

Weighted Average cost of capital = 12.86769%

Cash Flow = 6 million

Present Value of Future Cash Inflows (PV) = C * {[1 - (1 + i)-n] / i}
where C = Cash Flow
i = Weighted Average Cost of Capital = 12.86769%
n = number of years = 20 years

PV = 6000000 * {[1 - (1 + 0.1286769)-20] / 0.1286769}
= 6000000 * (0.911160263 / 0.1286769)
= 6000000 * 7.080993267
PV =  42,485,959.6021044

NPV = PV of Cash Inflow - PV of Cash Outflow
= 42,485,959.6021044 - 40,000,000
NPV =  $2,485,959.6021044

Since the NPV is positive, therefore, the company should accept the project.

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