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Homework answers / question archive / 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
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?
| 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.
