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# Calculating NPV, optimal capital structure, WACC and Ke

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1.Brown Corp is considering buying a new press with a total installed price of \$2.2 million. The old press (which will be sold if new one is purchased) cost \$2.1 million 10 years ago and can be sold for \$1.0 million today. If the new press is purchased, Brown Corp expected sales to increase by \$1.6 million each year for the next five years (operating costs are 60% of sales). Brown Corp's CCA rate is 15%, and its tax rate is 30%. (You can assume that old press is fully depreciated, that is, its book value is =0). Estimate the NPV of new press.

2.Pink Inc. has total assets of \$25,000,000 (twenty-five million). EBIT is expected to be \$4,500,000. Assume a tax rate of 30%. For various debt-to-total asset ratios shown below, Pink Inc has estimated its cost of debt, equity shares outstanding and cost of equity.
Debt ratio Cost of debt, Kd Number of shares Cost of Equity, Ke
0% 200,000 12%
15% 8% 170,000 13%
30% 9% 140,000 14%
45% 12% 110,000 16%
60% 15% 80,000 20%

3.Black Enterprise has the following information:
Long-term debt : The company can raise \$1 million by selling 10-year bond at part value with a coupon interest of 6%. These coupons pay semi annual coupons.
Common equity: The firm's EPS next year is expected to be \$3.00, with a projected long-term annual growth rate of 3%. Dividends are expected to average 40% of earnings. Black's most recent share price was \$15 per share.
Capital structure: Black goal is finance all projects with a debt-to-equity ratio of 0.4.
Tax: Black Enterprises has a tax rate of 30%
Calculate Black's WACC.

4.Inflation is bad for capital investments because, among other things, it reduces the value of the taxation shield calculated on a historical cost basis. In other words, while sales and other expenses may increase in tandem with inflation (thus preserving real \$ value), the depreciation amount is not allowed to be adjusted for inflation. Hence, the real value of depreciation tax shield falls with inflation.
Suppose that in order to encourage investment, the government supplies a grant of \$X. What should \$X be such that firm ABC is exactly compensated for the loss of profitability due to inflation?
ABC has a depreciation D=\$400 per year for N=10 years, and its cost of capital =9%. The relevant tax rate is 30% and inflation is expected to be 3% per year for the next 10 years.

5.Red's beta is 1.3. The risk free rate (Rf) is 6%, the expected returns on the market (Rm) is 11%.
a)What's Red's cost of equity?
b)Assume that inflation has increased by 1%, increasing Rf and Rm to go 7% and 12% respectively. What is the new cost of equity for Red.
c)Assume that investor have become more risk averse and that as a result, the expected market return has increased to 13%. What is new cost of equity for Red? Assume that Rf is 6%
d)What can you say about the impact of higher inflation and risk aversion on the cost of equity?

#### Solution Preview

Please refer attached file for better clarity of tables and formulas.

Solution 1
Cash flows in year 0
Purchase of new machine=\$(2.20) million
Sale of old machine=\$1.00 million
Tax on Sale of old machine=30%*1 million= \$(0.30) million
Net cash flows=\$(1.50) million
Cash Flows in 1-5 years
Increase in operating profits=1.6*(1-60%)=\$0.64 million
Tax on income=operating profit*Tax rate=\$(0.19) million
Net income= \$0.448 million

Let us calculate PV of cash flows Amount is million
Year Net Cash Flows PV factor at 10% PV value
=1/(1+10%)^t Cash flows*PV factor
0 \$(1.500) 1.0000 \$(1.5000)
1 \$0.448 0.9091 \$0.4073
2 \$0.448 0.8264 \$0.3702
3 \$0.448 0.7513 \$0.3366
4 \$0.448 0.6830 \$0.3060
5 \$0.448 0.6209 \$0.2782
NPV \$0.1983

Let us calculate PV of CCA tax shields
I assume that new machine is never ...

#### Solution Summary

There are five problems. Solution to first problem explains the steps to calculate NPV of the new press. Solutions to other problems depict the methodology to find out optimal capital structure, WACC and cost of equity.

\$2.19