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2.1. Potsdam Co has 3 million shares of common stock, each selling for $30, with β = 1.7. The company has $40 million in long-term bonds, selling at par, with coupon 7%. The tax rate of Potsdam is 30% and the risk-free rate is 5%. The expected return on the market is 12%. Find the WACC for Potsdam. 13.21% ♥

Solution: k = r + β [E(R ) – r] e m r = 5% β = 1.7 E (R ) = 12% m So, k e = 5% + 1.7(12%-5%) Or, ke = 16.9%

k = YTM = cF + ( F − B ) /n d (F + B)/2

c = 7% Assuming F = $1000 = B

So, Kd = (7%*1000 + 0)/[(1000+1000)/2]

Or, Kd = 7% t = 30%

After tax cost of debt = kd (1-t) = 7% (1-30%) = 4.9%

WACC = kd (1-t) B/V + ke S/V

B= $ 40 million S = $30*3million = $90million V = B+S = $40million + $90million V= $130 million

WACC = (4.9*40/130) + (16.9*90/130) Or, WACC = 13.21%2.2. Ohio Corporation has 6 million shares of common stock priced at $25 per share, which has just paid its annual dividend of $1.75. The dividends have grown steadily at the rate of 5% per year and the investors expect the growth to continue in the future. The 6% coupon bonds of the corporation have a face value of $60 million. The bonds will mature in 10 years and currently they sell at $857.14 each. The tax rate of Ohio is 25%. Calculate its WACC. 10.73% ♥

Solution: calculating cost of equity

ke = (D1/P0) + g

P0 = $25 g = 5%

D0 = $1.75

D1 = D0(1+g)

D1 = $1.75(1+5%)

Or, D1 = $1.8375

Therefore, ke = 1.8375/25 + 5%

Or, ke = 12.35%

Calculating cost of debt: k = YTM = cF + ( F − B ) /n d (F + B)/2

c = 6% Let F = $1000 B = $857.14 n = 10 years kd = [6%*1000 + (1000-857.14)/10]/[(1000+857.14)/2] kd = 8% After tax kd = 8%(1-25%) Or, after tax cost of debt = 6% Calculating WACC:

WACC = kd (1-t) B/V + ke S/V

Number of bonds = $60 million/$1000 per bond Or, number of bonds = 60000 B = 60000*857.14 Or, B = $51428400 S = 6 million shares * $25 per share Or, S = $150,000,000 V = $51,428,400 + $150,000,000 Or, V = $201,428,400 So, WACC = 6%*$51,428,400/$201,428,400 + 12.35%*$150,000,000/$201,428,400 Or, WACC = 10.73% 2.3. Erlangen Corporation needs a new machine that will cost $50,000. It will run for 5 years and the firm will depreciate it on a straight line basis, with no resale value. The machine will add $14,000 annually to Erlangen's earnings before taxes. The proper discount rate is 12% and the tax rate is 32%. Should Erlangen install the machine? NPV = −$4147, no ♥

Solution: The amount of annual depreciation will be $50,000/5 = $10000, because the machine does not have any residual value. The after-tax cash flow, C, is given by

C = 14000(1 − 0.32) + 0.32(10000) = $12,720

NPV = -$50,000 + $12,720*PVFA12%,5years

Where, PVFA is the present value factor for an annuity.

So, NPV = -50000 + 12720*3.6048

Or, NPV = -$4147

Since NPV is negative, hence Erlangen Corporation should not install the machine. 2.4. Freiburg Company wants to buy a machine that has expected life of 6 years. It costs $30,000, and increases the income of the company by $7,000 annually. It has a salvage value of $5,000. The proper discount rate is 12%, and the company pays no taxes at present. Should Freiburg purchase this machine? NPV = $1,313, yes. ♥

Solution: In this case, there is no tax hence we need not consider depreciation also.

NPV = -initial investment + present value of inflows

So, NPV = -$30,000 + $7,000*PVFA12%,6years + $5,000*PVF12%,6years

Where, PVF is the present value factor

Or, NPV = -$30,000 + $7,000*4.111 + $5,000*0.507

Or, NPV = $1,313

Since NPV is positive, hence Freiburg Company should purchase the machine.