Question

Consider the following information on Huntington Power Co.
Debt: 4,000, 7% semiannual coupon bonds outstanding, $1,000 par value, 18 years to maturity, selling for 102 percent of par; the bonds make semiannual payments.
Preferred Stock: 10,000 outstanding with par value of $100 and a market value of 105 and $10 annual dividend.
Common Stock: 84,000 shares outstanding, selling for $56 per share, the beta is 2.08

The market risk premium is 5.5%, the risk free rate is 3.5% and Huntington’s tax rate is 32%.

Huntington Power Co. is evaluating two mutually exclusive project that is somewhat riskier than the usual project the firm undertakes; management uses the subjective approach and decided to apply an adjustment factor of +2.1% to the cost of capital for both projects.

Project A is a five-year project that requires an initial fixed asset investment of $2.4 million. The fixed asset falls into the five-year MACRS class. The project is estimated to generate $2,050,000 in annual sales, with costs of $950,000. The project requires an initial investment in net working capital of $285,000 and the fixed asset will have a market value of $225,000 at the end of five years when the project is terminated.

Project B requires an initial fixed asset investment of $1.0 million. The marketing department predicts that sales related to the project will be $920,000 per year for the next five years, after which the market will cease to exist. The machine will be depreciated down to zero over four-year using the straight-line method (depreciable life 4 years while economic life 5 years). Cost of goods sold and operating expenses related to the project are predicted to be 25 percent of sales. The project will also require an addition to net working capital of $150,000 immediately. The asset is expected to have a market value of $120,000 at the end of five years when the project is terminated.

Use the following rates for 5-year MACRS: 20%, 32%, 19.2%, 11.52%, 11.52%, 5.76%

1. Calculate WACC for the firm

2. What is the appropriate discount rate for project A and project B?

3. Calculate project A’s cash flows for years 0-5

4. Calculate project B’s cash flows for year 0-5

5. Calculate NPV, IRR and PI for project A

6. Calculate NPV, IRR and PI for project B

7. Which project should be accepted if any and why?

8. What is the NPV profile’s crossover rate (incremental IRR)?

9. By just considering the crossover rate, and without recalculating NPV or IRR, which project would you select if the appropriate discount rate for both projects is 8% and why?

Answer 1

First, let us calculate the cost of debt, pref stock and equity:

Cost of debt : 7% semi annual coupon bonds, 18 years maturity, face value $1000 and current price is 102% par or $ 1020. The cost of debt will be YTM for this bond. Let semi annual YTM be r such that the annual YTM will be 2 * r, then:

1020 = 35/(1+r%) + 35/(1+r%)² + ... + (1000+35)/(1+r%)³⁶

solving we get annual YTM (2r) = 6.81%

After tax cost = 6.81% * ( 1-32%) = 4.63%

Cost of Pref stock = Dividend / current market value = 10/105 = 9.52%

Cost of equity : Beta = 2.08; Risk free rate = 3.5% and market risk premium = 5.5% ; Hence cost of equity = 3.5% + 2.08*5.5% = 14.94%

WACC - weighted average cost respective capital constituents.

Total debt value = 4000 * 1020 = 4,080,000 ; Total Pref stock = 10000 * 105 = 1,050,000 ; Total equity = 84000 * 56 = 4,704,000

Total capital = 9,834,000 ; Debt weightage = 0.41; Pref stock weightage = 0.11; equity weightage = 0.48

Hence WACC = 0.41 * 4.63% + 0.11 * 9.52% + 0.48* 14.94% = 10.08%

Since the management believes the project A & B to be more risky and requires an adjustment of 2.1% upwards the resultant discount rate will be = 10.08% + 2.1% = 12.18%

Project A & B cash flows, NPV, IRR and PI is as below:

Now we know that in mutually exclusive projects we should choose project with highest NPV, hence Project B should be chosen which is also better from IRR and PI perspective.

For the NPV cross over rate, lets denote the cross over rate as r. We use the cash for analysis row cash flows from above two work sheets and calculate the PV at r and then equate them to each other. The value of r which equates them is the cross over rate which will be 5.88%

Below the cross over rate Project A NPV is better and above that Project B's. Hence we should choose Project B at 8% discount rate