Question 5 Company A has a debt of $25,000,000 while its equity is $115,000,000.

Question

Question 5 Company A has a debt of $25,000,000 while its equity is $115,000,000. The beta of A's levered equity is 0.95 and the company keeps a constant debt-to- equity ratio. Company A's cost of debt is 4.35% and it bears no systematic risk. The expected return of the market portfolio is 9%. In the near future Company B is starting a new project with a life of 5 years, with asset similar to the assets of Company A. Company B will need to acquire new fixed assets for $12,450,000 in order to start the project. These assets will be depreciated straight-line through the life of the project. The CFO of the company has chosen to raise 113 of the necessary funds for the new project as debt, and 2/3 as equity. Moreover the debt level for the project will be kept constant through its life, and it bears no systematic risk. The corporate tax rate is 24%. (a) What is the unlevered return on equity of the new project of Company B? The assets of Company B?s project produce a constant expected EBITDA of $4,560,000 per year for the next 5 years, and the depreciation tax shield has a risk profile comparable to the risk of company?s debt. (b) What is the annual after-tax cash flow to equity holders from the new project at the end of each of the five years of its life? (c) What is the project?s NPV?

Explanation / Answer

a. Re(levered) = Re(unlevered) + D/E (Re(unlevered) - Rd)

where,

Re= required rate of return on equity, or cost of equity.
Rd= required rate of return on borrowings, or cost of debt = 4.35%
D/E is the debt-to-equity ratio.

Since the cost of debt involves no systematice risk, it is risk free rate of return with zero beta

Using CAPM, Re(levered) = Risk free rate of return + beta*(Return from market portfolio - Risk free rate of return)

= 4.35% + 0.95*(9 - 4.35) = 8.815%

D/E = 25,000,000/115,000,000 = 0.217

Re(levered) = Re(unlevered) + D/E (Re(unlevered) - Rd)

8.815 = Re(unlevered) + 0.217 *Re(unlevered) - 0.94395

9.75895 = 1.217* Re(unlevered)

Re(unlevered) = 8.01885 ~ 8.02%

b. Depreciation expense per annum( assuming no salvage value) = 12450000/5 = 2490000

EBITDA = 4560,000

EBIT = 4560,000 - 2490000 = 2070000

Interest Expense @ cost of debt = 4.35% * 2070000 = 90045

PBT = 2070000 - 90045 = 1979955

Tax @ 24% = 24% * 1979955 = 475189.2

PAT or Net Income = 1979955 - 475189.2 = 1504765.8

Annual cash flow at the end of each of the 5 years of the project = EBITDA(1-Tax rate) + Depreciation expense*Tax Rate - Fixed Capital Investment + Net Borrowing

= 4560,000 *(1-0.24) + 2490000*0.24 - 0 + 0

= 4063200

c. WACC of Company B = 1/3*4.35*(1-0.24) + 2/3* 8.815 = 6.978 ~ 7%

NPV = -12450000 + (4063200/1.07) + (4063200/1.07^2) +....+ (4063200/1.07^5)

= 4209922

Hope this helps, regards

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