6 (10pts) Project cost of capital: Using a comparable firm Currently, ABP starts

Question

6 (10pts) Project cost of capital: Using a comparable firm Currently, ABP starts ABP ine. is s provider of lumber and milling equipment and all equity financed firm s new project which is developing a GPs based inventory tracking division in ABP, Management views the risk of this investment as similar companies' investment. You have the following information about the comparable company to AP's technology investment which will be a separate to that of other technology system, the new Levered Comparable company betao, comparable firm, is 0.8 and Debt beta of comparable firm is 0.5·Leverage ratio-DUE+D) Risk free rate of 2% and a market risk premium of 5% leverage ratio 20%, average debt bond yield of 100%. Equity * (Spts) Estimate the cost of capital of the new project (using WACC equation) (Spts) Estimate the cost of capital of the new project using beta information of comparable firm.

Explanation / Answer

ABP is all equity financed which means that the debt in the company is zero. In order to calculate the cost of capital using WACC formula, we first need the cost of equity and cost of debt for ABP. Since the debt is zero, we only need to calculate the cost of equity which would then be equal to the cost of capital.

The cost of equity can be calculated using CAPM (Capital Asset Pricing Model) formula as below,

Re = Rf + B * (Rm - Rf)

where,

Re = the cost of equity

Rf = risk-free rate

Rm = market risk premium

B = beta of ABP

The risk-free rate is given as 2%, i.e. Rf = 2% and the market risk premium is 5%, i.e. Rm = 5%. To calculate beta of ABP, we can choose the non-leveraged or debt free beta or equity beta of the comparable firm (since ABP is debt free). The equity beta of comparable firm is 0.8

Using CAPM formula,

Cost of equity Re = Rf + B * (Rm - Rf) = 2% + 0.8 * ( 5% - 2%) = 2% + 0.8 * (3%) = 2% + 2.4% = 4.4%

Using WACC formula,

Cost of capital, r = (E/V) * Re + (D/V) * Rd

where,

E = equity in the copmany ABP

V = enterprise value of the company ABP

D = debt of company ABP

Rd = cost of debt

Since ABP is debt free, D = 0 and Rd = 0, and the enterprise value will be equal to equity in the company ABP since the company is all equity financed, i.e. E=V.

Cost of Capital, r = (E/V) * Re = (E/E) * Re = Re = 4.4%

Using comparable firm's beta information, the cost of equity and the cost of debt are calculated as follows,

Cost of equity, Re = Rf + B * (Rm - Rf)

Rf = risk-free rate = 2%

Rm = market risk premium = 5%

B = debt beta of firm = 0.5

Here, debt beta of the firm is being used since the firm being compared is not debt free i.e. there is some debt in the firm. In that case, debt beta or leveraged beta needs to be used while calculating the cost of equity.

Cost of equity, Re = Rf + B * (Rm - Rf) = 2% + 0.5 * ( 5% - 2%) = 2% + 0.5 * (3%) = 2% + 1.5% = 3.5 %

The cost of debt is the rate at which the debt is being taken i.e. the rate at which the debt needs to be serviced in regular intervals of time. The cost of debt is equal to the given average debt bond yield that the firm needs to pay to the bond holders i.e. cost of debt, Rd = 10%

Using WACC formula,

Cost of capital, r = (E/V) * Re + (D/V) * Rd

where,

E = equity in the copmany ABP

V = enterprise value of the company ABP

D = debt of company ABP

Rd = cost of debt

The leverage ratio in the firm is 20% which means that the debt in the company is 20% of the total enterprise value of the firm. This, in turn, means that the rest of 80% of the enterprise value is equity.

So, E/V = 80% or 0.8 and D/V = 20% = 0.2  

Cost of capital, r = (E/V) * Re + (D/V) * Rd = (0.8 * 3.5%) + (0.2 * 10%) = 2.8% + 2% = 4.8 %

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