Question

Hula Enterprises is considering a new project to produce solar water heaters. The finance manager wishes to find an appropriate risk adjusted discount rate for the project. The (equity) beta of Hot Water, a firm currently producing solar water heaters, is 1.6. Hot Water has a debt to total value ratio of 0.2. The expected return on the market is 0.08, and the riskfree rate is 0.06. Suppose the corporate tax rate is 40 percent. Assume that debt is riskless throughout this problem. (Round your answers to 2 decimal places. (e.g., 0.16))

a. The expected return on the unlevered equity (return on asset, R0) for the solar water heater project is %.

b. If Hula is an equity financed firm, the weighted average cost of capital for the project is %.

c. If Hula has a debt to equity ratio of 1, the weighted average cost of capital for the project is %.

d. The finance manager believes that the solar water heater project can support 20 cents of debt for every dollar of asset value, i.e., the debt capacity is 20 cents for every dollar of asset value. Hence she is not sure that the debt to equity ratio of 1 used in the weighted average cost of capital calculation is valid. Based on her belief, the appropriate debt ratio to use is %. The weighted average cost of capital that you will arrive at with this capital structure is %.

Answer 1

(a) Computation of the expected return on the unlevered equity (return on asset, R0) for the solar water heater project.We have,

Step1: Computation of the asset beta(Unlevered beta) for the project.We have,

Asset Beta = Equity Beta / [ 1 + (1- tax rate) debt / Equity]

Where,

Equity Beta = 1.6

Tax rate = 40%

debt/ equity = 0.2 / 0.8 = 1/4 (whent debt to total value ratio is 0.2)

putting these value in the above formula,we get:

Asset beta = 1.6 / [ 1 +(1 - 0.4) 1/4]

Asset beta = 1.6 / 1.15 = 1.39

Hence, the asset beta for the project is 1.39.

Step2: Computation of the expected return on the unlevered equity (return on asset, R0) for the solar water heater project.We have,

The expected return on the unlevered equity is calculated by capital asset pricing model(CAPM) and it is equal to unlevered cost of capital. It can be expressed as a function of risk free-rate of return, market premium risk and Asset beta.

Expected return on unlevered equity = Risk-free rate + Asset beta ( Expected return on market - Risk free return)

Expected return on unlevered equity = 0.06 + 1.39 ( 0.08 - 0.06) = 0.06 + 0.03 = 0.09*100 = 9 %

Hence, the expected return on unlevered equity for the project is 9 %.

(b) Computation of the weighted average cost of capital for the project.We have,

If Hula Enterprises is an all-equity financed firm, the weighted average cost of capital for the projectis just the unlevered cost of equity. The unlevered cost of equity is calculated by the CAPM and it is equal to expected return of the unlevered equity.

Hence, the weighted average cost of capital for the project is 9.00 %.

(c) Computation of the weighted average cost of capital for the project if debt to equity ratio is 1.We have,

Step1: We calculate levered equity beta corresponding to the debt to equity ratio is 1.

Levered equity beta = [ 1 + (1 - tax rate) Debt/ Equity] Beta Asset

Levered equity beta = [ 1 + ( 1 - 0.40) 1] 1.39 = 2.22

Hence, the levered equity beta is 2.22

Step2: Computation of the return on levered equity using the CAPM.We have,

Expected return on levered equtiy = 0.06 + 2.22( 0.08 - 0.06) = 0.06 + 0.04 = 0.10*100 = 10 %

Hence,the expected return on levered equity is 10%.

Step3: Computation of the weighted average cost of capital for the project.We have,

Weighted average cost of capital = (Debt/ (Debt + Equity) (1- tax rate) risk-free rate) + ( Equity / (Debt+Equity) expected rate of return)

Weighted average cost of capital = ( 0.5 ( 1 - 0.40) 0.06) + ( 0.5 x 0.10) = 0.018 + 0.05 = 0.068*100   

Weighted average cost of capital for the project = 6.8 %

(d)

Step1: We calculate levered equity beta corresponding to the debt to equity ratio is 0.2.

Levered equity beta = [ 1 + (1 - tax rate) Debt/ Equity] Beta Asset

Levered equity beta = [ 1 + ( 1 - 0.40) 1/4] 1.39 = 1.60

Hence, the levered equity beta is 1.60

Step2: Computation of the return on levered equity using the CAPM.We have,

Expected return on levered equtiy = 0.06 + 1.60( 0.08 - 0.06) = 0.06 + 0.03 = 0.09*100 = 9 %

Hence,the expected return on levered equity is 9%.

Step3: Computation of the weighted average cost of capital for the project.We have,

Weighted average cost of capital = (Debt/ (Debt + Equity) (1- tax rate) risk-free rate) + ( Equity / (Debt+Equity) expected rate of return)

Weighted average cost of capital = ( 0.2 ( 1 - 0.40) 0.06) + ( 0.8 x 0.09) = 0.007 + 0.079 = 0.079*100   

Weighted average cost of capital for the project = 7.90 %