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. Hot Water has a debt to total value ratio of 0.7. The expected return on the market is 0.1, and the riskfree rate is 0.07. Suppose the corporate tax rate is 37 percent. Assume that debt is riskless throughout this problem.

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 2, the weighted average cost of capital for the project is %.
d.	The finance manager believes that the solar water heater project can support 25 cents of debt for every dollar of asset value, i.e., the debt capacity is 25 cents for every dollar of asset value. Hence she is not sure that the debt to equity ratio of 2 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

Please round off your answers as per your requirement.

Your answers appear in Bold & underline.

The (equity) beta of Hot Water, a firm currently producing solar water heaters, is 1. Hot Water has a debt to total value ratio of 0.7.

Based on this: levered beta, B_L = 1

Debt to total value ratio = D / (D + E) = 0.70; Hence, 0.7(D + E) = D; hence D / E = 0.7 / 0.3 = 7 / 3

The corporate tax rate, T = 37%

Unlevered beta, B_U = B_L / [1 + (1 - T) x D / E] = 1 / [1 + (1 - 37%) x 7 / 3] = 0.4048583

Part (a)

The expected return on the unlevered equity (return on asset, R₀) for the solar water heater project = Risk free rate + B_U x (expected return on the market - risk free rate) = 0.07 +  0.4048583 x (0.10 - 0.07) = 0.082145749 = 8.21%

==============================

Part (b)

If Hula is an equity financed firm, the weighted average cost of capital for the project = same as expected return on the unlevered equity = 8.21%

================================

Part (c)

If Hula has a debt to equity ratio of 2, the weighted average cost of capital for the project is %.

D / E = 2; Proportion of debt in capital structure, Pd = D / (D + E) = 2 / 3 and proportion of equity in capital structure, Pe = 1 - Pd = 1 - 2/3 = 1/3

Hula's levered beta = B_H,L = B_U x [1 + (1- T) x D / E] = 0.4048583 x [1 + (1 - 37%) x 2] =  0.9150

Hula's cost of equity, Ke = Risk free rate + B_H,L x (expected return on the market - risk free rate) = 0.07 +  0.9150 x (0.10 - 0.07) = 0.082145749 = 9.74%

Pre tax cost of debt, Kd = risk less rate = 0.07 = 7%

Hence weighted average cost of capital for the project is = Pd x Kd x (1 - T) + Pe x Ke = 2 / 3 x 0.07 x (1 - 37%) + 1 / 3 x 9.74% = 0.061883131 = 6.19%

=====================

Part (d)

The finance manager believes that the solar water heater project can support 25 cents of debt for every dollar of asset value, i.e., the debt capacity is 25 cents for every dollar of asset value. Hence she is not sure that the debt to equity ratio of 2 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 %.

Debt to total asset = D / (D + E) = 0.25; D = 0.25 x (D + E); Hence, D / E = 09.25 / 0.75 = 1 / 3

Based on her belief, the appropriate debt ratio to use is 25.00%.

D / E = 1 / 3; Proportion of debt in capital structure, Pd = D / (D + E) = 0.25 and proportion of equity in capital structure, Pe = 1 - Pd = 1 - 0.25 = 0.75

Hula's levered beta = B_H,L = B_U x [1 + (1- T) x D / E] = 0.4048583 x [1 + (1 - 37%) x 1 / 3] = 0.4899

Hula's cost of equity, Ke = Risk free rate + B_H,L x (expected return on the market - risk free rate) = 0.07 +  0.4899 x (0.10 - 0.07) = 0.084696 = 8.47%

Pre tax cost of debt, Kd = risk less rate = 0.07 = 7%

Hence weighted average cost of capital at this capital structure = Pd x Kd x (1 - T) + Pe x Ke = 0.25 x 0.07 x (1 - 37%) + 0.75 x 8.47% =  0.0745473 = 7.45%