Question

Assume that your firm consists of Division 1 (40 percent of the firm) and Division 2 (60 percent of the firm). The capital structure for each of the divisions is the same as for the firm as a whole; 20.0 percent debt, at a before-tax cost of debt of 6.0 percent, and 80.0 percent equity (i.e., D/E-0.25). Also assume that the firm calculates the cost of equity for each division using a divisional beta, where Division 1 has an unlevered beta of 1.20, while Division 2 has an unlevered beta of 1.46. Finally assume that the risk-free rate is 4.0 percent and the expected return on the market is 12.0 percent, and the firm's tax rate is 40%.Given this information, determine the difference between the WACC for Division 1 and the WACC for Division 2 Answer in decimal format, rounded to 4 decimal places. For example, if your answer is 1.334%, enter "O.0133"

Answer 1

WACC of division 2 - WACC of division 1 = 1.9136%

Step-by-step explanation:

Firstly, when we adjust beta of firm (unlevered beta) for financial leverage, we wil have equity beta (levered beta). Equity beta will be calculated as below:

Levered beta = Unlevered beta x [1 + (1 - Tax rate) x (Debt/Equity)]

Putting relevant number together, we have:

Levered beta of division 1 = 1.2 x [1 + (1 - 40%) x 0.25] = 1.38.

Levered beta of division 2 = 1.46 x [1 + (1 - 40%) x 0.25] = 1.679.

Next, we will calculated cost of equity for each division using capital asset pricing model:

Cost of equity = Risk-free rate + Beta x (Expected market return - Risk-free rate)

Putting relevant number together, we have:

Cost of equity of division 1 = 4% + 1.38 x (12% - 4%) = 15.04%.

Cost of equity of division 2 = 4% + 1.679 x (12% - 4%) = 17.432%.

Finally we will calulate WACC of each divsion as below:

WACC = After tax cost of debt x (Debt/Asset) + Cost of equity x (Equity/Asset)

Putting all the numbers together, we have:

WACC of division 1 = 6% x (1 - 40%) x 20% + 15.04% x 80% = 12.752%.

WACC of division 2 = 6% x (1 - 40%) x 20% + 17.432% x 80% = 14.6656%.

So, WACC of division 2 - WACC of division 1 = 1.9136%.

Answer 2

Division 1's WACC - Division 2's WACC = 11.752% - 14.6656% = - 1.9136% or Division 1 has the lower cost of capital of 1.9136% in absolute term comparing to Division 2.

Step-by-step explanation:

Before starting, we need to convert unlevered beta into levered beta:

Levered beta of Division 1: 1.2 x ( 1 + (1-40%) x 0.25) = 1.38

Leverage beta of Division 2: 1.46 x ( 1+ (1-40%) x 0.25) = 1.679

Then, we start step by step as below:

First, using the CAPM model: Cost of equity = risk-free rate of return + beta *(Market Rate of Return – Risk-free Rate of Return) , we find the cost of equity for Division 1 and Division 2.

- Division 1's cost of Equity = 4% + 1.38 x( 12% -4%) = 15.04%

- Division 2's cost of equity = 4% + 1.46 x (12% - 4%) = 17.432%

Second, determine the post-tax cost of debt applied for both Division: 6% x (1-tax rate) = 6% x (1 -40%) = 3.60%

Third, calculate the WACC for each Division:

- Division 1's WACC = % of debt in capital structure x cost of debt + % of equity in capital structure x cost of equity = 20% x 3.6% + 80% x 15.04% = 11.752%;

- Division 2's WACC = % of debt in capital structure x cost of debt + % of equity in capital structure x cost of equity = 20% x 3.6% + 80% x 17.432% = 14.6656%;

Finally, compare the WACC between the two Division:

Division 1's WACC - Division 2's WACC = 11.752% - 14.6656% = - 1.9136% or Division 1 has the lower cost of capital of 1.9136% in absolute term comparing to Division 2.