Question

Carpetto Technologies Inc. has a market capitalisation of $50 million and $50 million in outstanding debt. Its corporate tax rate is 31%.

1. The beta of Carpetto Technologies Inc. is 1.7, the risk-free rate is 8.5%, and the return on market is 13.5%, what will be Carpetto’s cost of common equity using the Capital Asset Pricing Model (CAPM) approach?
2. Suppose Carpetto’s debt of cost of capital is 10.5%. What is Carpetto’s after tax debt of cost of capital?
3. What is unlevered cost of capital for Carpetto?    
4. What is the weighted average cost of capital (WACC) for Carpetto?
5. Why its WACC (in part (iv)) is lower than the unlevered cost of capital (in part (iii))?

Answer 1

Solution

i. Cost of common equity using Capital Asset Pricing Model approach = Rf + Beta ( Rm - Rf )

Cost of equity = 8.5 + 1.7 (13.5 - 8.5)

= 8.5 + 1.7 * 5

= 8.5 + 8.5

= 17 %

ii. Carpetto's debt of cost of capital = 10.5%

After tax cost of debt capital = cost of capital * ( 1 - tax rate)

= 10.5 ( 1 - 0.31)

= 7.245%

iii. Unlevered cost of capital is the rate of return a company expects without the debt.

Unlevered means no debt only equity

At 100 % equity, Equity beta is equal to Overall beta

Overall beta = Equity beta * { Value of Equity / value of equity + value of debt( 1 - tax) }+ Debt beta * { Value of debt / Value of equity + Value of debt(1 - tax) }

Unlevered cost of capital = Rf + Beta ( Rm - Rf)

= 8.5 + 1.7 ( 13.5 - 8.5)

= 17 %

iv. Weighted Average Cost of Capital ( WACC)

= Cost of equity * ( Value of equity / Total Capital ) + Cost of debt (1 - tax rate) * (Value of debt/ Total Capital)

= 17 * 50/100 + 10.5(1- 0.31) * 50/100

= 8.5 + 3.623

= 12.123 %

Total capital = Equity + Debt

$ 50 million + $ 50 million

= $100 million

v. Carpetto's WACC in point iv is less than unlevered cost of capital in point iii because in calculating WACC the cost of equity and cost of debt both has been taken into account and in unlevered option where the company has no debt but only equity.

The cost of equity is higher that is 17 % so unlevered cost of equity will be higher. While calculating WACC cost of equity has been proportioned to the vlaue of equity in the company and same for debt. And the fkst of debt is less than cost of equity so the resulting WACC is less.