Activity 1

An all-equity company operates in an industry where its beta factor is 0.90. It is considering whether

to invest in a completely different industry. In this other industry, the average debt/equity ratio is

40% and the average beta factor is 1.25. The risk-free rate of return is 4% and the average market

return is 7%. If the company does invest in this other industry, it will remain all-equity financed. The

rate of taxation is 30%. Assume that debt is risk-free. Required

What cost of capital should be used to evaluate the proposed investment?

 

Activity 2

A company is planning to invest in a project in a new industry where it has not invested before. The

asset beta for the project has been estimated as 1.35. The project will be financed two-thirds by

equity capital and one-third by debt capital. The rate of taxation on company profits is 30%. Assume

that the debt capital is risk-free. The risk-free rate of return is 3% and the market return is 8%. What cost of equity should be used to

calculate the marginal cost of capital for this project?

 

Activity 3

A company is considering whether to invest in a new capital project where the business risk will be

significantly different from its normal business operations. The company is financed 80% by equity

capital and 20% by debt capital. It has identified three companies in the same industry as the

proposed capital investment and has obtained the following information about them:

(1) Company 1 has an equity beta of 1.05 and is financed 30% by debt capital and 70% by equity. (2) Company 2 has an equity beta of 1.24 and is financed 50% by debt capital and 50% by equity. (3) Company 3 has an equity beta of 1.15 and is financed 40% by debt capital and 60% by equity. The risk-free rate of return is 5% and the market rate of return is 8%. Tax on company profits is at

the rate of 30%. Assume that the debt capital in each company is risk-free. Required:

Calculate a project-specific discount rate for the project, assuming that this is:

(a) the project-specific cost of equity for the project, or

(b) the weighted average of the project-specific equity cost and the company's cost of debt capital.

1. Cost of capital = 6.31%

Cost of capital in case of all-equity firm = 6.7%

 

2. Cost of capital = 7.23%

 

3. Company 1:

Cost of equity = 8.15%

Cost of capital = 6.76%

 

Company 2:

Cost of equity = 8.72%

Cost of capital = 6.11%

 

Company 3:

Cost of equity = 8.45%

Cost of capital = 5.48%

Step-by-step explanation

1. Risk-free rate = 4%

Average market return = 7%

Beta = 1.25

 

Cost of equity = Risk-free rate + [Beta * (Market return - Risk-free rate)]

                      = 4% + [1.25 * (7% - 4%)]

                      = 7.75%

 

Cost of debt = 4% * (1 - 0.30)

                   = 2.8%

 

Debt/equity ratio = 40/100

Weight of debt = 40/140 = 0.29

Weight of equity = 100/140 = 0.71

 

Cost of capital = (Cost of debt * Weight of debt) + (Cost of equity * Weight of equity)

                        = (2.8% * 0.29) + (7.75% * 0.71)

                        = 6.31%

 

Beta factor = 0.90

 

Cost of capital in case of all-equity firm = 4% + [0.90 * (7% - 4%)]

                                                              = 6.7%

 

2. Risk-free rate = 3%

Average market return = 8%

Beta = 1.35

 

Cost of equity = Risk-free rate + [Beta * (Market return - Risk-free rate)]

                      = 3% + [1.35 * (8% - 3%)]

                      = 9.75%

 

Cost of debt = 3% * (1 - 0.30)

                   = 2.1%

 

Weight of debt = 1/3 = 0.33

Weight of equity = 2/3 = 0.67

 

Cost of capital = (Cost of debt * Weight of debt) + (Cost of equity * Weight of equity)

                        = (2.1% * 0.33) + (9.75% * 0.67)

                        = 7.23%

 

3. Risk-free rate = 5%

Average market return = 8%

 

Company 1:

Beta = 1.05

Cost of equity = Risk-free rate + [Beta * (Market return - Risk-free rate)]

                      = 5% + [1.05 * (8% - 5%)]

                      = 8.15%

 

Cost of debt = 5% * (1 - 0.30)

                   = 3.5%

 

Weight of debt = 30%

Weight of equity = 70%

 

Cost of capital = (Cost of debt * Weight of debt) + (Cost of equity * Weight of equity)

                        = (3.5% * 0.30) + (8.15% * 0.70)

                        = 6.76%

 

Company 2:

Beta = 1.24

Cost of equity = Risk-free rate + [Beta * (Market return - Risk-free rate)]

                       = 5% + [1.24 * (8% - 5%)]

                       = 8.72%

 

Cost of debt = 5% * (1 - 0.30)

                   = 3.5%

 

Weight of debt = 50%

Weight of equity = 50%

 

Cost of capital = (Cost of debt * Weight of debt) + (Cost of equity * Weight of equity)

                        = (3.5% * 0.50) + (8.72% * 0.50)

                        = 6.11%

 

Company 3:

Beta = 1.15

Cost of equity = Risk-free rate + [Beta * (Market return - Risk-free rate)]

                       = 5% + [1.15 * (8% - 5%)]

                       = 8.45%

 

Cost of debt = 5% * (1 - 0.30)

                    = 3.5%

 

Weight of debt = 40%

Weight of equity = 60%

 

Cost of capital = (Cost of debt * Weight of debt) + (Cost of equity * Weight of equity)

                        = (3.5% * 0.60) + (8.45% * 0.40)

                        = 5.48%