Question

Before-tax cost of debt (B-T rd) 8%

Tax rate 34%

Net Price of Preferred stock (after deducting floatation costs) $32.00

Dividend per share of Preferred $3.40

Current price of Common stock stock $52.00

Dividend paid in the recent past for Common $2.50

Growth rate 6%

Stock Beta 0.81

Market risk premium, (MRP) 6.2%

Risk free rate ( rf ) 5.5%

Flotation cost for common stock 5%

Weight of debt in the target capital structure 40%

Weight of preferred stock in the target capital structure 10%

Weight of common stock in the target capital structure 50%

Calculate the cost of debt (after tax cost of debt), cost of preferred stock,

the cost of equity (ignoring flotation costs) with the DCF method and the CAPM method.

1. Cost of Common Equity:

CAPM   R = Rf + β*(RM - Rf) R=

(RM - Rf) = Market Risk Premium

DDM   R = D1 + g R=

Po

2. Cost of Preferred stock: RP = D Rp=

   PV

3. Cost of Debt:

a. Cost of debt is calculated as before-tax and after-tax.

Before tax calculation is the same as the YTM calculation (will show you an example in class)

YTM can be calculated using TVM on a financial calculator.

b. Coverting before tax cost of debt into after-tax cost of debt:

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

4. Weighted Average Cost of Capital (WACC)

Include Preferred stock into the equation.

e. Suppose Gao is evaluating three projects with the following characteristics:

(1) Each project has a cost of $1 million. They will all be financed using the target mix of

long ter debt, preferred stock, and common equity.

The cost of the common equity for each project should be based on the beta estimated for

the project. No new equity will be issued.

(2) Equity invested in Project A would have a beta of 0.6 and an expected return of 9.2%.

(3) Equity invested in Project B would have a beta of 1.2 and an expected return of 10.8%.  

(4) Equity invested in Project C would have a beta of 1.90 and an expected return of 10.8%.

f. Analyze the company’s situation and explain why each project should be accepted or rejected.

Beta rs rps rd(1-T) WACC Expected return on project Accept Reject

Project A

Project B

Project C

You can accepot the project as long as the WACC is less than expected return.

Answer 1

1) Cost of common equity using CAPM

R = Rf + β*(RM - Rf)

= 5.5% + 0.81*6.2%

= 10.52%

cost of equity using DDM

Price of share = D₁ / K-g (where k is the required rate of return and g is the growth rate)

52 = (2.5*1.06) / k - 0.06

k = 11.09%

Cost of common equity = average of cost of equity

= (10.52%+ 11.09%)/2

= 10.81%

2) Cost of preferred stock = dividend / price of stock

= 3.4 / 32

= 10.62%

3) Cost of debt = before tax cost of debt * (1-tax rate)

= 8% (1-0.34)

= 5.28%

4) WACC

	Cost	Weight	Weighted cost
Common Equity	0.1081	0.5	0.0540
Preferred stock	0.1063	0.1	0.0106
Debt	0.0528	0.4	0.0211
WACC			0.0858

hence WACC is 8.58%