Chapter 10, Problem 18P

WACC AND OPTIMAL CAPITAL BUDGET Adamson Corporation is considering four average-risk projects with the following costs and rates of return:

Project	Cost	Expected Kate of Return
1	$2,000	16.00%
2	3,000	15.00
3	5,000	13.75
4	2,000	12.30

The company estimates that it can issue debt at a rate of r_d = 10%, and its tax rate is 30%. It can issue preferred stock that pays a constant dividend of $5.00 per year at $50.00 per share. Also, its common stock currently sells for $38.00 per share; the next expected dividend, D₁, is $4.25, and the dividend is expected to grow at a constant rate of 5% per year. The target capital structure consists of 75% common stock, 15% debt, and 10% preferred stock.

1. a. What is the cost of each of the capital components?
2. b. What is Adamson's WACC?
3. c. Only projects with expected returns that exceed WACC will be accepted. Which projects should Adamson accept?

Summary Introduction

To determine: The cost of each of the capital components.

Introduction:

Cost of Capital:

In any company there is a need of fund for various purposes. The companies raise capital through various sources such as equity, debt, and preferred stock. The cost of capital is the total cost of raising capital. It consists of cost of debt, cost of equity, and cost of the preferred stock.

After-Tax Cost of Debt:

It can be defined as relevant cost of new debt considering tax deductibility in interest. It is the cost of debt after tax savings.  The interest on the debt is tax deductible. The tax can be saved on the interest paid on the debt. It is used to calculate the weighted average cost of capital.

Cost of Preferred Stock:

The return earned by the firm’s preferred stockholders from the investment in preferred stock is a cost of the preferred stock. It is computed by dividing the dividend received on preferred stock by the current price of the preferred stock.

Cost of Equity:

It is the cost of the company while raising finance by issuing equity. It is the earnings from the investment to the firm’s equity investors. It is the return to the stockholders’  equity investments. The issue of new stock incurs the flotation cost.

Explanation of Solution

Cost of debt:

Given,

Before-tax cost of debt is 10%.

Tax rate is 30%.

The formula to calculate after-tax cost of debt is:

$\text{After-Tax Cost of Debt}={\text{r}}_{\text{d}}\left(1-\text{T}\right)$

Where

• ${\text{r}}_{\text{d}}$ is the interest on new debt.
• T is the tax rate

Substitute 10% for ${\text{r}}_{\text{d}}$ and 0.30 for the rate in above formula.

$\begin{array}{c}\text{After-Tax Cost of Debt}=10\%\left(1-0.30\right)\\ =10\%\times 0.70\\ =7\%\end{array}$

Thus, after-tax cost of debt is 7%.

Cost of Preferred stock:

Given,

Dividend per share is $5.

Price of stock is $50 per share.

The formula to calculate the cost of preferred stock is:

$\text{Cost of Preferred Stock}=\frac{{\text{D}}_{\text{P}}}{{\text{P}}_{\text{P}}}$

Where,

• ${\text{D}}_{\text{P}}$ is the preferred dividend.
• ${\text{P}}_{\text{P}}$ is the current price of preferred stock.

Substitute $5 for ${\text{D}}_{\text{P}}$ and $50 for ${\text{P}}_{\text{P}}$ in above formula.

$\begin{array}{c}\text{Cost of preferred stock}=\frac{\$5}{\$50}\\ =0.10\text{ or }10\%\end{array}$

Thus the cost of preferred stock is 10%.

Cost of Equity

Given,

Expected dividend, ${\text{D}}_{\text{1}}$ is $4.25.

Current market price ${\text{P}}_{\text{0}}$ is $38 per share.

Growth rate is 5% or 0.05.

The formula to calculate cost of the equity is:

$\text{r}=\frac{{\text{D}}_1}{{\text{P}}_0}+\text{g}$

Where,

• ${\text{D}}_1$ is the next expected divided.
• ${\text{P}}_{\text{0}}$ is the current market price
• g is the growth rate

Substitute $4.25 for ${\text{D}}_1$, $38 for ${\text{P}}_0$, 0.05 for g in above formula.

$\begin{array}{l}\text{r}=\frac{\$4.25}{\$38}+0.05\\ =0.1118+0.05\\ =0.1618\text{ or }16.18\%\end{array}$

Thus, the cost of equity is 16.18%.

Conclusion

Therefore, after tax cost of debt, cost of preferred stock and cost of equity are 7%, 10% and 16.18% respectively.

Summary Introduction

To determine: WACC of A Corporation.

Introduction:

Weighted Average Cost of Capital:

It is the weighted average cost of capital of all the sources through which a firm finances its capital. It is the rate that a company will pay to all for raising finance. It can be termed as firm’s cost of capital. The company raises money through various sources such as common stock and preference share debt. The WACC is computed by taking the relative weight of each item of capital structure.

Explanation of Solution

Given information:

Weight of debt is 15%.

Weight of equity is 75%.

Weight of preferred stock is 10%

Calculated info,

After tax cost of debt is 7%.

Cost of common equity is 16.18 %.

Cost of preferred stock is 10 %.

The formula to compute the WACC is:

$\text{WACC}={\text{W}}_{\text{d}}{\text{r}}_{\text{d}}\left(1-\text{t}\right)+{\text{W}}_{\text{P}}{\text{r}}_{\text{p}}+{\text{W}}_{\text{c}}{\text{r}}_{\text{s}}$

Where,

• ${\text{W}}_{\text{d}}$ is the weight of the debt.
• ${\text{W}}_{\text{P}}$ is the weight of the preferred stock.
• ${\text{W}}_{\text{c}}$ is the weight of the equity.
• ${\text{r}}_{\text{d}}$ is cost of the debt.
• ${\text{r}}_{\text{P}}$ is cost of the preferred stock.
• ${\text{r}}_{\text{c}}$ is the cost of the equity.

Substitute 0.07 for ${\text{r}}_{\text{d}}$, 0.15 for ${\text{W}}_{\text{d}}$, 0.1618 for ${\text{r}}_{\text{s}}$ and 0.75 for ${\text{W}}_{\text{c}}$, 0.10 for ${\text{W}}_{\text{p}}$ and 0.10 for ${\text{r}}_{\text{p}}$ in the above formula.

$\begin{array}{c}\text{WACC}=0.15\times 0.07+0.75\times 0.1618+0.10\times 0.10\\ =0.0105+0.12135+0.01\\ =0.1419\text{ or }14.19\%\end{array}$

Conclusion

Therefore, WACC of A Corporation is 14.19%.

Summary Introduction

To identify: The projects that should be accepted by A Corporation. If only the project with expected returns more than WACC should be accepted.

Answer to Problem 18P

The WACC is 14.19%. So, the both projects 1 and 2 should be accepted.

Explanation of Solution

• The expected return from project is 1 is 16% which is higher than WACC. So it should be accepted because the expected return is higher than the cost of capital.
• The expected return from project 2 is `15% which is higher than WACC. So it should be accepted because the expected return is higher than the cost of capital
• The expected return from the remaining projects is less than WACC.

Conclusion

Therefore, the projects 1 and 2 should be accepted.