Chapter 10, Problem 22IC

a.

1.

Summary Introduction

To determine: The sources of capital should be included while estimating WACC.

Introduction:

Cost of Capital:

In any company, there is need of the 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 the cost of debt, cost of equity, and cost of preferred stock.

Weighted Average Cost of Capital:

It is the weighted average cost of capital of all the sources through which firm finances its capital. It is that rate that 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, preference share debt the WACC is calculated taking the relative weight of each item of capital structure.

Answer to Problem 22IC

The capital sources that should be included when you estimate WACC are:

• Non-callable bonds.
• Preferred stock
• Common stock

Explanation of Solution

• The fixed amount of interest is paid to non-callable bonds.
• The dividend is paid on to common stockholders and preferred stockholders.

Conclusion

Therefore, non-callable bonds, preferred stock,and common stock are the sources of capital which should be included while estimating WACC of the company.

2.

Summary Introduction

To discuss: The component cost should be figured on before-tax or an after-tax basis.

Explanation of Solution

WACC should be calculated after considering the tax expenses to the company because the net income remaining is distributed to the stakeholders.

Conclusion

Therefore, the component cost must be figured on an after-tax basis.

3.

Summary Introduction

To discuss: The cost should be historical (embedded cost or new (marginal) costs.

Explanation of Solution

The marginal cost is more relevant than historical cost.

While making a decision regarding the investment in the new project, the cost in present is relevant on this case. The historical cost is not used to make an estimation of the project and it seems irrelevant.

Conclusion

Therefore, the marginal cost should be used.

b.

Summary Introduction

To determine: The market interest rate in C company debt and its component cost of debt.

Introduction:

Yield to Maturity

The rate of return which is received by the bondholder if the bonds are held up to the ending year is called Yield to maturity.

After-Tax Cost of Debt

It can be defined as the 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 save on the interest paid on the debt. It is used to calculate the weighted average cost of capital.

Explanation of Solution

Yield to maturity (Market rate)

Given,

The current price of the bond (P) is $1,153.72.

Interest payment on the bond is semi-annual

Coupon rate(C) ID 12%

Maturity amount (F) is $1000.00.

Period of the bond is 15 years

No of interest payment (n) is 30.

The formula to calculate yield to maturity (market interest rate):

$\text{YTM}=\frac{\text{C}+\left(\frac{\text{F}-\text{P}}{\text{n}}\right)}{\left(\frac{\text{F}+\text{P}}{2}\right)}$

Where,

• YTM is a yield to maturity.
• C is a Coupon value.
• F is a face value.
• P is a current price.
• N is a period of the bond.

Substitute $60 for C, $1,000 for F, $1,153.72 for P and 30 for n in above formula.

$\begin{array}{c}\text{YTM}=\frac{\$60+\left(\frac{\$1,000-\$1,153.72}{30}\right)}{\left(\frac{\$1,000+\$1,153.72}{2}\right)}\\ =\frac{\$54.876}{\$1076.86}\\ =5\%\end{array}$

The annual rate of YTM is

$\begin{array}{r}\text{YTM}\left(\text{Annual}\right)=5\%\times 2\\ =10\%\end{array}$

Thus, yield to maturity is 10%.

The after-tax cost of debt

Given,

Before-tax cost of debt is 10%

The tax rate is 40%.

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 0.40 for the t in above formula.

$\begin{array}{c}\text{After-Tax Cost of Debt}=10\%\left(1-0.40\right)\\ =10\%\times 0.60\\ =6\%\end{array}$

Thus, the after-tax cost of debt is 6%.

Conclusion

Therefore, market interest rate and component cost of debt is 10% and 6%.

c.

1.

Summary Introduction

To determine: The firm’s cost of preferred stock.

Introduction:

Cost of Preferred Stock

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

Explanation of Solution

Given information:

Dividend per share is $10 per share.

The current price of the stock is $111.10 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 the preferred stock

Substitute $10 ${\text{D}}_{\text{P}}$ and $111.10 for ${\text{P}}_{\text{P}}$ in above formula.

$\begin{array}{c}\text{Cost of Preferred Stock}=\frac{\$10}{\$111.10}\\ =9\%\end{array}$

Thus the cost of preferred stock is 9%.

Conclusion

Therefore, the cost of preferred stock is 9%.

2.

Summary Introduction

To determine: The selection of the riskier investment in preferred stock which yields less return to investors in comparison is a mistake or not.

Explanation of Solution

The dividend on preferred stock is non-taxable in the most cases, but interest payable on debt is taxable. The investors are liable to pay tax on interest earned on debt. Thus even if the return in preferred stock is lower than the return from the debt it is not a mistake to choose preferred stock over-investment in debt.

The preferred stocks are normally tax-free so investors would prefer to preferred stock rather than debt.

Conclusion

Therefore, choosing the riskier investment in preferred stock which yields less return to investors in comparison is not a mistake.

d.

1.

Summary Introduction

To determine: The reason for cost associated with retained earnings.

Introduction:

Cost of Retained Earnings

The Company can raise its capital by issuing new shares by retaining its current earnings. The companies normally retain a certain percentage of their earnings and after some time it is invested by the company. The cost is retained earnings is determined on the basis of opportunity cost principle.

Capital Assets Pricing Model (CAPM)

As per this approach, the equity cost is the required return to the investors which is minimum return expected by the investors to take an additional risk. This can be calculated by adding the risk premium to the risk-free rate. The risk premium is the cost of taking additional risk. The formula of cost of equity as per this approach is:

${\text{r}}_{\text{s}}={\text{r}}_{\text{RF}}+\left({\text{r}}_{\text{M}}-{\text{r}}_{\text{RF}}\right){\text{b}}_{\text{i}}$

Where,

• ${\text{r}}_{\text{s}}$ is the rate of return on the stock
• ${\text{r}}_{\text{RF}}$ is the is risk-free return.
• ${\text{r}}_{\text{M}}$ is the market rate of return
• ${\text{b}}_{\text{i}}$ is the beta of security

Answer to Problem 22IC

The certain percent of the net income of the company is retained. The retained earnings are further invested with an expectation of return. Thus, the cost is associated with it.

Explanation of Solution

The retained earnings are assumed as free cost generally but it is wrong because the cost of retained earnings can be measured as per opportunity cost principle If the company has no retained earning company issues new shares in which the shareholders earn the dividend. Thus, the lost of dividend can be considered as the opportunity cost of the retained earnings.

Conclusion

Therefore, the retained earnings are held as an investment so the cost is associated with it.

2.

Summary Introduction

To determine: The cost of common equity using CAPM approach.

Explanation of Solution

Given information:

The risk-free rate of return is 7%.

Beta is 1.2.

The market risk premium is 6%.

The formula of cost of equity is:

$\begin{array}{c}\text{Cost of Equity}=\text{Risk-free Rate}+\text{Beta}\left(\text{Market return}-\text{ Risk-free return}\right)\\ ={\text{R}}_{\text{f}}+\text{β}\left({\text{R}}_{\text{m}}-{\text{R}}_{\text{f}}\right)\end{array}$

Substitute 7% for ${\text{R}}_{\text{f}}$1.2 for $\text{β}$ and 6% for $\left({\text{R}}_{\text{m}}-{\text{R}}_{\text{f}}\right)$ in above formula.

$\begin{array}{c}\text{Cost of Equity}=7\%+1.2\times 6\%\\ =7\%+7.2\%\\ =14.2\%\end{array}$

Conclusion

Therefore, cost of common equity as per CAPM approach is 14.2%.

(e)

Summary Introduction

To determine: The estimated cost of equity using the DCF approach.

Introduction:

DCF Approach

In this approach, the value of the stock of the company is the present value of its all cash flows discounted at the required return of the investors. The formula to find the cost of equity assuming the expected growth rate constant is:

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

Where

• ${\text{D}}_1$ is the next expected dividend
• ${\text{P}}_0$ is the current price of the stock
• g is the constant growth rate.

Explanation of Solution

Given information:

The last dividend is $4.19.

The growth rate is 5% or 0.05.

The current price of the stock is $50.

The formula for the cost of common equity is:

${\text{r}}_{\text{s}}=\frac{{\text{D}}_0\left(1+\text{g}\right)}{{\text{P}}_0}+\text{g}$

Where

• ${\text{D}}_0$ is the last dividend.
• ${\text{r}}_{\text{s}}$ is the rate return on equity
• ${\text{P}}_0$ is the current price of the stock
• g is the constant growth rate.

Substitute $4.19 for ${\text{D}}_0$, $50 for ${\text{P}}_0$ and 0.05 for constant growth rate in above formula.

$\begin{array}{c}{\text{r}}_{\text{s}}=\frac{\$4.19\left(1+0.05\right)}{\$50}+0.05\\ =\frac{\$4.40}{\$50}+0.05\\ =0.088+0.05\\ =13.8\%\end{array}$

Thus,the cost of common equity is 13.8%.

Conclusion

Therefore, the estimated cost of equity using DCF approach is 13.8%.

f.

Summary Introduction

To determine: The estimated cost of equity using bond-yield-plus-risk-premium.

Introduction:

Bond-Yield-Plus-Risk-Premium

As per this approach, the cost of equity is the total of the bond yield and risk premium.

Explanation of Solution

Given information:

Bond yield is 10%.

The riskpremium is 4%.

The formula to calculate the cost of equity is:

$\text{Cost of Equity}=\text{Bond Yeild}+\text{Risk Premium}$

Substitute 10% for bond yield and 4% for the risk premium in above formula.

$\begin{array}{c}\text{Cost of Equity}=10\%+4\%\\ =14\%\end{array}$

Thus, cost of equity is 14%.

Conclusion

Therefore, the cost of equity as per bond-yield-risk-premium is 14%.

g.

Summary Introduction

To determine: The final estimate for ${\text{r}}_{\text{s}}$

Explanation of Solution

Given information:

Cost of equity as per CAMP approach is 14.2%

Cost of equity as per Constant growth model is 13.8%.

Cost of equity as per Bond-yield-plus-risk-premium is14%.

The estimated cost of common equity of C Company is average of all above approaches, so the average is:

$\begin{array}{c}\text{Cost of Equity}=\text{Average of all Above Approches}\\ =\frac{\text{14}\text{.2\%+13}\text{.8\%+14\%}}{3}\\ =14\%\end{array}$

Thus the average cost of equity is 14%.

Conclusion

Therefore, the final estimate for ${\text{r}}_{\text{s}}$ is 14%.

(i)

1.

Summary Introduction

To determine: The two approaches that can be used to adjusted for flotation costs.

Introduction:

Flotation Cost

The cost which occurred when the new shares are issued by the company is called floatation cost. It increases the cost of newly issued shares.

Answer to Problem 22IC

The 2 approaches that can be used to adjust the flotation costs are:

• Up-front cost
• Adjust cost of capital

Explanation of Solution

Among above mentioned two approaches, the most common technique used to adjust for the flotation cost is Adjust cost of capital.

Conclusion

Therefore, Up-front cost and adjust the cost of capital are the two approaches to adjust for flotation costs.

2.

Summary Introduction

To determine: The projected cost of newly issued common stock, considering flotation cost.

Explanation of Solution

Given information:

The last dividend is $4.19.

Current market price ${\text{P}}_{\text{0}}$ is $50 per share.

The growth rate is 5%

Flotation cost is 15%.

The formula to calculate the cost of the equity is:

${\text{r}}_{\text{s}}=\frac{{\text{D}}_0\left(1+\text{g}\right)}{{\text{P}}_0\left(1-\text{F}\right)}+\text{g}$

Where,

• ${\text{D}}_0$ is the last dividend.
• ${\text{r}}_{\text{s}}$ is the rate return on equity
• ${\text{P}}_0$ is the current price of the stock
• g is the constant growth rate.
• F is the flotation cost.

Substitute $4.19 for ${\text{D}}_0$ $50 for ${\text{P}}_0$, 0.05 for g and 0.15 for flotation cost in above formula.

$\begin{array}{c}{\text{r}}_{\text{s}}=\frac{\$4.19\left(1+0.05\right)}{\$50\left(1-0.15\right)}+0.05\\ =\frac{\$4.19\times 1.05}{\$50\times 0.85}+0.05\\ =\frac{\$4.40}{42.50}+0.05\\ =15.4\%\end{array}$

Conclusion

Therefore, the cost of common equity, considering the flotation cost is 15.4%.

(j)

Summary Introduction

To determine: The overall, or weighted average, cost of capital (WACC).

Explanation of Solution

Component	After-tax Cost	Proportion	WACC
Common Stock	14%	0.60	8.4%
Preferred Stock	9%	0.10	0.90%
Debt	6%	0.30	1.80%
Total			11.10%

Table (1)

Conclusion

Therefore, weighted average cost of capital is 11.10%.

k.

Summary Introduction

To identify: The factors which influence C company composite WACC.

Answer to Problem 22IC

• Capital structure
• Dividend policy
• Rate of interest
• Corporate tax rates
• The risk associated with the investment.

Explanation of Solution

• The capitalstructure of the firm influences the WACC. The proportion of debt and equity in the capital structure
• Dividend policy of the company influences the WACC.
• The WACC is influenced by the interest rate. Increase or decrease in interest rate changes WACC accordingly
• Corporate tax rateaffects the calculation of the WACC.
• The higher the risk in investment higher chances of return and higher cost of capital

Conclusion

Therefore above-mentioned factors like Capital structure, interest rate. Tax rates dividend policy and risk factors influence the WACC.

l.

Summary Introduction

To identify: The Company should use the composite WACC as the hurdle rate each of its projects.

Answer to Problem 22IC

The company should not use the composite WACC as the hurdle rate for each of its projects because different projects are exposed different risk.

Explanation of Solution

The WACC is influenced by the risk associated with the project. It is based on risk factors. Some projects are highly exposed to a risk which other are comparatively less risk. The WACC of the project should be adjusted with the risk associated with the project.

Conclusion

Therefore, the Company should not use the composite WACC as the hurdle rate for each of its projects because risk level in projects is different.