Chapter 9, Problem 23IC

MUTUAL Of CHICAGO INSURANCE COMPANY

9-23 STOCK VALUATION Retort Balik and Carol Kiefer we senior vice presidents of the Mutual of Chicago Insurance Company. They are co-directors of the company’s pension fund management division, with Balik having responsibility for fixed-income securities (primarily bonds) and Kiefer being responsible for equity investments. A major new client, the California League of Cities, has requested that Mutual of Chicago present an investment seminar to the mayors of the represented cities, and Balik and Kiefer, who will make the actual presentation, have asked you to help them.

To illustrate the common stock valuation process, Balik and Kiefer have asked you to analyze the Bon Temps Company, an employment agency that supplies word-processor operators and computer programmers to businesses with temporarily heavy workloads. You are to answer the following questions:

1. a. Describe briefly the legal rights and privileges of common stockholders.
   1. 1. Write a formula that can to used to value any stock, regardless of its dividend pattern.
   2. 2. What is a constant growth stock’ How are constant growth stocks valued?
   3. 3. What air the implications if a company forecasts a constant g that exceeds its r_s? Will many stocks have expected g > r_s in the short run (that is, for the next few years)? In the long run (that is, forever)?
2. b. Assume that Bon Temps has a beta coefficient of 1.2, that the risk-free rate (the yield on T-bonds) is 7%, and that the required rate of return on the market is 12%. What is Bon Temps’ required rate of return?
3. c. Assume that Bon Temps is a constant growth company whose last dividend (D₀, which was paid yesterday) was $2.00 and whose dividend is expected to grow indefinitely at a 6% rate.
   1. 1. What is the firm’s expected dividend stream over the next 3 years?
   2. 2. What is its current stock price?
   3. 3. What is the stock’s expected value 1 year from now?
   4. 4. What are the expected dividend yield, capital gains yield, and total return during the first year?
4. d. Now assume that the stock is currently selling at $30.29. What is its expected rate of return?
5. e. What would the stock price to if its dividends were expected to have zero growth?
6. f. Now assume But Bon Temps is expected to experience nonconstant growth of 30% for the next 3 years, then return to its long-run constant growth rate of 6%. What is the stock’s value under these conditions? What are its expected dividend and capital gains yields in Year 1? Year 4?
7. g. Suppose Bon Temp’s expected to experience zero growth during the first 3 years and then resume its steady-state growth of 6% in the fourth year. What would be its value then?. What would to its expected dividend and capital gains yields in Year 1 In Year 4?
8. h. Finally, assume that Bon Temps’s comings and dividends are expected to decline at a constant rate of 6% per year, that is, g = −6%. Why would anyone be willing to buy such a stock, and at what price should it sell? What would to its dividend and capital gains yields in each year?
9. i. Suppose Bon Temps embarked on an aggressive expansion that requires additional capital Management decided to finance the expansion by borrowing $40 million and by halting dividend payments to increase retained earnings. Its WACC is now 10%, and the protected free cash flows for the next 3 years are −$5 million, $10 million. and $20 million. After Year 3, free cash flow is protected to grow at a constant 6%. What is Bon Temps‘s total value? If it has 10 million shares of stock and $40 million of debt and preferred stock combined, w hat is the price per share?
10. j. Suppose Bon Temps decided to issue preferred stock that would pay an annual dividend of $500 and that the issue price was $50.00 per share What would be the stock’s expected return? Would the expected rate of return he the same if the preffered was a perpetual issue or if it had a 20-year

Summary Introduction

To determine: The legal rights and privileges of common stockholders.

Explanation of Solution

Following are the legal rights and privileges of common stockholders:

• The common stockholders have the right to elect its firm’s directors.
• The common stockholders are the owner of the company who bears the risk of failure to a certain level and shares some part of net income as well.
• Right to buy shares in case company issues new shares in the market.
• The common stockholders have the right to vote in annual general meeting of the company having an agenda related to business and management.

Above mentioned points are some of the legal rights and privileges of common stockholders.

Summary Introduction

To determine: The formula that can be used to value any stock, regardless of its dividend.

Explanation of Solution

The present value of all the expected cash flows from the stock computes value of a stock. Therefore, the value of the stock issuing dividend at a fixed rate can be computed by dividing the dividend by the rate of return required by its shareholders.

Following is the formula used for valuation of any stock regardless of its dividend:

${\text{Value}}_{\text{share}}=\frac{\text{Dividend}}{\text{Required rate of return}}$

Therefore, by using the above mentioned formula the value of stock can be computed

Summary Introduction

To determine: The constant growth stock and they way is valued.

Explanation of Solution

Constant Growth Stock:

When a stock’s dividend grows at a certain percentage for an indefinite period, that stock will be termed as constant growth stock.

Following is the formula by which constant growth stock can be computed:

${\text{Value}}_{\text{share}}=\frac{\text{previous dividend}\times \left(1+\text{growth rate}\right)}{\left(\text{required rate of return}-\text{growth rate}\right)}$

Therefore, by using the above mentioned formula the value of constant growth stock can be computed.

Summary Introduction

To determine: The implications if a company forecasts a constant g (capital gains yield) that exceeds its ${\text{r}}_s$(rate of return).

Explanation of Solution

Stock Valuation Model:

The constant growth stock valuation model is based on the principle that the required rate of return will always be greater than the growth rate. In case there is a higher growth rate than the required rate of return then it will result in negative value for the stock.

Therefore, the implication to this is that the high growth companies might have a growth rate in dividend more than the required rate of return and in the long run companies manage growth rate less than the required rate of return.

Summary Introduction

To determine: The required rate of return.

Explanation of Solution

Given,

Beta coefficient is of 1.2.

Risk free rate is 7%.

Market required rate of return is 12%.

Capital Asset Pricing Model (CAPM):

Under this model the required rate of return is measured through establishing a relationship between risk free rate return, market rate of return and risk on stock, which is beta (β) and is a measure of systematic risk.

Following is the formula used for the calculation of expected rate of return using CAPM:

$k_e=R_f+\beta \left(R_m-R_f\right)$

Where,

• $k_e$=Required rate of return.
• $R_f$=Risk free rate.
• $R_m$=Market return.
• $\beta$=Beta

Put the given values in the above mentioned formula:

$\begin{array}{c}{k}_e=R_f+\beta \left(R_m-R_f\right)\\ =7\%+1.2\left(12\%-7\%\right)\\ =7\%+1.2\times 5\%\\ =13\%\end{array}$

Therefore, the required rate of return is computed as 13%.

Conclusion

Thus, the required rate of return is 13%.

Summary Introduction

To determine: The firm’s expected dividend stream over the next 3 years.

Explanation of Solution

Given,

Constant growth rate is 2%.

Dividend growth rate is 6%.

Following is the computation of firm’s expected dividend stream over the next 3 years:

Year	Expected dividend (in %)
0	2
1	$\left(2\%{\left(1+6\%\right)}^1\right)=2.12$
2	$\left(2\%{\left(1+6\%\right)}^2\right)=2.24$
3	$\left(2\%{\left(1+6\%\right)}^3\right)=2.38$

Table (1)

Therefore, expected dividend stream over the next 3 years is 2.12%, 2.24% and 2.38%.

Conclusion

Thus, expected dividend stream over the next 3 years is 2.12%, 2.24% and 2.38%.

Summary Introduction

To determine: The current stock price.

Explanation of Solution

Since it is being provided that the stock is growing at a constant rate, its value can be computed using the constant growth rate model as follows:

Following is the computation of current stock price by using formula of constant growth stock:

$\begin{array}{c}{\text{Value}}_{\text{share}}=\frac{\text{previous dividend}\times \left(1+\text{growth rate}\right)}{\left(\text{required rate of return}-\text{growth rate}\right)}\\ =\left(\frac{\$2\times \left(1+6\%\right)}{13\%-6\%}\right)\\ =\$30.29\end{array}$

Therefore, current stock price computed as $30.29 using formula of constant growth stock.

Conclusion

Thus, current stock price is $30.29.

Summary Introduction

To determine: The stock expected value 1 year from now.

Explanation of Solution

As provided in the case, it is being noted that after one year ${\text{D}}_0$ will already have been paid, therefore the expected dividend stream will then be ${\text{D}}_1{\text{,D}}_2{\text{ and D}}_3$ and so on. Hence, the expected value one year from is computed as follows:

$\begin{array}{c}{\text{Value}}_{\text{share}}=\frac{\text{previous dividend}\times \left(1+\text{growth rate}\right)}{\left(\text{required rate of return}-\text{growth rate}\right)}\\ =\left(\frac{\$2.21\times \left(1+6\%\right)}{13\%-6\%}\right)\\ =\$32.10\end{array}$

Therefore, the expected value one year from now will be $32.10.

Conclusion

Thus, the expected value one year from now is $32.10.

Summary Introduction

To determine: The expected dividend yield, capital gains yield and the total return during the first year.

Explanation of Solution

Following is the formula and computation of expected dividend yield:

$\begin{array}{c}\text{Dividend yield}=\frac{{\text{D}}_1}{\text{current price of stock}}\\ =\frac{\$2.12}{\$30.29}\\ =7\%\end{array}$

Therefore, dividend yield computed is 7%.

Following is the formula and computation of capital gain yield:

$\begin{array}{c}\text{Capital gain yield}=\left(\frac{{\text{Price}}_1-{\text{Price}}_0}{{\text{Price}}_0}\right)\times 100\%\\ =\left(\frac{\$32.10-\$30.29}{\$30.29}\right)\times 100\%\\ =6\%\end{array}$

Hence, capital gain yield is 6%.

Following is the formula and computation of total return during the first year:

$\begin{array}{c}\text{Total return}=\text{Dividend yield}+\text{Capital gains yield}\\ =7\%+6\%\\ =13\%\end{array}$

Total return is the sum total of dividend yield and capital gain yield hence computed as 13%.

Conclusion

Thus, expected dividend yield, capital gains yield and the total return during the first year is 7%, 6% and 13%.

Summary Introduction

To determine: The expected rate of return assuming stock current price to be $30.29.

Explanation of Solution

Following is the formula and computation of expected rate of return assuming stock current price to be $30.29:

$\begin{array}{c}\text{Expected rate of return}=\frac{{\text{D}}_1+\left(\text{Expected value}-\text{Current value}\right)}{\text{Currentvalue}}\\ =\frac{\$2.12+\left(\$32.10-\$30.29\right)}{\$30.29}\\ =12.97\%\end{array}$

Therefore, expected rate of return assuming stock current price to be $30.29 is coming to be 12.97% or 13%.

Conclusion

Thus, expected rate of return is 13%.

Summary Introduction

To determine: The stock price if its dividend were expected to have zero growth.

Explanation of Solution

In case the company’s dividends were not expected to grow at all, then its dividends stream would be perpetuity. Following is the computation of stock price:

$\begin{array}{c}{\text{Value}}_{\text{share}}=\frac{\text{previous dividend}\times \left(1+\text{growth rate}\right)}{\left(\text{required rate of return}-\text{growth rate}\right)}\\ =\left(\frac{\$2\times \left(1+0\%\right)}{13\%-0\%}\right)\\ =\$15.38\end{array}$

Therefore, the stock price if its dividend were expected to have zero growth is $15.38.

Conclusion

Thus, the stock price will be $15.38.

Summary Introduction

To determine:  The stock value, expected dividend and capital gains yield in first and fourth year.

Explanation of Solution

Given,

Non-constant growth is 30% for the next three years.

Growth rate is 6%.

Following is the computation of value of stock:

Year	Expected dividend (in %)	Value of stock (in $)
0	2
1	$\left(2\%{\left(1+30\%\right)}^1\right)=2.62$	$\$2.62/{\left(1.13\right)}^1=2.301$
2	$\left(2\%{\left(1+30\%\right)}^2\right)=3.38$	$\$3.38/{\left(1.13\right)}^2=2.647$
3	$\left(2\%{\left(1+30\%\right)}^3\right)=4.39$	$\$4.39/{\left(1.13\right)}^3=3.045$
4	$\left(2\%{\left(1+6\%\right)}^4\right)=4.65$	$\begin{array}{l}\frac{\$4.65}{7\%}=66.54\\ 66.542/{\left(1.13\right)}^4=46.116\end{array}$
Total		$54.109

Table (2)

Therefore, the stock value is $54.109.

Following is the formula and computation of expected dividend yield:

$\begin{array}{c}\text{Dividend yield}=\frac{{\text{D}}_1}{\text{current price of stock}}\\ =\frac{\$2.6}{\$54.109}\\ =4.8\%\end{array}$

Therefore, dividend yield computed is 4.8%.

Following is the formula and computation of capital gain yield:

$\begin{array}{c}\text{Capital gain yield}=\mathrm{Re}\text{quired rate of return }-\text{dividend yield}\\ =\text{13\%}-4.8\%\\ =8.2\%\end{array}$

Hence, capital gain yield is 8.2%.

Conclusion

Thus, the stock value, expected dividend and capital gains yield is $54.109, 4.8% and 8.2%.

Summary Introduction

To determine: The stock value, expected dividend and capital gains yield in year 1 and 4 if the growth rate is zero for the first three years.

Explanation of Solution

Given,

Growth is zero for the first three years,

Growth rate in the fourth year is 6%.

Following is the computation of value of stock:

Year	Expected dividend (in %)	Value of stock (in $)
0	2
1	2	$\$2/{\left(1.13\right)}^1=1.77$
2	2	$\$2/{\left(1.13\right)}^2=1.57$
3	2	$\$2/{\left(1.13\right)}^3=1.39$
4	$\left(2\%\left(1+6\%\right)\right)=2.12$	$\begin{array}{l}\frac{\$2.12}{7\%}=30.29\\ 30.29/{\left(1.13\right)}^4=20.99\end{array}$
Total		$25.72

Table (3)

Therefore, the stock value is $25.72

Following is the formula and computation of expected dividend yield:

$\begin{array}{c}\text{Dividend yield}=\frac{{\text{D}}_1}{\text{current price of stock}}\\ =\frac{\$2}{\$25.72}\\ =7.78\%\end{array}$

Therefore, dividend yield computed is 7.78%.

Following is the formula and computation of capital gain yield:

$\begin{array}{c}\text{Capital gain yield}=\mathrm{Re}\text{quired rate of return }-\text{Dividend yield}\\ =\text{13\%}-7.78\%\\ =5.22\%\end{array}$

Hence, capital gain yield is 5.22%.

Conclusion

Thus, the stock value, expected dividend and capital gains yield is $25.72, 7.78% and5.22%.

Summary Introduction

To determine: Dividend and capital gains yields in each year.

Explanation of Solution

Given,

Constant decline in growth rate is at 6%.

Here, in the provided case it can be noted that the company is earning something and paying some dividends, therefore it can be clearly seen that the value must be greater than zero. That value can be found with constant growth formula but as it is given that the growth rate is negative, there will be constant growth stock.

Hence, capital gains yield will be -6%.

Following is the computation of dividend yield:

$\begin{array}{c}\text{Dividend yield}=\text{13\%}-\left(-6\%\right)\\ =19\%\end{array}$

Therefore, dividend yield computed is 19%.

Therefore, it can be noted that the dividend and capital gains yields are constant over time but high dividend yield is needed to offset the negative capital gains yield.

Conclusion

Thus, dividend and capital gains yields in each year will be constant that is 19% and -6%.

Summary Introduction

To determine: The total value and price per share.

Explanation of Solution

Given,

Debt is worth $40 million.

WACC is 10%.

Constant growth rate is 6% after the third year.

Cash flow projected for first year is -$5 million.

Cash flow projected for second year is $ 10 million.

Cash flow projected for third year is $ 20 million.

Following is the computation of value of stock:

Year	Expected cash flow (in $ million)	Value of stock (in $)
0	0
1	-5	$-\$5/{\left(1.10\right)}^1=-4.54$
2	10	$\$10/{\left(1.10\right)}^2=8.26$
3	20	$\$20/{\left(1.10\right)}^3=15.026$
4	$\left(20\%\left(1+6\%\right)\right)=21.2$	$\frac{\$21.2}{{\left(1.1\right)}^4}\times \frac{1.1}{0.04}=398.197$
Total		$416.942

Table (4)

Here, value of stock is being calculated at present value in the fourth year by using perpetuity formula as there is life span given for the project.

Following is the formula and computation of value of equity:

$\begin{array}{c}\text{Value of equity}=\text{Value of operations }-\text{ Debt}\\ =\$\text{416}\text{.94}-\$40\\ =\$376.94\text{ million}\end{array}$

Therefore, value of equity is $376.94 million.

Following is the formula and computation of price per share:

$\begin{array}{c}\text{Price per share}=\frac{\text{Total value of equity}}{\text{value of share stock}}\\ =\frac{\$376.94}{\$10}\\ =\$37.69\end{array}$

Therefore, price per share is $37.69.

Conclusion

Thus, the total value and price per share is $376.94 and $37.69

Summary Introduction

To determine: The stock expected return.

Explanation of Solution

Given,

Annual dividend is $5.

Issue price is $50 per share

Maturity life is 20 years.

Following is the formula to calculate stock expected return:

$\text{Expected return}=\left(\frac{\text{Dividend}}{\text{Net proceeds of issue}}\right)\times 100\%$

Put the provided values in the above mentioned formula:

$\begin{array}{c}\text{Expected return}=\left(\frac{\text{Dividend}}{\text{Net proceeds of issue}}\right)\times 100\%\\ =\left(\frac{\$5}{\$50}\right)\times 100\%\\ =10\%\end{array}$

Therefore, expected return is 10% and it can also be noted that there will be no change in the expected return whether the preferred stock was a perpetual issue or having a 20 years maturity.

Conclusion

Thus, the stock expected return is 10%.