Chapter 9, Problem 22SP

Comprehensive/Spreadsheet Problem

NONCONSTANT GROWTH AND CORPORATE VALUATION Rework problem 9-18, parts a, b, and c, using a spreadsheet model. For part b, calculate the price, dividend yield, and capital gains yield as called for In the problem. After completing parts a through c, answer the following additional question, using the spreadsheet model.

d. TTC recently introduced a new line of products that has been wildly successful. On the basis of this success and anticipated future success, the following free cash flows were projected:

After the tenth year, TTC’s financial planners anticipate that its free cash flow will grow at a constant rate of 6%. Also, the firm concluded that the new product caused the WACC to fall to 9%. The market value of TTC’s debt is $1,200 million; it uses no preferred stock; and there are 20 million shares of common stock outstanding. Use the corporate valuation model to value the stock.

9-18 NONCONSTANT GROWTH STOCK VALUATION Taussig Technologies Corporation (TTC) has been growing at a rate of 20% per year in recent years. This same growth rate is expected to last for another 2 years, then decline to g_n =6%.

1. a. If D₀ = $1.60 and r_s = 10%, what is TIC’s stock worth today? What are its expected dividend, and capital gains yields at this time, that is, during Year 1?
2. b. Now assume that ITC’s period of supernormal growth is to last for 5 years rather than 2 years. Flow would this affect the price, dividend yield, and capital gains yield? Answer in words only.
3. c. What will TTC’s dividend and capital gains yields be once its period of supernormal growth ends? (Hint: These values will be the same regardless of whether you examine the case of 2 or 5 years of supernormal growth; the calculations are very easy.)
4. d. Explain why investors are interested in the changing relationship between dividend and capital gains yields over time.

Summary Introduction

To identify: The stock value, expected dividend and capital gain at year 1.

Introduction:

Corporate Value Model:

The model that evaluates a firm on the basis of its future operations and the results of those operations is called corporate valuation model. It is a useful tool to analyze a firm’s stock for investment purposes.

Explanation of Solution

The dividend for the first year is $1.92. (Calculated in working note)

The dividend for the second year is $2.30. (Calculated in working note)

The horizon value is $60.95. (Calculated in working note)

The interest rate is 10%. (Calculated in working note)

Formula to calculate the present value of share,

${\text{P}}_{\text{0}}=\frac{{\text{Div}}_{\text{1}}}{{\left(1+\text{r}\right)}^1}+\frac{{\text{Div}}_2}{{\left(1+\text{r}\right)}^2}+\mathrm{...}+\frac{{\text{Div}}_{\text{n}}+\text{Horizon}\text{value}}{{\left(1+\text{r}\right)}^{\text{n}}}$

Where,

• ${\text{P}}_0$ is the stock value.
• ${\text{Div}}_{\text{1}}$ is the dividend for the first year.
• ${\text{Div}}_2$ is the dividend for the second year.
• ${\text{Div}}_{\text{n}}$ is the dividend for the third year.
• n is the number of years.
• r is the interest rate.

Calculation of stock value

Table (1)

Calculation of expected dividend yield is,

The dividend for the first year is $1.92. (Calculated in working note)

The stock value is $64.99545. (Calculated above)

Formula to calculate the expected dividend yield,

$\text{Expected}\text{dividend}\text{yield}=\frac{{\text{Div}}_{\text{1}}}{{\text{P}}_{\text{0}}}$

Where,

• ${\text{P}}_0$ is the stock value.
• ${\text{Div}}_{\text{1}}$ is the dividend for the first year.

Table (2)

Compute the capital gain yield.

Given,

The expected return is 10% or 0.10.

The dividend yield is 0.029541 or 2.9541%

Formula to calculate the capital gain yield is

$\text{Capital}\text{gain}\text{yield}=\text{Expected}\text{return}-\text{Dividend}\text{yield}$

Table (3)

Working notes:

Computation of dividend for the first year,

${\text{Div}}_{\text{1}}={\text{Div}}_{\text{0}}\left(1+\text{g}\right)$

Table (4)

The dividend for the first year is $1.92.

Computation of dividend for the second year,

${\text{Div}}_2={\text{Div}}_0{\left(1+\text{g}\right)}^{\text{n}}$

Table (5)

The dividend for the second year is $2.30.

Computation of value of Div_n+ Horizon value for the second year,

$\begin{array}{c}{\text{Div}}_{\text{n}}+\text{Horizon}\text{value}=\frac{{\text{Div}}_2{\left(1+\text{g}\right)}^1}{\text{r}-\text{g}}\\ =\frac{\$2.30\left(1+0.06\right)}{0.10-0.06}\\ =\frac{\$2.438}{0.04}\\ =\$60.95\end{array}$

Conclusion

The stock value is $64.99545, the expected dividend is 2.95% and the capital gain yield is 7%.

Summary Introduction

To calculate: The effect in the stock price, dividend yield and capital gain yield if the TTC’s period of supernormal growth is to last five years rather than two years.

Explanation of Solution

The dividend for the first year is $1.92, for the second year is $2.30, for the third year is $2.76, for the fourth year is $3.32 and for the fifth year is $3.98. (Calculated in working note)

The horizon value is $125.63. (Calculated in working note)

The interest rate is 10%. (Calculated in working note)

Formula to calculate the present value of share,

${\text{P}}_{\text{0}}=\frac{{\text{Div}}_{\text{1}}}{{\left(1+\text{r}\right)}^1}+\frac{{\text{Div}}_2}{{\left(1+\text{r}\right)}^2}+\mathrm{...}+\frac{{\text{Div}}_{\text{n}}+\text{Horizon}\text{value}}{{\left(1+\text{r}\right)}^{\text{n}}}$

Where,

• ${\text{P}}_0$ is stock value.
• ${\text{Div}}_{\text{1}}$ is dividend for the first year.
• ${\text{Div}}_2$ is dividend for the second year.
• Div₃ is the dividend for the third year.
• Div₄ is the dividend for the fourth year.
• Div₅ is the dividend for the fifth year.
• ${\text{Div}}_{\text{n}}$ is dividend for the third year.
• n is number of years.
• r is interest rate.

Calculation of stock value

Table (6)

Calculation of expected dividend yield is,

The dividend for the first year is $1.92. (Calculated in working note)

The stock value is $183.61. (Calculated above)

Formula to calculate the expected dividend yield,

$\text{Expected}\text{dividend}\text{yield}=\frac{{\text{Div}}_{\text{1}}}{{\text{P}}_{\text{0}}}$

Where,

• ${\text{P}}_0$ is stock value.
• ${\text{Div}}_{\text{1}}$ is dividend for the first year.

Table (7)

Compute the capital gain yield.

Given,

The expected return is 10% or 0.10.

The dividend yield is 0.010457 or 1.0457%

Formula to calculate the capital gain yield is

$\text{Capital}\text{gain}\text{yield}=\text{Expected}\text{return}-\text{Dividend}\text{yield}$

Table (8)

Working notes:

Computation of dividend for the first year,

${\text{Div}}_{\text{1}}={\text{Div}}_{\text{0}}\left(1+\text{g}\right)$

Table (9)

The dividend for the first year is $1.92.

Computation of dividend for the second year,

${\text{Div}}_2={\text{Div}}_0{\left(1+\text{g}\right)}^2$

Table (10)

The dividend for the second year is $2.30.

Computation of dividend for the third year

${\text{Div}}_3={\text{Div}}_0{\left(1+\text{g}\right)}^3$

Table (11)

The dividend for the third year is $2.76.

Computation of dividend for fourth year

${\text{Div}}_4={\text{Div}}_0{\left(1+\text{g}\right)}^4$

Table (12)

The dividend for the fourth year is $3.32.

Computation of dividend for fifth year

${\text{Div}}_5={\text{Div}}_0{\left(1+\text{g}\right)}^5$

Table (13)

The dividend for the fifth year is $3.98.

Computation of value of Div_n+ Horizon value for the second year,

$\begin{array}{c}{\text{Div}}_{\text{n}}+\text{Horizon}\text{value}=\frac{{\text{Div}}_5{\left(1+\text{g}\right)}^4}{\text{r}-\text{g}}\\ =\frac{\$3.98{\left(1+0.06\right)}^4}{0.10-0.06}\\ =\frac{\$5.025}{0.04}\\ =\$125.63\end{array}$

Summary Introduction

To identify: The capital gain yield and dividend yield.

Answer to Problem 22SP

As given the capital gain yield of the company would be 6%, if the supernormal growth of the company ends.

Explanation of Solution

Compute the dividend yield.

Given,

The expected return is 10%.

The capital gain yield is 6%.

Formula to calculate the dividend yield,

$\text{Dividend}\text{yield}=\text{Expected}\text{return}-\text{Capital}\text{gain}\text{yield}$

Table (14)

The dividend yield is 4%.

Conclusion

Hence, the dividend yield for the end of supernormal growth is 4%.

Summary Introduction

To calculate: The value of stock by using corporate valuation model.

Explanation of Solution

Given information:

Present value of future cash flow is $422.0045 million (Working notes).

Present value of horizon is $5,699.33 million (Working notes).

Market value of debt is $1,200 million.

Shares outstanding are 20 million

Computation of the value of stock

Table (15)

Working notes:

Calculation of FCF₍₁₀₊₁₎

Given,

FCF₁₀ is 161.3.

After 10^th year, cash flow will increase @ 6%.

Formula to calculate the FCF₍₁₀₊₁₎

${\text{FCF}}_{\left(10+1\right)}={\text{FCF}}_{10}\times (1+\text{g})$

Where,

• FCF is future cash flow
• G is the growth rate.

FCF₁₀

Table (16)

Calculation of Horizon value₁₀

Formula to calculate the horizon value

${\text{Horizon value}}_{10}={\text{FCF}}_{\left(10+1\right)}/\left(\text{WACC}-{\text{g}}_{\text{FCF}}\right)$

Table (17)

Calculation of Present value of future cash flows

Table (18)

Conclusion

The value of stock is $246.07.