Chapter 9, Problem 28QP

Stock Valuation and Cash Flows Fincher Manufacturing has projected sales of $135 million next year. Costs are expected to be $76 million and net investment is expected to be $15 million. Each of these values is expected to grow at 14 percent the following year, with the growth rate declining by 2 percent per year until the growth rate reaches 6 percent, where it is expected to remain indefinitely. There are 5.5 million shares of stock outstanding and investors require a return of 13 percent return on the company’s stock. The corporate tax rate is 40 percent.

1. a. What is your estimate of the current stock price?
2. b. Suppose instead that you estimate the terminal value of the company using a PE multiple. The industry PE multiple is 11. What is your new estimate of the company’s stock price?

Summary Introduction

To compute: The current share prices.

Stock Valuation:

Stock valuation is a kind of valuation exercise of stock; basically in this the value of the stock is calculated theoretically and the value of firm is determined. With the help of stock valuation technique the company can predict the future value of stock prices.

Cash Flows:

Cash flow is the inflow and outflow of cash. The initial investment outlay made by the investor to purchase the security is the outflow of cash and the return on this investment to the investor is the inflow of cash from the investment.

Explanation of Solution

Given,

Number of share outstanding is 5,500,000.

Calculated values,

Present value of the company is $343,007,648.

Formula to calculate the current share price is,

$\text{Stock price}=\frac{\text{Present value of the comapny}}{\text{Number of share outstanding}}$

Substitute $343,007,648 for present value of the company and 5,500,000 for number of share outstanding in the above equation.

$\begin{array}{c}\text{Stock price}=\frac{\$343,007,648}{5,500,000}\\ =\$62.37\end{array}$

Working notes:

Statement that shows the cash flows of six years.

Table (1)

Calculate terminal value in the 6^th year.

$\begin{array}{c}\text{Terminal value}=\frac{\text{Cash flow in 6th year}\left(1+\text{Growth rate}\right)}{\left(\text{Required rate of return}-\text{Growth rate}\right)}\\ =\frac{\$32,800,114\left(1+0.06\right)}{\left(0.13-0.06\right)}\\ =\frac{34,768,121}{0.07}\\ =\$496,687,434\end{array}$

Calculate present value of cash flows,

$\begin{array}{c}\text{Present values}=\left[\begin{array}{l}\frac{\text{Year }1\text{ cash flow}}{{\left(1+\text{rate of return}\right)}^1}+\frac{\text{Year }2\text{ cash flow}}{{\left(1+\text{rate of return}\right)}^2}+\frac{\text{Year }3\text{ cash flow}}{{\left(1+\text{rate of return}\right)}^3}+\\ \frac{\text{Year }4\text{ cash flow}}{{\left(1+\text{rate of return}\right)}^4}+\frac{\text{Year }5\text{ cash flow}}{{\left(1+\text{rate of return}\right)}^5}+\\ \frac{\left(\text{Year }6\text{ cash flow}+\text{Terminal vallue}\right)}{{\left(1+\text{rate of return}\right)}^6}\end{array}\right]\\ =\left[\begin{array}{l}\frac{\$20,400,000}{{\left(1+0.13\right)}^1}+\frac{\$23,256,000}{{\left(1+0.13\right)}^2}+\frac{\$26,046,720}{{\left(1+0.13\right)}^3}+\frac{\$28,651,392}{{\left(1+0.13\right)}^4}+\\ \frac{\$30,943,503}{{\left(1+0.13\right)}^5}+\frac{\left(\$32,800,114+\$496,687,434\right)}{{\left(1+0.13\right)}^6}\end{array}\right]\\ =\left[\begin{array}{l}\$18,053,097+\$18,212,859+\$18,051,684\\ +\$17,572,435+\$16,794,894+\$254,322,680\end{array}\right]\\ =\$343,007,648\end{array}$

Conclusion

Thus, the value of current stock price is $62.37.

Summary Introduction

To compute: New estimate of company’sstock price.

Explanation of Solution

Given,

Number of share outstanding is 5,500,000.

Calculated values,

Present value of the company is $405,165,117.

Formula to calculate the current share price is,

$\text{Stock price}=\frac{\text{Present value of the comapny}}{\text{Number of share outstanding}}$

Substitute $405,165,117 for present value of the company and 5,500,000 for number of share outstanding in the above equation.

$\begin{array}{c}\text{Stock price}=\frac{\$405,165,117}{5,500,000}\\ =\$73.67\end{array}$

Working notes:

Calculate terminal value if price earning multiple is 11 and earnings after tax is $56,917,844,

$\begin{array}{c}\text{Terminal value}=\text{Price earning multiple}\times \text{Earning after tax in year 6}\\ =11\times \$56,917,844\\ =\$626,096,284\end{array}$

Calculate present value of cash flows,

$\begin{array}{c}\text{Present values}=\left[\begin{array}{l}\frac{\text{Year }1\text{ cash flow}}{{\left(1+\text{rate of return}\right)}^1}+\frac{\text{Year }2\text{ cash flow}}{{\left(1+\text{rate of return}\right)}^2}+\frac{\text{Year }3\text{ cash flow}}{{\left(1+\text{rate of return}\right)}^3}+\\ \frac{\text{Year }4\text{ cash flow}}{{\left(1+\text{rate of return}\right)}^4}+\frac{\text{Year }5\text{ cash flow}}{{\left(1+\text{rate of return}\right)}^5}+\\ \frac{\left(\text{Year }6\text{ cash flow}+\text{Terminal vallue}\right)}{{\left(1+\text{rate of return}\right)}^6}\end{array}\right]\\ =\left[\begin{array}{l}\frac{\$20,400,000}{{\left(1+0.13\right)}^1}+\frac{\$23,256,000}{{\left(1+0.13\right)}^2}+\frac{\$26,046,720}{{\left(1+0.13\right)}^3}+\frac{\$28,651,392}{{\left(1+0.13\right)}^4}+\\ \frac{\$30,943,503}{{\left(1+0.13\right)}^5}+\frac{\left(\$32,800,114+\$626,096,284\right)}{{\left(1+0.13\right)}^6}\end{array}\right]\\ =\left[\begin{array}{l}\$18,053,097+\$18,212,859+\$18,051,684\\ +\$17,572,435+\$16,794,894+\$316,480,148\end{array}\right]\\ =\$405,165,117\end{array}$

Conclusion

Thus, the value of current stock price is $73.67.