Chapter 4, Problem 28PS

Valuing Tree cash flow Phoenix Corp. faltered in the recent recession but is recovering. Free cash flow has grown rapidly. Forecasts made in 2016 are as follows.

Phoenix’s recovery will be complete by 2021, and there will be no further growth in free cash flow.

1. a. Calculate the PV of free cash flow, assuming a cost of equity of 9%.
2. b. Assume that Phoenix has 12 million shares outstanding. What is the price per share?
3. c. If the 2016 net income is $1 million, what is Phoenix’s P/R ratio? How do you expect that P/E ratio to change from 2017 to 2021?
4. d. Confirm that the expected rate of return on Phoenix stock is exactly 9% in each of the years from 2017 to 2021.

Summary Introduction

To determine: Present value of free cash flow

Explanation of Solution

Compute the present value of free cash flow:

$\begin{array}{c}{\text{PV}}_{\text{2016}}=\frac{{\text{DIV}}_{\text{2017}}}{1+r}+\frac{{\text{DIV}}_{\text{2018}}}{{\left(1+r\right)}^2}+\frac{{\text{DIV}}_{2019}}{{\left(1+r\right)}^3}+\frac{{\text{DIV}}_{2020}}{{\left(1+r\right)}^4}+\frac{{\text{DIV}}_{2021}}{{\left(1+r\right)}^5}\text{+}\frac{\frac{{\text{DIV}}_{\text{2021}}}{r}}{{\left(1+r\right)}^5}\\ \text{=}\frac{\$0}{1.09}\text{+}\frac{\$1}{{1.09}^2}+\frac{\$2}{{1.09}^3}+\frac{\$2.3}{{1.09}^4}+\frac{\$2.6}{{1.09}^5}+\frac{\left(\frac{\$2.6}{0.09}\right)}{{1.09}^5}\\ =\$24.48\text{ million}\end{array}$   

Hence, the present value is $26.68 million.

Summary Introduction

To determine: Price per share

Explanation of Solution

 Note:

 Assume no debt, the share price are as follows,

 $\begin{array}{c}{\text{Price per share}}_{201}=\frac{{\text{PV}}_{2017}}{\text{Number of shares}}\\ =\frac{\$24.48}{12}\\ =\$2.04\end{array}$

 Hence, the price per share is $2.04.

Summary Introduction

To determine: PE ratio and change in PE ratio from 2017 to 2021.

Explanation of Solution

 Compute PE ratio:

 $\begin{array}{c}{\frac{\text{P}}{\text{E}}}_{2016}=\frac{\$24.48}{\$1}\\ =\$24.48\end{array}$

 Compute PV of the cash flows at various points in time:

 $\begin{array}{c}{\text{PV}}_{2017}=\frac{\$1}{1.09}+\frac{\$2}{{1.09}^2}+\frac{\$2.3}{{1.09}^3}+\frac{\$2.6}{{1.09}^4}+\frac{\left(\frac{\$2.6}{0.09}\right)}{{1.09}^4}\\ =\$26.68\end{array}$

 $\begin{array}{c}{\text{PV}}_{2018}=\frac{\$2}{1.09}+\frac{\$2.3}{{1.09}^2}+\frac{\$2.6}{{1.09}^3}+\frac{\left(\frac{\$2.6}{.09}\right)}{{1.09}^3}\\ =\$28.09\end{array}$

 $\begin{array}{c}{\text{PV}}_{2019}=\frac{\$2.3}{1.09}+\frac{\$2.6}{{1.09}^2}+\frac{\left(\frac{\$2.6}{.09}\right)}{{1.09}^2}\\ =\$28.61\end{array}$

 $\begin{array}{c}{\text{PV}}_{2020}=\frac{\$2.6}{.09}\\ =\$28.89\end{array}$

 $\begin{array}{c}{\text{PV}}_{2021}=\frac{\$2.6}{0.09}\\ =\$28.89\end{array}$

 Changes in PE ratio:

 $\begin{array}{c}{\frac{\text{P}}{\text{E}}}_{2017}=\frac{\$26.68}{\$1}\\ =\text{ \$}26.68\end{array}$

 $\begin{array}{c}{\frac{\text{P}}{\text{E}}}_{2018}=\frac{\$28.09}{\$2}\\ =\text{ \$14}\text{.04}\end{array}$

 $\begin{array}{c}{\frac{\text{P}}{\text{E}}}_{2019}=\frac{\$28.61}{\$3.2}\\ =\text{ \$8}\text{.94}\end{array}$

 $\begin{array}{c}{\frac{\text{P}}{\text{E}}}_{2020}=\frac{\$28.89}{\$3.7}\\ =\text{ \$7}\text{.81}\end{array}$

 $\begin{array}{c}{\frac{\text{P}}{\text{E}}}_{2011}=\frac{\$28.89}{\$4}\\ =\text{ \$7}\text{.22}\end{array}$

Summary Introduction

To confirm: The expected rate of return is 9%.

Explanation of Solution

 Compute rate of return using the formula $r_0=\frac{\left({\text{DIV}}_1+{\text{P}}_1–{\text{P}}_0\right)}{{\text{P}}_0}$

 $\begin{array}{c}{\text{Rate of return}}_{2018}=\frac{\left(\$1+\$28.09-\$26.68\right)}{\$26.68}\\ =0.09,\text{ or }9\%\end{array}$

 $\begin{array}{c}{\text{Rate of return}}_{2019}=\frac{\left(\$2+\$28.61-\$28.09\right)}{\$28.09}\\ =0.09,\text{ or }9\%\end{array}$

 $\begin{array}{c}{\text{Rate of return}}_{2020}=\frac{\left(\$2.3+\$28.89-\$28.61\right)}{\$28.61}\\ =0.09,\text{ or }9\%\end{array}$

 $\begin{array}{c}{\text{Rate of return}}_{2021}=\frac{\left(\$2.6+\$28.89-\$28.89\right)}{\$28.89}\\ =0.09,\text{ or }9\%\end{array}$

 Thus, the above calculation shows that the rate of return on Company P is exactly 9%.