Chapter 7, Problem 22P

Summary Introduction

To determine: Current value of stock.

Given information:

Earning growth rate for starting three years will be = 50%

Earning growth rate for following three years will be = 25%

After that earning growth rate will be = 8%

Required equity return will be 20% (2-4 years), afterwards 50%

Calculation of current value of stock:

Year	Earnings ($)	Dividends ($)
0	1.00	0.00
1	1.50	0.00
2	2.25	0.45
3	3.375	0.675
4	4.219	0.844
5	5.273	2.637
6	6.592	3.296
7	7.119	3.560

    $P_m=\frac{D_{m+1}}{k_e-g_2}$

Here,

$P_m$ is the stock value at the end of period,

$D_{m+1}$ refer to the dividend payment after non constant growth,

$k_e$ refer to expected rate of return,

$g_2$ is expected growth after nonconstant growth.

    $P_6=\$3.56/\left(0.20-0.08\right)=\$29.667$

    $P_0=\text{}F{V}_n(PVI{F}_{i,n})$

Here,

FV refers to future value of investment,

i is interest rate,

n is number of periods,

PVIF refers to a used for calculation.

    $\begin{array}{l}{P}_0=\$0+\$0.45\left(PVI{F}_{0.2,2}\right)+\$0.675\left(PVI{F}_{0.2,3}\right)+\$0.844\left(PVI{F}_{0.2,4}\right)+\$2.637\left(PVI{F}_{0.2,5}\right)\hfill \\ \hfill \\ +\left(\$3.296+\$29.667\right)\left(PVI{F}_{0.2,6}\right)=\$\mathrm{<mn>1</mn><mn>3</mn>}.\mathrm{<mn>2</mn><mn>1</mn>}\hfill \end{array}$

Hence, the price of stock will be $13.21

Explanation of Solution

Given information:

Earning growth rate for starting three years will be = 50%

Earning growth rate for following three years will be = 25%

After that earning growth rate will be = 8%

Required equity return will be 20% (2-4 years), afterwards 50%

Calculation of current value of stock:

Year	Earnings ($)	Dividends ($)
0	1.00	0.00
1	1.50	0.00
2	2.25	0.45
3	3.375	0.675
4	4.219	0.844
5	5.273	2.637
6	6.592	3.296
7	7.119	3.560

    $P_m=\frac{D_{m+1}}{k_e-g_2}$

Here,

$P_m$ is the stock value at the end of period,

$D_{m+1}$ refer to the dividend payment after non constant growth,

$k_e$ refer to expected rate of return,

$g_2$ is expected growth after nonconstant growth.

    $P_6=\$3.56/\left(0.20-0.08\right)=\$29.667$

    $P_0=\text{}F{V}_n(PVI{F}_{i,n})$

Here,

FV refers to future value of investment,

i is interest rate,

n is number of periods,

PVIF refers to a used for calculation.

    $\begin{array}{l}{P}_0=\$0+\$0.45\left(PVI{F}_{0.2,2}\right)+\$0.675\left(PVI{F}_{0.2,3}\right)+\$0.844\left(PVI{F}_{0.2,4}\right)+\$2.637\left(PVI{F}_{0.2,5}\right)\hfill \\ \hfill \\ +\left(\$3.296+\$29.667\right)\left(PVI{F}_{0.2,6}\right)=\$\mathrm{<mn>1</mn><mn>3</mn>}.\mathrm{<mn>2</mn><mn>1</mn>}\hfill \end{array}$

Hence, the price of stock will be $13.21