Chapter 7, Problem 25P

Summary Introduction

To determine:  Current value of stock.

Given information:

Expected dividend rate = $2per share

Expected growth of dividend = 15% (for first three years)

Thereafter dividend growth = 10% (for 2 years)

Calculation of current value of stock:

Year	Earnings ($)	Dividends ($)
0	0.00	0.00
1	0.00	0.00
2	2	0.45
3	2(1.15)	2.30
4	2.30(1.15)	2.645
5	2.645(1.15)	3.042
6	3.042(1.10)	3.346

$\begin{array}{l}P6=estimatedEPSxestimatedP/Emultiple\hfill \\ =\$7x15=\$105\hfill \end{array}$

$P_0=\text{}F{V}_n(PVI{F}_{i,n})$

Here,

FV refers to future value of investment,

i is interest rate,

n is number of periods,

PVIF refers to a used for calculation.

$\begin{array}{c}{P}_0=\left[\begin{array}{c}\$2\left(PVI{F}_{0.15,2}\right)+\$2.30\left(PVI{F}_{0.15,3}\right)+\$2.645\left(PVI{F}_{0.15,4}\right)+\$3.042\left(PVI{F}_{0.15,5}\right)+\\ \left(\$3.346+\$105\right)\left(PVI{F}_{0.15,6}\right)\end{array}\right]\\ =\$52.89\end{array}$

Hence, a person can pay for the stock is $52.89