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 P 6 = e s t i m a t e d E P S x e s t i m a t e d P / E m u l t i p l e = $ 7 x 15 = $ 105 P 0 = F V n ( P V I 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. P 0 = $ 2 P V I F 0.15 , 2 + $ 2.30 P V I F 0.15 , 3 + $ 2.645 P V I F 0.15 , 4 + $ 3.042 P V I F 0.15 , 5 + $ 3.346 + $ 105 P V I F 0.15 , 6 = $ 52.89 Hence, a person can pay for the stock is $52.89

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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

P6= estimated EPS x estimated P/E multiple = $7 x 15 = $105

P0=FVn(PVIFi,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.

P0=$2PVIF0.15,2+$2.30PVIF0.15,3+$2.645PVIF0.15,4+$3.042PVIF0.15,5+$3.346+$105PVIF0.15,6=$52.89

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

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