# Price of stocks

1) Price a stock that pays a dividend of $3 for the next ten years and then $2 forever after that. Assume the discount rate is 20%. Show in dollars and percent what you would earn if you held this stock for three years.

2) Price a stock that pays no dividend for five years, then pays a $1 dividend in year 6 after which the dividend grows by 10% annually. Assume the discount rate is 15%. Show in dollars and percent what you would earn if you held this stock for two years.

3) XYZ Corp. has earnings per share of $4, a payout ratio of 50% and a return on equity of 10%. This company's stock has a discount rate of 15%. Calculate the price of its stock. What change in the payout ratio would make the price of this stock increase? Intuitively, why?

#### Solution Preview

Please see attached file

Note: the abbreviations have the following meanings

PVIF= Present Value Interest Factor

PVIFA= Present Value Interest Factor for an Annuity

They can be read from tables or calculated using the following equations

PVIFA( n, r%)= =[1-1/(1+r%)^n]/r%

PVIF( n, r%)= =1/(1+r%)^n

1) Price a stock that pays a dividend of $3 for the next ten years and then $2 forever after that. Assume the discount rate is 20%. Show in dollars and percent what you would earn if you held this stock for three years.

METHOD 1

Step 1: Calculate the present value of $ 3 per year for next 10 years

n= 10

r= 20.00%

PVIFA (10 periods, 20.% rate ) = 4.192472

Annuity= $3.00

Therefore, present value= $12.58 =3x4.192472

Step 2: Calculate the present value of a perpetuity of $ 2 per year from 11th year forever

Perpetuity= $2.00

r= 20.00%

Therefore value of perpetuity in year 10= $10.00 =2/20.%

PV of this amount at time t=0 is calculated using PVIF

n= 10

r= 20.00%

PVIF (10 periods, 20.% rate ) = 0.161506

Future value= 10

Therefore, present value= $1.62 =10x0.161506

Therefore, value of the stock= $14.20 =12.58+1.62

Alternatively;

We have a perpetuity of $ 2 and additional $1 for the first 10 years

Step 1: Calculate the present value of $ 1 per year for next 10 years

n= 10

r= 20.00%

PVIFA (10 periods, 20.% rate ) ...

#### Solution Summary

The solution calculates price of stocks for different growth rates of dividends.