Explore BrainMass
Share

Explore BrainMass

    Price of stocks

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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?

    © BrainMass Inc. brainmass.com October 9, 2019, 7:58 pm ad1c9bdddf
    https://brainmass.com/economics/finance/price-of-stocks-135178

    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.

    $2.19