# Estimating the current value of a stock

Problem 1

Suppose a dividend of $1.25 was paid. The stock has a required rate of return of 11.2% and investors expect the dividend to grow at a constant rate of 10%. Complete parts (a) through (e) below.

a) Compute D0, D1, D2, D3 and D7.

b) Compute the present value of the dividends for t = 3 years.

c) Compute the current market price.

d) Assume that the constant growth rate is actually 0%. What is the current market price?

e) Describe the behavior of the present value of each future dividend (i.e. the behavior as t increases).

Problem 2

Suppose a dividend that pays at $1.07 has a growth rate of 20% for the first 3 years. After the 3 years, there is a long-run growth rate of 8%. The stock has a required rate of return of 12.4%. Find the current market price of a share of common stock.

Problem 3

Assume the beta coefficient for a company's stock is B = 0.2, the risk-free rate of return, rRF, is 8% and the required rate of return on the market, rM, is 14%. Assume the dividend expected during the coming year is D1 = $2.50 and the growth rate is a constant 7%. Complete parts (a) through (c) below.

a) Compute the price at which the company's stock should sell.

b) Find the new price of the stock assuming the risk-free rate of return is 5% and the required rate of return on the market is 11%.

c) What would be needed for a stock to be in equilibrium?

#### Solution Preview

Problem 1

a) Compute D0, D1, D2, D3 and D7.

Current dividend=Do=$1.25

Growth Rate=g=10%

Expected dividend to be paid at the end of year 1=D1=Do*(1+g)=1.25*(1+10%)=$1.375

Expected dividend to be paid at the end of year 2=D2=Do*(1+g)^2=1.25*(1+10%)^2=$1.5125

Expected dividend to be paid at the end of year 3=D3=Do*(1+g)^3=1.25*(1+10%)^3=$1.66375

Expected dividend to be paid at the end of year 7=D7=Do*(1+g)^7=1.25*(1+10%)^7=$2.435896

b) Compute the present value of the dividends for t = 3 years.

PV of dividend to received at the end of Year 3=PV3=D3/(1+r)^3=1.66375/(1+11.2%)^3=$1.209968

c) Compute the current market ...

#### Solution Summary

Solution depicts the steps to estimate the current value of stock in the given cases. Calculations are carried out with the help of suitable formulas.