Question

1. The following information is given for a stock. Investors assume that the return of the stock is best explained by a two-factor model that includes the market factor and a second risk factor. Using a dividend discount model, what is the price for this stock?

Stock covariance with the market= 0.5

Market variance = 0.25

Stock covariance with a second risk factor= 0.6

Variance of the second factor= 0.3

Market Premium:3%

Second factor risk premium=1%

Risk free rate =2 %

Current earnings per share= $5,

The ROE is expected to shrink (decrease) at the rate 10% for first 5 years

The ROE is expected to grow at the rate 8% forever after the first 5 years

Payout for the first 5 years: 50%

Payout after 5 years: 50%

Answer 1

E(r): expected return on stock or cost of equity

E(r) = Rf + beta1*R1 + beta2*R2

Rf: risk free rate = 2%

R1: Market Premium = 3%

R2: Second factor risk premium = 1%

beta1 = (Stock covariance with market)/(market variance) = 0.5/0.25 = 2

beta2 = (Stock covariance with second risk factor)/(variance of second factor) = 0.6/0.3 = 2

E(r) = 2%+2*3%+2*1% = 10%

Current earnings = 5

*Growth in ROE = growth in earnings = growth in dividend

dividend payout = 50% (constant)

Current dividend = 50%*5 = 2.5

Year	0	1	2	3	4	5
Dividend	2.500	2.750	3.025	3.328	3.660	4.026
Terminal value						217.419

*dividend for year 0 not be considered for discounting

Dividend for each of the years 1 to 5 increased by 10%

e.g 2.5*(1+10%) = 2.750

2.750*(1+10%) = 3.025... and so on

Terminal value = 4.026*(1+g)/(E(r)-g)

where g: long term growth rate = 8%

E(r): expected return = 10%

Price of stock = 2.750/(1+10%)^1+3.025/(1+10%)^2+3.328/(1+10%)^3+3.660/(1+10%)^4+(4.026+217.419)/(1+10%)^5 = $147.5