Question

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

Beta = covariance/variance
Beta for the market = 0.5/0.25 = 2
Beta for the second risk factor = 0.6/0.3 = 2

cost of equity (Ke) = risk free rate + Beta1(market risk premium) + Beta2(second factor risk premium)
Ke = 2% + 2(3%) + 2(1%) = 10%

Dividend = ROE * [(1+g)^time] * payout ratio
Dividend (1 year from now) = $5 * (1-10%) * 0.5 = 2.25
Dividend (2 year from now) = $5 * ((1-10%)^2) * 0.5 = 2.025
Dividend (3 year from now) = $5 * ((1-10%)^3) * 0.5 = 1.8225
Dividend (4 year from now) = $5 * ((1-10%)^4) * 0.5 = 1.6402
Dividend (5 year from now) = $5 * ((1-10%)^5) * 0.5 = 1.4762
Dividend (6 year from now) = $5 * ((1-10%)^5) * 1.08 * 0.5 = 1.5943

We now use the Gordon growth model to value the equity per share after the end of 5 years
As per GGM, value of equity = expected dividends next year / (cost of equity - expected growth rate)
Value of equity at the end of 5 years = 1.5943 / (10% - 8%) = 79.7161

dividend discount model (DDM) is the present value of the sum of all of its future dividend payments when discounted back to their present value

Price of share today = 2.25/(1.1^1) + 2.025/(1.1^2) + 1.8225/(1.1^3) + 1.6402/(1.1^4) + 1.4762/(1.1^5) + 79.7161/(1.1^5)

Price of share today = 2.0454 + 1.6735 + 1.3963 + 1.1040 + 0.9166 + 49.4974 = $ 56.6062