9. Harrison Clothiers\' stock currently sells for $20 ashare. It just paid a div
ID: 2770967 • Letter: 9
Question
9.
Harrison Clothiers' stock currently sells for $20 ashare. It just paid a dividend of $1.00 a share (that isD0 = $1.00). The dividend is expected to grow at aconstant rate of 6 percent a year. What stock price isexpected 1 year from now? What is the required rate ofreturn?
10.
A stock is expected to pay a dividend of $0.50 at the end of theyear (that is, D1 = 0.50), and it should continue togrow at a constant rate of 7 percent a year. If its requiredreturn is 12 percent, what is the stock's expected price 4 yearsfrom today?
Explanation / Answer
(9) Current Stock price (P0) = $20
Dividendpaid (D0) = $1.00
Dividend growth rate (g) = 6%
D1 = D0 (1+g)
= $1.00 (1+0.06)
D1 = $1.06
P0 = D1 / R-g
R-g = D1 / P0
Required return (R) = (D1 / P0)+ g
R = ($1.06 / $20) + 0.06
Required return (R ) = 0.113 (or)11.3%
P1 = $1.06 (1+0.06) / (0.113 – 0.06)
= $1.1236 / 0.053
P1 = $21.20
Expected Stock Price After One year(P1) = $21.20
(10) Dividend paid (D1) = $0.50
Growthrate (g) = 7%
Required return (R) = 12%
Dividend in 1st year (D1) = $0.50
Dividend in 2nd year(D2) = $0.50(1.07) = $0.535
Dividend in 3rd year (D3) = $0.535 (1.07) = $0.57245
Dividend in 4th year (D4) = $0.57245 (1.07) = $0.6125
P4 = D4 * (1+g) / (R-g)
= D5 / (R-g)
P4 = $0.6125(1.07) / (0.12 – 0.07)
= $0.655 / 0.05
= $13.10
Calculating Current Stock Price of the Company(P0):
P0 = [D1/(1+R) +D2/(1+R)2 + D3/(1+R)3 + D4/(1+R)4 +P4/(1+R)4]
= [$0.50 /(1.12) + $0.535 / (1.12)2 + $0.57245 /(1.12)3 + $0.6125 / (1.12)4
+$13.10 / (1.12)4
= $9.99
P0 = $10
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