The MicroSoft currently pays no dividend because of depressed earnings. A recent

Question

The MicroSoft currently pays no dividend because of depressed earnings. A recent change in management promises, however, a brighter future. Investors expect MicroSoft to pay a dividend of $1 next year ( the end of the year). This dividend is expected to increase to $2 the following year and to grow at a rate of 10 percent per annum for the following two years ( years 3 and 4), Dr. Udeh, a new investor, expects the price of the stock to increase 50 percent in value between now (time zero) and the end of year 3.

If Dr. Udeh plans to hold the stock for two years and requires a rate of return of 20 percent on the investor, what value would he place on the stock today?

Explanation / Answer

let the long term growth rate of company be 'gf'
D1 = $ 1

D2 = $ 2

D3 = D2 * ( 1 + 0.1) = 2 * 1.1 = $ 2.2>

D4 = D3 * ( 1 + 0.1 ) = 2.2 *1.1 = $ 2.42

D5 = D4 * ( 1 + gf) = 2.42 * ( 1 + gf)

r = 0.2

P4 = D5/(r - gf)

P0 = D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4 + D5 * ( 1 +r)^-4/(r-gf)

given

P4 = 1.5 P0

2.42 * ( 1 + gf) /(0.2 - gf) = 1.5*(1/1.2 + 2/1.2^2 + 2.2/1.2^3 + 2.42/1.2^4 + 2.42 * (1 + gf)/((0.2 - gf)*1.2^4))

6.994 + 1.751 * ( 1 + gf)/(0.2 - gf) = 2.42 * ( 1 + gf)/(0.2 - gf)

(1 + gf)/(0.2 - gf) = 6.994/(2.42 - 1.751)

1 + gf = 10.454(0.2 - gf)

11.454 * gf = 10.454*0.2 - 1

gf =1.0908/11.454 = 9.52 %

current price is

P0 = D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4 + D5 * ( 1 +r)^-4/(r-gf)

P0 = 1/1.2 + 2/1.2^2 + 2.2/1.2^3 + 2.42/1.2^4 + 2.42 * (1 + 0.0952)/((0.2 - 0.0952)*1.2^4) = $ 16.86

Today's stock price would be $ 16.86

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