Question

Quantitative Problem 3: Assume today is December 31, 2013. Imagine Works Inc. just paid a dividend of $1.35 per share at the end of 2013. The dividend is expected to grow at 18% per year for 3 years, after which time it is expected to grow at a constant rate of 6% annually. The company's cost of equity (r_s) is 9%. Using the dividend growth model (allowing for nonconstant growth), what should be the price of the company's stock today (December 31, 2013)? Round your answer to the nearest cent. Do not round intermediate calculations.
$ ____________per share

Answer 1

2 Dividend paid at end of 2013 $ 1.35 YEAR CASHFLOWS =1.35*1.18 =1.593*1.18 =1.88*1.18 =2.218*1.06/(0.09-0.06) 1.59 1.88 2.22 78.37 PV OF PVF @ 9% CASHFLOW 0.917 $ 1.46 0.842 $ 1.58 0.772 $ 1.71 0.772 $ 60.52 TOTAL $ 65.27 4 AND ON $ 10

COMPUTATION OF PRICE OF STOCK - TWO STAGE DIVIDEND GROWTH MODEL

In the given problem there is two stage of dividend growth. During the initial 3 years, the dividend grows at rate of 18% and at 6% thereafter. The price of stock is present value of future cashflows, ie, dividends.

The dividend of years 1 to 3 are computed by multiplying dividend of previous period with (1+growth rate).

The dividend of year 4 onwards is growing at constant rate of 6%. Hence the formula is used for arriving at the value at beginning of year 4 .

(D3 x (1+g))/(ke-9)

These values are then discounted at cost of equity to arrive at present value of cash flows. The sum of present values give the Price of Stock today.