Quantitative Problem 3: Assume today is December 31, 2013. Imagine Works Inc. ju
ID: 2786723 • Letter: Q
Question
Quantitative Problem 3: Assume today is December 31, 2013. Imagine Works Inc. just paid a dividend of $1.15 per share at the end of 2013. The dividend is expected to grow at 15% per year for 3 years, after which time it is expected to grow at a constant rate of 5% annually. The company's cost of equity (rs) 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
Explanation / Answer
Price of a stock is the present value of all future cash flows discounted at required rate of return
Cash flows are dividend and expected future price
Dividend for year 1 = Present dividend x ( 1 + Growth)
= $1.15 x 1.15
= $ 1.3225
Dividend for year 2
= $ 1.3225 x 1.15
= $ 1.521
Dividend for year 3
= $ 1.521 x 1.15
= $ 1.749
Terminal value at the end of year 3
= Expected dividend of year 4 / (Re – G)
= Dividend for year 3 x (1 + Growth) / [ Re – G]
= $1.749 x 1.05 / [ 0.09 – 0.05]
= $ 1.8364 / 0.04
= $45.91
PV Factor
= 1 / (1 + r) ^ n
Where,
r = Rate of interest = 9% or 0.09
n = Years 1 to 3
So, PV Factor for year 2
= 1 / (1.09 ^ 2)
= 1 / 1.1881
= 0.841680
The following table shows the calculation of price of the stock
So, the price of the stock today is $39.3
Calculations A B C = A x B Year Cash Flows PV Factor Present Value 1 1.3225 0.917431 1.213303 2 1.521 0.84168 1.280195 3 1.749 0.772183 1.350549 3 45.91 0.772183 35.45094 Price 39.3