Quantitative Problem 3: Assume today is
December 31, 2019. Imagine Works Inc. just paid a dividend of $1.15
per share at the end of 2019. The dividend is expected to grow at
12% 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
(rs) is 10%. Using the dividend growth model (allowing
for nonconstant growth), what should be the price of the company's
stock today (December 31, 2019)? Do not round intermediate
calculations. Round your answer to the nearest cent.
$ per share
Solution: | |||
Price of the company's stock today is $35.74 per share | |||
Working Notes: | |||
Notes: | We have to compute dividend for each year till 3rd year by growing recent each dividend by 12% growth rate and at end of 3rd year we compute price of the stock as terminal value using constant growth formula , then we discount each dividend and terminal value with cost of equity as discount rate. | ||
Current stock price we compute using Dividend Growth Model | |||
P0= D1/(1+r)^1 + D2/(1+r)^2 + D3/(1+r)^3 + P3/(1+r)^3 | |||
Where | |||
P0 = current stock price=?? | |||
D0=Just paid dividend =$1.15 | |||
D1 = D0 x (1+g) = $1.15 x (1+ 12%)=1.2880 | |||
D2 = D1 x (1+g) = $1.2880 x (1+ 12%)=1.442560 | |||
D3 = D2 x (1+g) = $1.442560 x (1+ 12%) =1.61566720 | |||
D4 = D3 x (1+g) = $1.61566720 x (1+ 6%)=1.712607232 | |||
cost of equity =r = 10% | |||
Notes: | As after 3rd year dividend will constantly growth , hence we will compute the stock price as terminal value using Gordon growth model at end of 3rd year as below: | ||
Using Gordon growth model : | |||
P3 = D4 /( r - g) | |||
= $1.712607232/( 10% - 6%) | |||
= 42.8151808 | |||
At last | P0= D1/(1+r)^1 + D2/(1+r)^2 + D3/(1+r)^3 + P3/(1+r)^3 | ||
P0= 1.2880/(1+10%)^1 + 1.442560/(1+10%)^2 + 1.61566720/(1+10%)^3 + 42.8151808/(1+10%)^3 | |||
P0= $35.74466116 | |||
P0= $35.74 | |||
Hence | Price of the company's stock today is $35.74 | ||
Please feel free to ask if anything about above solution in comment section of the question. |
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