Question

Smith Construction, Inc. is expected to pay a $2.78 dividend next year. The dividend is expected to grow by 4% each year for the next three years. After that the company will never pay another dividend ever again. If your required return on the stock investment is 10%, what should the stock sell for today?

Group of answer choices

• $9.31
• $28.91
• $7.46
• $35.06
• Not enough information to answer the question

Answer 1

The present value of the stock is the discounted value of all the future cash flows i.e. the dividends paid ahead in the future.

Next year i.e. Year 1 dividend = $2.78

The dividend will grow by 4% thereafter for the next three years and no dividends paid after that. So there are total of 4 cash flows to be received from the stock as a dividend.

Year 1 dividend (D1) = $2.78

Year 2 dividend (D2) = 2.78*1.04 = 2.8912

Year 3 dividend (D3) = 2.8912*1.04 = 3.006848

Year 4 dividend (D4) = 3.006848*1.04 = 3.12712192

Year 5 dividend = 0 = Year 6 dividend = Year 7 .........

where therequired return k = 10%

PV of stock = D1/(1+k) + D2/(1+k)^2 + D3/(1+k)^3 + D4/(1+k)^4 = $9.311

So the answer is option A.