Question

In: Finance

Find the present value of ACME stock to an investor who has a required rate of...

Find the present value of ACME stock to an investor who has a required rate of return of 10 percent. The current dividend of $1.00 per share has been just paid out today and the dividends are expected to grow 8 percent per year for 3 years. At the end of 3 years the investor expects to sell the security for $80.

Solutions

Expert Solution

Present value of ACME stock is $ 63.00

As per dividend discount model, current share price is the present value of future dividends.
Price at the end of year 3 represents present value of future dividends after 3rd year.
Step-1:Present value of dividend of next 3 years
Year Dividend Discount factor Present value
a b c=1.10^-a d=b*c
1 $       1.08 0.909091 $       0.98
2 $       1.17 0.826446 $       0.96
3 $       1.26 0.751315 $       0.95
Total $       2.89
Working:
Dividend of Year :
1 = $       1.00 * 1.08 = $       1.08
2 = $       1.08 * 1.08 = $       1.17
3 = $       1.17 * 1.08 = $       1.26
Step-2:Present value of selling price of stock at the end of year 3
Present value = $    80.00 * (1.10^-3)
= $    80.00 * 0.751315
= $    60.11
Step-3:Present value of stock
Present value of stock = Sum of present value of dividends
= $       2.89 + $    60.11
= $    63.00

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