USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
The National Motor Company's last dividend was $1.25, and the directors expect to maintain the historic 4 percent annual rate of growth. You plan to purchase the stock today because you feel that the growth rate will increase to 7 percent for the next three years and the stock will then reach $25.00 per share.
-Refer to Exhibit 8.2. How much should you be willing to pay for the stock if you require a 16 percent return?
A) $17.34
B) $18.90
C) $19.09
D) $19.21
E) $20.35

Question

Quizplus · Accepted Answer

To find the present value of the stock, we calculate the dividends for the next three years using the 7% growth rate and then find the present value of the stock price at the end of year 3. The calculation is as follows:1. Calculate future dividends:- D1 = $1.25 * (1 + 0.07) = $1.3375- D2 = $1.3375 * (1 + 0.07) = $1.4312- D3 = $1.4312 * (1 + 0.07) = $1.53162. Calculate the present value of these dividends:- PV of D1 = $1.3375 / (1 + 0.16) = $1.1530- PV of D2 = $1.4312 / (1 + 0.16)^2 = $1.0637- PV of D3 = $1.5316 / (1 + 0.16)^3 = $0.98043. Calculate the present value of the stock price at the end of year 3:- PV of stock price = $25.00 / (1 + 0.16)^3 = $15.97494. Sum the present values to find the total value you should be willing to pay for the stock today:- Total PV = $1.1530 + $1.0637 + $0.9804 + $15.9749 = $19.21Therefore, the correct answer is D) $19.21.