The answer to the question is highlighted in red. Explanations are highlighted in green.
9. Actuarial Risk Company (ARC) has paid a constant $2 per share dividend to its common stockholders for the past 25 years. ARC expects to continue this policy for the next two years, and then begin to increase the dividend at a constant rate equal to 2 percent per year into perpetuity. Investors require a 12 percent rate of return to purchase ARC’s common stock. What is the market value of ARC’s common stock?
a. $16.26
b. $20.00
c. $19.64
d. $20.40
e. None of the above is correct.
The value of the stock is determined by computing the
present value of the future dividends. The dividends are expected to be:
Year Dividend
1 $2.00
2 2.00
3 2.04 = 2.00(1.02)1
4 2.0808 = 2.00(1.02)2
.
.
.
100 13.9267 = 2.00(1.02)98
Because dividends begin to grow at a
constant rate at the beginning of Year 3 (non-constant growth ends at the end of
Year 2), the constant growth model can be applied to compute the price of the
stock at the end of Year 2. Thus, at the end of
Year 2, the price of the stock will be
Based on this
information, the cash flow time line and the solution for the price of of this stock would be:
