Sew 'N More just paid an annual dividend of $1.42 a share. The firm plans to pay annual dividends of $1.45, $1.50, and $1.53 over the next 3 years, respectively. After that time, the dividends will be held constant at $1.60 per share. What is this stock worth today at a discount rate of 11.7 percent?

Question

Quizplus · Accepted Answer

To find the present value of the stock, we calculate the present value of the dividends for the first three years and the present value of the perpetuity starting from year 4 onwards. The formula for the present value of a perpetuity is $PV = \frac{D}{r}$, where $D$ is the dividend and $r$ is the discount rate. However, since the perpetuity starts in year 4, we need to discount it back to today's value.1. Year 1 Dividend: $\frac{1.45}{(1 + 0.117)^1} = 1.298$2. Year 2 Dividend: $\frac{1.50}{(1 + 0.117)^2} = 1.199$3. Year 3 Dividend: $\frac{1.53}{(1 + 0.117)^3} = 1.090$For the perpetuity starting in year 4:- Perpetuity value at year 4: $\frac{1.60}{0.117} = 13.675$- Discounted back to today (PV of perpetuity): $\frac{13.675}{(1 + 0.117)^3} = 9.853$Adding these up:- Total value = $1.298 + 1.199 + 1.090 + 9.853 = 13.440$Rounding to two decimal places, the stock is worth approximately $13.44 today, which is closest to option E, $13.41.

Sew 'N More Just Paid an Annual Dividend of $1