Question

Lincoln, Inc. expects to pay no dividends for the next four years. It has projected a growth rate of 35 percent for the next four years. After four years, the firm will grow at a constant rate of 6 percent. Its first dividend to be paid in year 5 will be worth $4.25. If your required rate of return is 20 percent, what is the stock worth today?

1) $14.64
2) $32.18
3) $36.43
4) $21.82

Answer 1

To calculate the present value of a stock, we use the present value of growing perpetuity formula. We calculate the present value of dividends from years 5 to infinity and add it to the present value of the dividend in year 4. The stock is worth $275.24 today.

Step-by-step explanation:

To calculate the present value of a stock, we can use the formula for the present value of growing perpetuity. In this case, the dividends are expected to start in year 5. We'll calculate the present value of dividends from years 5 to infinity, and then add that to the present value of the dividend in year 4.

First, let's calculate the present value of dividends from years 5 to infinity. We can use the formula:

PV = D / (r - g)

where PV is the present value of dividends, D is the dividend in the first year, r is the required rate of return, and g is the growth rate. In this case, D = $4.25, r = 20%, and g = 6%.

So, PV = $4.25 / (20% - 6%) = $42.50 / 0.14 = $303.57.

Next, let's calculate the present value of the dividend in year 4. The formula is the same:

PV = D / (r - g)

In this case, D = $4.25, r = 20%, and g = 35%.

So, PV = $4.25 / (20% - 35%) = $4.25 / -15% = -$28.33.

Finally, to calculate the present value of the stock today, we need to sum up the present values of dividends from year 5 to infinity and the present value of the dividend in year 4:

Present Value = PV of dividends from year 5 to infinity + PV of dividend in year 4 = $303.57 + (-$28.33) = $275.24.

Therefore, the stock is worth $275.24 today.