What is the market price of this stock if the market rate of return is 15 percent?

Question

New Corp. last paid a $1.50 per share annual dividend. The company is planning on paying $1.62, $1.68, $1.75, and $1.80 a share over the next four years, respectively. After that the dividend will be a constant $2.25 per share per year. What is the market price of this stock if the market rate of return is 15 percent?

Answer 1

The value of a stock is equal to the PV of its expected future dividends. In this problem, we have 4 years of known dividends, followed by a known perpetual dividend after year 4. We need the sum of all 5 of those components to determine the market price per share.

To value the known dividend amounts for years 1-4, we simply use the formula for PV of a future cash flow:

PV = FV/((1+r)^n), where r is the rate of return and n is the number of years.

Thus, the PV of D1 is 1.68/(1.15^1) = $1.41. By repeating this calculation for the other 4 known dividends, we get a value of $4.86.

Next, we need to calculate the value of the perpetual $2.25 dividend. The formula for a perpetuity is:

PV = P1/r, where r is the rate of return and P1 is the amount to be paid one year from now. This gives us a PV of the perpetuity of $15 (2.25/.15). However, this is the value of the perpetuity when the $2.25 payment is one year away. In the problem, this payment is actually five years away, which means the value of that perpetuity is worth $15 four years from now. We need to discount the $15 back to present day value using the original PV formula. By doing so, we calculate the perpetuity to be worth $8.58 today.

To get the final value of the stock, we need to add the value of the perpetuity to the value of the 4 known dividends, which gives us an ultimate stock price of $13.44.