cpu company currently pays a divdend of $2.50. dividends are expected to increase at the rate of $.25 per share for the next several years. determine the current rate of CPU's common stock to an investor who expects to be able to sell the stock for $35 per share after 3 years, given that the investor requires a 14% rate of return,.
$68.75
To determine the current rate of CPU's common stock, we need to calculate the present value of the expected future dividends and the future selling price, taking into account the investor's required rate of return.
First, let's calculate the present value of the future dividends using the dividend discount model formula:
Present Value = Dividend / (1 + Rate of Return)^n
Where:
- Dividend = the current dividend payment ($2.50)
- Rate of Return = the investor's required rate of return (14% or 0.14)
- n = the number of years in the future (3 years)
- ^ denotes exponentiation
Present Value of Dividends after 3 years:
PV(Dividends) = $2.50 / (1 + 0.14)^3
PV(Dividends) = $2.50 / (1.14)^3
PV(Dividends) = $2.50 / 1.4888
PV(Dividends) ≈ $1.68 (rounded to the nearest cent)
Next, let's calculate the present value of the future selling price using the same formula:
Present Value = Future Selling Price / (1 + Rate of Return)^n
Where:
- Future Selling Price = the expected selling price after 3 years ($35)
Present Value of Selling Price after 3 years:
PV(Selling Price) = $35 / (1 + 0.14)^3
PV(Selling Price) ≈ $24.86 (rounded to the nearest cent)
Now, to determine the current rate of CPU's common stock, we need to sum the present values of dividends and the present value of the selling price:
Current Rate = PV(Dividends) + PV(Selling Price)
Current Rate = $1.68 + $24.86
Current Rate ≈ $26.54 (rounded to the nearest cent)
Therefore, the current rate of CPU's common stock to an investor who expects to be able to sell the stock for $35 per share after 3 years, given a 14% rate of return, is approximately $26.54.