Jack Hammer invests in a stock that will pay dividends of $2.00 at the end of the first year; $2.20 at the end of the second year; and $2.40 at the end of the third year. Also, he believes that at the end of the third year he will be able to sell the stock for $33. What is the present value of all future benefits if a discount rate of 11 percent is applied?
To find the present value of all future benefits, you need to calculate the present value of each individual cash flow and then sum them up. The present value is the value of a future amount of money today, accounting for the time value of money.
In this case, we have three dividend payments at the end of each year (Year 1, Year 2, and Year 3) and the selling price of the stock at the end of Year 3.
Step 1: Calculate the present value of each cash flow.
To calculate the present value, we use the formula:
PV = CF / (1 + r)^n
Where:
PV is the present value
CF is the cash flow
r is the discount rate
n is the number of years
For Year 1, the cash flow is $2.00:
PV1 = $2.00 / (1 + 0.11)^1 = $1.8
For Year 2, the cash flow is $2.20:
PV2 = $2.20 / (1 + 0.11)^2 = $1.72
For Year 3, the cash flow is $2.40:
PV3 = $2.40 / (1 + 0.11)^3 = $1.54
For the selling price at the end of Year 3, the cash flow is $33:
PV4 = $33 / (1 + 0.11)^3 = $22.42
Step 2: Sum up the present values.
PV(total) = PV1 + PV2 + PV3 + PV4 = $1.8 + $1.72 + $1.54 + $22.42
PV(total) = $27.48
Therefore, the present value of all future benefits, considering a discount rate of 11 percent, is $27.48.