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?
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To calculate the present value of future benefits, we need to discount each cash flow back to its present value. In this case, we have the dividends at the end of each year and the future selling price of the stock.
Here's how you can calculate the present value:
1. Calculate the present value of each dividend payment using the formula:
Present Value = Dividend / (1 + Discount Rate)^n
For the first year dividend of $2.00, the present value is:
PV1 = $2.00 / (1 + 0.11)^1
For the second year dividend of $2.20, the present value is:
PV2 = $2.20 / (1 + 0.11)^2
For the third year dividend of $2.40, the present value is:
PV3 = $2.40 / (1 + 0.11)^3
2. Calculate the present value of the future selling price using the same formula:
Present Value = Selling Price / (1 + Discount Rate)^n
The selling price at the end of the third year is $33, so the present value is:
PV4 = $33 / (1 + 0.11)^3
3. Finally, add up all the present values to get the total present value:
Total Present Value = PV1 + PV2 + PV3 + PV4
Calculate each present value from step 1 and substitute them into the formula above to find the total present value.
By following these steps, you can calculate the present value of all future benefits based on the given discount rate of 11 percent.