John Doe wins the lottery and may pick from the following three choices: in total.
Assume that John Doe uses a discount rate of 5% to evaluate his choices. If he selects the third option, how much is the present value of that alternative?

Question

John Doe wins the lottery and may pick from the following three choices:  in total.
Assume that John Doe uses a discount rate of 5% to evaluate his choices. If he selects the third option, how much is the present value of that alternative?

Quizplus · Accepted Answer

To find the present value of the third option, we need to discount the future cash flows with the discount rate of 5%. The cash flows are:

- $500,000 a year for 20 years
- $1,000,000 at the end of 20 years

Using the formula for the present value of an annuity, we get:

PV of annuity = C * ((1 - (1 + r)^(-n)) / r)

where C is the annual cash flow, r is the discount rate, and n is the number of years. Plugging in the values, we get:

PV of annuity = $500,000 * ((1 - (1 + 0.05)^(-20)) / 0.05) = $5,732,893

Using the formula for the present value of a lump sum, we get:

PV of lump sum = FV / (1 + r)^n

where FV is the future value, r is the discount rate, and n is the number of years. Plugging in the values, we get:

PV of lump sum = $1,000,000 / (1 + 0.05)^20 = $376,889

Adding the two present values, we get:

PV of option 3 = $5,732,893 + $376,889 = $6,109,782

Therefore, the present value of option 3 is $6,109,782.

Since this is the highest present value among the three options, option 3 is the best choice.

John Doe Wins the Lottery and May Pick from the Following