Question

Congratulations! You just won the Very Little Chance Sweepstakes. Spokesperson Ferd McMoney has indicated that you have the choice of receiving $12,000 a year for the next 20 years with the first payment to be provided in one year, or alternatively, a one-time payment today of $90,000 in cash. If you believe that your opportunity cost of return is 11%, based on the time value of money concept, you should choose____________.

a.The $90,000
b.The $12,000 per year payments for 20 years
c.Either is acceptable as the flows are equivalent
d.Cannot be determined from the information provided
e.None of the answers provided is correct

Answer 1

To determine which option is better, we need to calculate the present value of each option and compare them. The present value of the $12,000 per year payments for 20 years can be calculated using the formula for present discounted value. On the other hand, the present value of the $90,000 one-time payment today is simply $90,000. Therefore, based on the time value of money concept and an assumed interest rate of 11%, you should choose the $90,000 option.

Step-by-step explanation:

To determine which option is better, we need to calculate the present value of each option and compare them. The present value of the $12,000 per year payments for 20 years can be calculated using the formula for present discounted value. Using an 11% interest rate, the present value of these payments is:

$12,000/(1.11) + $12,000/(1.11)^2 + $12,000/(1.11)^3 + ... + $12,000/(1.11)^20

This calculates to approximately $113,578.82. On the other hand, the present value of the $90,000 one-time payment today is simply $90,000.

Therefore, based on the time value of money concept and an assumed interest rate of 11%, you should choose the $90,000 option.