Question

Suppose you win a small lottery and have the choice of two ways to be paid: You can accept the money in a lump sum or in a series of payments over time. If you pick the lump sum payout, you get $3,000 today. If you pick the payments over time payout, you get three payments: $1,000 today, $1,000 one year from today, and $1,000 two years from today.

At an interest rate of 6% per year, the winner would be better off accepting the ________ , since it has the greater present value.
At an interest rate of 9% per year, the winner would be better off accepting ________ , since it has the greater present value.

Years after you win the lottery, a friend in another country calls to ask your advice. By wild coincidence, she has just won another lottery with the same payout schemes. She must make a quick decision about whether to collect her money under the lump sum or the payments over time. What is the best advice to give your friend?

a. The lump sum is always better.
b. The payments over time are always better.
c. It will depend on the interest rate; advise her to get a calculator.
d. None of these answers is good advice.

Answer 1

Answer:

Part 1:

At an interest rate of 6% per year, the winner would be better off accepting the lump sum, since it has the greater present value.

At an interest rate of 9% per year, the winner would be better off accepting  lump sum, since it has the greater

Part 2:

a. The lump sum is always better.

Explanation:

This question can be answered in two parts as follows:

Part 1: Decision to accept lump sum or series of payment

This can be deteermined using the present values of both forms of payments.

Present value of the lump sum = $3,000

Present values of the series of payment at 6% and 9%

Since the amount to receive is an equal amount of $1,000 annually, we use the formula for calculating the present value of an ordinary annuity as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value =?

P = Annual receipt payment = $1,000

r = Interest rate = as given

n = number of years = 3

Substitute the values into equation (1), we have:

PV of series of payment at 6% annual interest = $1,000 * ((1 - (1 / (1 + 6%))^3) / 6%) = $2,673.01

PV of series of payment at 9% annual interest = $1,000 * ((1 - (1 / (1 + 9%))^3) / 9%) = $2,531.29

Therefore, we have:

At an interest rate of 6% per year, the winner would be better off accepting the lump sum, since it has the greater present value.

At an interest rate of 9% per year, the winner would be better off accepting  lump sum, since it has the greater

Part 2: Advising a friend

a. The lump sum is always better.

This is because the idea of a present value is that the worth of an amount of money today is more than the worth of the same amount in the future.

From part 1 above, future series of payment have to bee discouted at 6% and 9% and the present values are less than the lump sum using both interest rates. In addition, the higher the interest rate, the lower the present value.

Therefore, the lump sum is always better.