Suppose that you have a winning lottery ticket for $100,000. The State of California doesn't pay this amount up front - this is the amount you will receive over time. The State offers you two options. The first pays you $80,000 up front and that will be the entire amount. The second pays you winnings over a three year period. The last option pays you a large payment today with small payments in the future. The payment options are detailed in the table below: Option #1Option #2Option #3Amount paid today$80,000$22,000$50,000Amount paid after 1 years-$22,000$12,000Amount paid after 2 years-$22,000$12,000Amount paid after 3 years-$22,000$12,000 Compute the present value of each payment option, assuming the interest rate is 12%. Now, compute the present values based on an interest rate of

5%. Compare your answers, explaining why they are different when the interest rate changes. When the interest rate is 5%, the present values are as follows:Present Values (i=5%)Option #1Option #2Option #3Amount paid today$80,000$22,000$50,000Amount paid after 1 years$0$20,952$11,429Amount paid after 2 years$0$19,955$10,884Amount paid after 3 years$0$19,004$10,366Total Present Value$80,000$81,911$82,679

What will be an ideal response?

When the interest rate is 12%, the present values are as follows:

Present Values (i=12%)Option #1Option #2Option #3
Amount paid today$80,000$22,000$50,000
Amount paid after 1 years$0$19,643$10,714
Amount paid after 2 years$0$17,538$9,566
Amount paid after 3 years$0$15,659$8,541
Total Present Value$80,000$74,840$78,822
From the computations above, when the interest rate is 5%, Option #3 has the highest present value. When the interest rate is 12%, Option #1 has the highest present value. When the interest rate increases from 5% to 12%, the opportunity cost of foregoing future payments is higher. That is, while the winner is waiting to receive his/her future payments, he/she is forgoing interest that could be earned on a bank deposit or other investment. When the interest rate is low, this opportunity cost is relatively low, making Option #3 (with larger fixed payments similar to coupon payments on a bond) more attractive. When the interest rate is relatively high, these future fixed payments have less value, making Option #1 more attractive.

Economics

You might also like to view...

If people expect an inflation rate of 3.3 percent, and the real interest rate is 3 percent, the nominal interest rate equals (approximately)

A) 0.3 percent. B) 8.6 percent. C) 6.3 percent. D) 9.9 percent.

View
Economics

What is the optimal scale of plant?

What will be an ideal response?

View
Economics

Supply chain is the entire vertical process of a firm

Indicate whether the statement is true or false

View
Economics

Studying how the management of Hewlett Packard decides how many computers to produce and the price to charge for its computers would be considered

A. microeconomics. B. empirical economics. C. macroeconomics. D. descriptive economics.

View
Economics