Question

Use the following information to answer the next 3 questions: Otis just won the lottery and has been given the choice of two payout options:

• Option #1: He can receive $25,000 every six months for twenty years.
• Option #2: He can wait and receive $28,500 every six months for twenty years with the first payment coming one and a half years from now.

The appropriate discount rate is 13 percent compounded semiannually.

What is the present value of Option #1?

What is the present value of Option #2?

Which option should be chosen? Why should that particular option be chosen?

Answer 1

Answer:

Annual interest rate = 13.00%
Semiannual interest rate = 6.50%

Option 1:

Semiannual payment = $25,000
Number of payments = 40

Present value = $25,000/1.065 + $25,000/1.065^2 + … + $25,000/1.065^39 + $25,000/1.065^40
Present value = $25,000 * (1 - (1/1.065)^40) / 0.065
Present value = $25,000 * 14.14553
Present value = $353,638.25

Option 2:

Semiannual payment = $28,500
Number of payments = 40

Present value = $28,500/1.065^3 + $28,500/1.065^4 + … + $28,500/1.065^41 + $28,500/1.065^42
Present value = $28,500 * (1/1.065)^2 * (1 - (1/1.065)^40) / 0.065
Present value = $28,500 * 12.47154
Present value = $355,438.89

Otis should choose Option 2 as its present value is higher