Question

7.         You have just won the Virginia Lottery and they have offered you two different payout arrangements. Option A: You can choose to receive $1,000,000 per year for the next ten years paid at the end of each year. Option B: You can receive $750,000 per year for the next ten years paid at the end of each year, along with a $1,500,000 payment today. If the interest rate is 10% which option will you prefer and why? Show Calculations. (4 pts)

Answer 1

Option A:

Present value = Annuity * [1 - 1 / (1 + r)^n] / r

present value = 1,000,000 * [1 - 1 / (1 + 0.1)^10] / 0.1

Present value = 1,000,000 * [1 - 0.385543] / 0.1

Present value = 1,000,000 * 6.144567

Present value = $6,144,567.11

Option B:

Present value = Initial payment + Annuity * [1 - 1 / (1 + r)^n] / r

Present value = 1,500,000 + 750,000 * [1 - 1 / (1 + 0.1)^10] / 0.1

Present value = 1,500,000 + 750,000 * [1 - 0.385543] / 0.1

Present value = 1,500,000 + 750,000 * 6.144567

Present value = 6,108,425.33

You should prefer option A as it has the higher present value.