Question

You have just been notified that you have won the jackpot in a lottery. You can accept your winnings in one of the following cashflow streams. Assume you are not liable for any income taxes on the winnings. Compare the alternatives assuming a long-term average interest rate on any investments of 8%. (1) RM 900,000 per year for ten years, first payment received immediately. (2) RM 750,000 per year for twenty years, first payment received immediately. (3) RM 75,000 per month for the next 15 years, beginning at the end of the first month.

Answer #1

Rate of Interest = 8%

Monthly rate of interest = (8% / 12) = 0.67%

Present value of annuity is calculated as: Amount * {[1 - (1 +
r)^^{-n}] / r}

where n is duration of payment

Keep in mind that monthly payment will have monthly rate of interest

a) Present value = 900,000 * {[1 - (1 + 0.08)^^{-10}] /
0.08} = 6,039,073.25

b) Present value = 750,000 * {[1 - (1 + 0.08)^^{-20}] /
0.08} = 7,363,610.55

c) Present value = 75,000 * {[1 - (1 + 0.0067)^^{-180}]
/ 0.0067} = 7,829,114.75

Present value of monthly payment is highest, you must choose option c.

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