Question

You won the lottery, and can choose one of two (guaranteed) payments: Choice A pays $5,000,000 today; Choice B pays $350,000 at the end of the next 20 years (first payment is one year from today).

A. If the discount rate is 5%, which option should you choose?

B. If the discount rate is 2%, which option should you choose?

C. At what discount rate would you be indifferent between these two choices? (Hint: When will the two choices have the same present value?)

***To receive credit for the question, you must show work!!****

Answer 1

a). PV of Choice B = Annuity * [{1 - (1 + r)^-n} / r]

= $350,000 * [{1 - (1 + 0.05)^-20} / 0.05]

= $350,000 * [0.6231 / 0.05]

= $350,000 * 12.4622 = $4,361,773.62

Option A has a higher PV and hence, it is a better choice.

b). PV of Choice B = Annuity * [{1 - (1 + r)^-n} / r]

= $350,000 * [{1 - (1 + 0.02)^-20} / 0.02]

= $350,000 * [0.3270 / 0.02]

= $350,000 * 16.3514 = $5,723,001.67

Option B has a higher PV and hence, it is a better choice.

c). To find the indifferent rate, we need to put the following values in the financial calculator:

N = 20; PV = -5,000,000; PMT = 350,000; FV = 0;

Press CPT< then I/Y, which gives us 3.44

So, the rate at which both choices will be indifferent is 3.44%