Congratulations you have just won the tuition lottery! The lottery pays out four beginning-of-the-year cash flows of $50,000 each with the first cash flow today and the remaining cash flows to follow at the start of years 2,3,and 4.Since the lottery is managed by the Fergetaboutit University system you are considering their offer of a lump sum of $160,000 today.If after considering all of he relevant economic factors,you conclude it is reasonable to use a 12% interest rate to compare these two offers.Which offer should you take and why?
A)Take the lump sum because the annuity PV is only $151,867.47.
B)Take the annuity because the PV of $170,091.56 is greater than the lump sum.
C)Take the annuity because the PV of $238,966.40 is greater than the lump sum.
D)Take the lump sum because the annuity PV is only $135,595.95.

Question

Quizplus · Accepted Answer

To compare the two offers, we need to find the present value (PV) of the annuity cash flows. Using the formula for the present value of an annuity, we get:

PV = C * [(1 - (1+r)^(-n)) / r]

where C is the cash flow, r is the interest rate, and n is the number of periods.

So for this lottery, we get:

PV = $50,000 * [(1 - (1+0.12)^(-4)) / 0.12]
PV = $170,091.56

This means that the lump sum offer of $160,000 is less than the present value of the annuity, so it would be better to take the annuity. Therefore, choice B is correct.

Congratulations You Have Just Won the Tuition Lottery! the Lottery