Question

Enhance Reinsurance Company was reported to have offered $4.2 million. Find the return that the company was looking for.

Answer 1

Question:

Several years ago The Wall Street Journal reported that the winner of the Massachusetts State Lottery prize had the misfortune to be both bankrupt and in prison for fraud. The prize was $9,420,713 to be paid in 19 equal annual installments. (There were 20 installments, but the winner had already received the first payment.) The bankruptcy court judge ruled that the prize should be sold off to the highest bidder and the proceeds used to pay off the creditors.

a. If the interest rate was 8%, how much would you have been prepared to bid for the prize?

b. Enhance Reinsurance Company was reported to have offered $4.2 million. Use Excel to find the return that the company was looking for.

 

Answer:

a. The amount I would have been prepared to bid for the prize is $4,761,724

b. The rate of return (r) they (that is Enhance Reinsurance Company) was looking for is r = 9.81%.

Explanation (a):

I would be willing to pay approximately USD 4.76 Million for the lottery because my Present Value calculations show me that the total value of the money now is worth less than it will be by the time I have collected the last installment 19 years later.

Present Value in finance refers to the incumbent value of cash or money or stream of cash flows to be received at a future date and or time subject to a rate of return. Its formula is given as follows

PV = $FV\frac{1}{(1+r)^{2} }$

Step 1:

If there were 20 installments and the winner had already received the first installment, then the remaining monthly installments (that is the Future Values) are given as follows:

Balance divided by 19 years

$9,420,713 / 19 = $495,827

Step 2:

PV=$495,827 $[\frac{1}{0.08} - \frac{1}{0.08 X (1.08^{19} )} ]$

PV = $4,761,724

Explanation (b):

Given that Enhance Reinsurance Company (ERC) was willing to pay $4.2 Million, the rate of return they were looking at can be calculated as follows:

$4,200,000 = $495,827 x $[\frac{1}{r} - \frac{1}{r X (1+r)^{19} } ]$

Computing the above with excel, we arrive at 9.81%.

Cheers!