oe Smith, age 75, from Vienna, IL has the winning Powerball lottery numbers which will pay out $13 million at the beginning of each of the next 30 years (reported prize of $390 million). Before claiming his prize, Trusty Insurance Company offers Joe $200 million today in exchange for his winning lottery ticket and prize payout. What rate of return would Trusty Insurance earn if Joe accepts their offer?

The IRR is 5%. Rate of return would be 12.5% assuming a discount rate of 4%

Explanation:

The answer depends entirely on the discount rate. The question covers a 30 period timeframe and in each period, the pay off is $13 million. This is a simple time value of money concept in which to calculate the present value, you will simply calculate the present value of each of the cash flows. The formula is 13Mn/[(1+r)^n] where n is the year from 1 to 30, r is the discount rate.

The question requires us to calculate the return that is the variable 'r'. For this you need to have the present value today so that you can then use the equation to solve for 'r'. However, the only information we have is the time period and the cash flow. We are given $200mn as the initial outlay. So, we can at least use this to calculate the internal rate of return (IRR) which is simply the rate of return (or the value of 'r') at which the present value of each of the 13 Mn to be received over the next 30 years is equal to the initial outlay (i.e 200mn). In short, IRR is the rate of return at which the net present value (NPV) is equal to zero. In our example, and using the formula for each of the cash flow from years 1 to 30, the IRR is computated at 5%. So if the discount rate that the company uses is less than 5%, the company would be better of with Joe accepting the offer because any discount rate below 5% would result in the present value of the cash flows to be in excess of $200Mn.

Lets take an example and assume that the discount rate is 4%, using the formula from year 1 to 30 and summing the values would give us a present value of $225 Mn. So the rate lf return in this case would be (225-200)/200 x 100 = 12.5%.

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