Assume that an uncle of yours was injured on 1/1/15 in an automobile accident. The accident was serious, and it was the other driver's fault. As the result of the accident, your uncle will not be able to return to his medical practice where he earned $280,000 during calendar year 2014. Your uncle's accident occurred on his 60th birthday (some birthday) and he planned (prior to the accident) to work another eight years (until the end of 2022). 

Your uncle has sustained a large economic loss because he can no longer count on his substantial earnings from his medical practice. To recover his economic loss, your uncle filed suit against the other driver and the driver's insurance company in Wisconsin Civil Court. The case comes to trial at the end of this month, but your uncle has just received a settlement offer from the insurance company of $2,300,000 to compensate him for his loss of past (2015) and future (2016-2022) earning capacity. Your uncle seeks your advice in evaluating the settlement offer. In particular, he asks you whether $2,300,000 meets the standard required in Wisconsin Civil Courts "that all future economic damages be expressed in present value terms". [You should know also that the convention in such legal proceedings is to use the U.S. Treasury bond rate as the discount rate.]

To give your uncle the advice he seeks you must calculate the present value of his expected earnings for the years 2015-2022. In making this calculation, assume the following: a) Your uncle (absent the accident) would have continued to work full time in his medical practice from the date of the accident (1/1/15 until his projected retirement on 12/31/2022; b) Your uncle earned $280,000 in 2014 and expected to have his earnings increase in 2015 and each future year by 3% per year; c) Use 2.0% as the annual discount rate to discount projected future earnings to present value. [2.0% is the approximate current yield of U.S. Treasury bonds maturing in 2022.]

1. Explain and show your calculations (using the template at the end of this assignment) of how you would set up the present value calculation in your uncle's case. What is the present value of his lost expected earnings if we use 2.0% as the discount rate? [Hint: Remember that we are assuming that his earnings will increase by 3.0% each year over the entire eight-year period. Thus your first task is to calculate his projected earnings in each year (2015-2022). Once you have his projected earnings calculated, you then proceed to the discounting calculation. The template at the bottom of this assignment should help you.]

2. Does the $2,300,000 settlement offer equal or exceed the full present value of the loss of earnings sustained by your uncle? Ignoring the cost of the trial (and the chance that the jury might not find in his favor), should he accept this settlement? Explain

3. Would your answer in #2 change if you were to use 4.0 percent as the discount rate? Be specific.

[Hints: To ease the computational busy work in this problem, please be advised of the following:

The present value of $1 discounted at 2.0% (and received at the end of each of the following years) is:

2015             $1.00

2016              $.9804

2017              $.9612

2018              $.9423

2019              $.9238

2020              $.9057

2021              $.8880

2022              $.8706

Likewise, the present value of $1 discounted at 4% (and received at the end of each of the following years) is:

2015              $1.00

2016              $.9615

2017              $.9246

2018              $.8890

2019              $.8548

2020              $.8219

2021              $.7903

2022              $.7599

[Note in both cases that income that would have been received in 2015 is not reduced in the present value calculation. Put differently, assume that January 1, 2016 is the beginning of the future period.]

Perhaps the following will help you sort this out:

The information provided in your assignment for this week (see below) just performs these individual calculations for you (on the assumption of $1 received at the end of each future year). 

Thus (using the 2.0% case), if you want to calculate the present value of $300,000 received in 2017, the PV = $300,000*.9612 = $288,360.

The same calculation using a 4.0% discount rate is: $300,000*.9246 = $277,380.

This example illustrates a very important result: other things being equal, the present value of any fixed sum of money to be received at a future date will vary inversely with the discount rate. The higher the discount rate, the lower the present value. This explains why the stock market generally declines when interest rates rise and why housing prices decline when mortgage interest rates rise, etc.