You are serving on a jury. A plaintiff is suing the city for injuries sustained

Question

You are serving on a jury. A plaintiff is suing the city for injuries sustained after falling down an uncovered manhole. In the trial, the doctor testified that it will be 5 years before the plaintiff is able to return to work. The jury has already decided in favor of the plaintiff. You are the foreman of the jury and propose that the jury gives the plaintiff an award to cover the following items:

a)     The present value of 2 years of back-pay ($34,000 and $36,000).

b)     The present value of 5 years of future salary. Assume that the salary would increase at a rate of 3 percent a year.

c)     $100,000 for pain and suffering

d)     $20,000 for court costs

e)     Assume an interest rate of 7%. What should be the size of the settlement?

Need to see how this is worked out.

Thanks

Explanation / Answer

The compensation should be equal to the sum of present value of all costs associated with injury.

Suppose this is period T. We have been given that the rate of interest r = 7%.

A. First calculate the present value of back pay:

34000 was earned in period T - 1, so present value of 34000 in period T - 1 = 34000 * (1 + r)1 = 34000 * 1.07 = 36380

36000 was earned in period T, so the present value of 36000 in period T = 36000 * (1+r)0 = 36000

Present value of 2 years of back pay = 36380 + 36000 = 72380

B. Next calculate the present value of 5 years of future salary. Given salary grows by 3% every year

S1 = Salary in period T + 1 = Salary in period T * (1 + 0.03) = 36000 * (1 + 0.03) = 37080

S2 = Salary in period T + 2 = Salary in period T + 1 * (1 + 0.03) = 37080 * (1 + 0.03) = 38192.4

S3 = Salary in period T + 3 = Salary in period T + 2 * (1 + 0.03) = 38192.4 * (1 + 0.03) = 39338.17

S4 = Salary in period T + 4 = Salary in period T + 3 * (1 + 0.03) = 39338.17 * (1 + 0.03) = 40518.32

S5 = Salary in period T + 5 = Salary in period T + 4 * (1 + 0.03) = 40518.32 * (1 + 0.03) = 41733.87

Present value of future salary = S1/(1 + r)1 + S2/(1 + r)2 + S3/(1 + r)3 + S4/(1 + r)4 + S5/(1 + r)5

= 160791.49

C. Next calculate the present value of all costs:

Present value of all costs = Present value of back-pay + Present value of future salary + Cpsts pain and suffering + Court costs

= 72380 + 160791.49 + 100000 + 20000

= $353171.49

Hence, the settlement size should be $353,171.49 (approximately $353,171)

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