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Chapter 4: Q11-3BP (page 363)

A brilliant young scientist is killed in a plane crash. It is anticipated that he could have earned $240,000 a year for the next 50 years. The attorney for the plaintiff’s estate argues that the lost income should be discounted back to the present at 4 percent. The lawyer for the defendant’s insurance company argues for a discount rate of 8 percent. What is the difference between the present value of the settlement at 4 percent and 8 percent? Compute each one separately

Short Answer

Expert verified

Present value annuity of the settlement at 4% is $5,155,680 and 8% is $2,935,920. A higher discount rate is generated a lower present value. Insurance is lower by $2,219,760.

Step by step solution

01

Computing present value annuity-

Presentvalueannuity=Principal×[1−(1+r)−nr]=$240,000×[1−(1+0.04)−500.04]=$240,000×21.482=$5,155,680

02

Computing present value annuity-

Presentvalueannuity=Principal×[1−(1+r)−nr]=$240,000×[1−(1+0.08)−500.08]=$240,000×12.233=$2,935,920

03

Computing the difference between the present value of the settlement at 4% and 8%-

Present value annuity 4%

$5,155,680

Less: Present value annuity 8%

($2,935,920)

$2,219,760

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