A brilliant young scientist is killed in a plane crash. It is anticipated that h

Question

A brilliant young scientist is killed in a plane crash. It is anticipated that he could have earned $200,000 a year for the next 40 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 12 percent. What is the difference between the present value of the settlement at 4 percent and 12 percent? Compute each one separately. Use Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Explanation / Answer

NPV = CF * (1 - ( 1 + i)-n)i Scenario 1 CF = 200000 i = 4% - 0.04 n = 40 NPV = 200000 * ( 1 - ( 1+0.04)-40)/0.04          = 200000 * ( 1 - 0.2083) /0.04          = 200000 * 0.7917/0.04           = 200000 * 19.7925            = 3958500 Scenario 2 CF = 200000 i = 12% = 0.12 n = 40 NPV = 200000 * ( 1 - ( 1+0.12)-40)/0.12          = 200000 * ( 1 - 0.0107) /0.12          = 200000 * 0.9893/0.12           = 200000 * 8.2442            = 1648833 Present value at discount rate of 4% 3958500 Present value at discount rate of 12% 1648833 Difference 2309667

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