Question

A brilliant young scientist is killed in a plane crash. It is anticipated that he could have earned $430,000 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 9 percent.
What is the difference between the present value of the settlement at 4 percent and 9 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.)

PV at 4% =

PV at 9% =

Difference =

Answer 1

Present Value (PV) at 4%

Annual Payment (P) = $430,000

Annual Interest Rate (r) = 4% per year

Number of years (n) = 50 Years

Present Value of an Ordinary Annuity = P x [{1 - (1 / (1 + r) n} / r]

= $430,000 x [{1 - (1 / (1 + 0.04)⁵⁰} / 0.04]

= $430,000 x [{1 - (1 / 7.10668)} / 0.04]

= $430,000 x [(1 - 0.14071) / 0.04]

= $430,000 x [0.85929 / 0.04]

= $430,000 x 21.48218

= $92,37,339.39

Present Value (PV) at 9%

Annual Payment (P) = $430,000

Annual Interest Rate (r) = 9% per year

Number of years (n) = 50 Years

Present Value of an Ordinary Annuity = P x [{1 - (1 / (1 + r) n} / r]

= $430,000 x [{1 - (1 / (1 + 0.09)⁵⁰} / 0.09]

= $430,000 x [{1 - (1 / 74.35752)} / 0.09]

= $430,000 x [(1 - 0.01345) / 0.09]

= $430,000 x [0.98655 / 0.09]

= $430,000 x 10.96168

= $47,13,523.65

Difference between the present value of the settlement at 4 percent and 9 percent

Difference = Present Value (PV) at 4% - Present Value (PV) at 9%

= $92,37,339.39 - $47,13,523.65

= $45,23,815.74