Question

Sally is injured in a work accident and the court is trying to determine the discounted value of her future income. At the time of the accident, she was earning $50,000 a year and planned to retire in 31 years. She anticipated getting a 3% raise for the first 8 years and a 6.5% raise each year after. Assuming the payments are at the end of the year and the first is $50,000, determine the discounted value of her future income is money is worth j1= 2.3%.

Answer 1

Salary till retirement consists of 2 cash flow streams-

(1 ) First 9 years, beginning at $50,000 in year 1 and growing at 3% from year 2 to year 9 (Growing annuity-ordinary)

(2) Next 22 years, growing at 6.5% from year 10 to year 31 (Growing annuity-ordinary).

First payment (year 10) = $50,000*(1+3%)^9= $50,000*1.304773 = $65,238.66

Present value of first set of payments= $452,116.71 as follows:

Present value of second set of payments at the end of year 9= $2,210,989.39 as follows:

Present value of the above amount now= $2,210,989.39 *PVF(2.3%,9)

= $2,210,989.39 * 0.814928 = $1,801,797.39

Total present value of future salary= $452,116.71 + $1,801,797.39 = $2,253,914.10