Question

You are leaving your job as an agribusiness manager and your pension plan is offering you two options. Take a lump sum payout of $150,000 or leave it in the fund and beginning 20 years from now they will pay you annually $10,000 until you die with an adjustment for inflation of 3% growth rate per year on that payment. Assume you expect to live for 25 years after retirement and you could invest the $150,000 at 4% for the next 20 years. Assume interest rates remain at 4% after retirement.   What is the value of the payments  after retirement that you would use to compare to investing on your own? State the answer rounded to the nearest dollar.

Answer 1

FV at the end of 20 years from now of your own investment = FV (Rate, Nper, PMT, PV) = FV (4%, 20, 0, -150000) = $ 328,668.47

Let's say this is good enough to pay us a year beginning annuity of A adjusted for inflation, g = 3% over n = 25 years. Hence, PV of these growing annuities should same a the FV calculated above.

$328,668.47 = \frac{A(1+r)}{r-g}[1-\frac{(1+g)^n}{(1+r)^n}]=\frac{A(1+0.04)}{0.04-0.03}[1-\frac{(1+0.03)^{25}}{(1+0.04)^{25}}]$

Hence, 22.3172A = 328,668.47

Hence, A = 328,668.47 / 22.3172 = $14,727

Hence, the value of the payments after retirement that you would use to compare to investing on your own = A = $ 14,727