413.3
3.Let’s say that during your salary negotiations with Lucasfilm you are given the following offer: either get $10,000 a year extra in salary for the next 40 years, or get $80,000 a year extra in pension for 25 years, starting 41 years from now. Assuming an interest rate of 12%, which should you take (ignore any tax considerations)? (10)
Better draw a cash flow timeline for this one:
| 0 | 1 … | 40 | 41 … | 65 |
| 10 | 10 | 80 | 80 |
Compare the PV of these 2 annuities:
The first one is straightforward:
The second one is trickier because it is deferred. First find the value in year 40 (one year before the annuity starts). Then find the value of that annuity in the present.
\( \Large Value in Year 40 = 80000 \left [ \frac{1}{.12} - \frac{1}{.12 \left(1+.12 \right )^{25} } \right ] = 627{,}451.13\)
\( \Large Value in Year 0 = \frac{627{,}451.13}{1.12^{40} } = 6743.09\)
So the first offer (extra $10,000 per year for 40 years) is way better.