Your grandfather has offered you a choice of one of the ...
Your grandfather has offered you a choice of one of the three following alternatives: $5,000 now; $1,000 a year for each years; or $12,000 at the end of eight years. Assuming you could earn 11 percent annually, which alternative should you choose? If you could earn 12 percent annually, would you still choose the same alternative?
| |
|Solution: |
| |
|(first alternative) Present value of $5,000 received now: |
|$5,000 |
| |
|(second alternative) Present value of annuity of $1,000 for eight years: Appendix D |
|PVA = A * PVIFA |
|= $1,000 * PVIFA (11%, 8 years) |
|= $1,000 * 5.146 |
|= $5,146 |
| |
|(third alternative) Present value of $12,000 received in eight years: Appendix B |
|PV = FV * PVIF |
|= $12,000 * PVIF (11%, 8 years) |
|= $12,000 * .434 |
|= $5,208 |
| |
|Select $12,000 to be received in eight years. |
| |
|Revised answers based on 12%. |
| |
|(first alternative) Present value of $5,000 received today: $5,000 |
| |
| |
| |
|(second alternative) Present value of annuity of $1,000 at 12% for 8 years: Appendix D |
|PVA = A * PVIFA |
|= $1,000 * PVIFA (12%, 8 years) |
|= $1,000 * 4.968 |
|= $4,968 |
| |
|(third alternative) Present value of $12,000 received in 8 years at 12%: Appendix B |
|PV = FV * PVIF |
|= $12,000 * PVIF (12%, 8 years) |
|= $12,000 * .404 |
|= $4,848 |
| |
|Select $5,000 now. |
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