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Jesse just won the state lottery. He has been given the option of receiving either $62.9...
Jesse just won the state lottery. He has been given the option of receiving either $62.9 million today or $5 million a year for the next 35 years, with the first payment paid today. Describe the process that Jesse should use to determine which payment option he prefers. Ignore all taxes and assume that Jesse will live for at least 40 more years.
Solutions
Expert Solution
| Option 1 - option of receiving either $62.9 million today | |||||
| Option 2 - $5 million a year for the next 35 years | |||||
| In Million $ | |||||
| Year | Cash Flows | Discount Factor @5% | Discount Factor @10% | Discounted Values | Discounted Values |
| 0 | 5.00 | 1.00 | 1.00 | 5.00 | 5.00 |
| 1 | 5.00 | 0.95 | 0.91 | 4.76 | 4.55 |
| 2 | 5.00 | 0.91 | 0.83 | 4.54 | 4.13 |
| 3 | 5.00 | 0.86 | 0.75 | 4.32 | 3.76 |
| 4 | 5.00 | 0.82 | 0.68 | 4.11 | 3.42 |
| 5 | 5.00 | 0.78 | 0.62 | 3.92 | 3.10 |
| 6 | 5.00 | 0.75 | 0.56 | 3.73 | 2.82 |
| 7 | 5.00 | 0.71 | 0.51 | 3.55 | 2.57 |
| 8 | 5.00 | 0.68 | 0.47 | 3.38 | 2.33 |
| 9 | 5.00 | 0.64 | 0.42 | 3.22 | 2.12 |
| 10 | 5.00 | 0.61 | 0.39 | 3.07 | 1.93 |
| 11 | 5.00 | 0.58 | 0.35 | 2.92 | 1.75 |
| 12 | 5.00 | 0.56 | 0.32 | 2.78 | 1.59 |
| 13 | 5.00 | 0.53 | 0.29 | 2.65 | 1.45 |
| 14 | 5.00 | 0.51 | 0.26 | 2.53 | 1.32 |
| 15 | 5.00 | 0.48 | 0.24 | 2.41 | 1.20 |
| 16 | 5.00 | 0.46 | 0.22 | 2.29 | 1.09 |
| 17 | 5.00 | 0.44 | 0.20 | 2.18 | 0.99 |
| 18 | 5.00 | 0.42 | 0.18 | 2.08 | 0.90 |
| 19 | 5.00 | 0.40 | 0.16 | 1.98 | 0.82 |
| 20 | 5.00 | 0.38 | 0.15 | 1.88 | 0.74 |
| 21 | 5.00 | 0.36 | 0.14 | 1.79 | 0.68 |
| 22 | 5.00 | 0.34 | 0.12 | 1.71 | 0.61 |
| 23 | 5.00 | 0.33 | 0.11 | 1.63 | 0.56 |
| 24 | 5.00 | 0.31 | 0.10 | 1.55 | 0.51 |
| 25 | 5.00 | 0.30 | 0.09 | 1.48 | 0.46 |
| 26 | 5.00 | 0.28 | 0.08 | 1.41 | 0.42 |
| 27 | 5.00 | 0.27 | 0.08 | 1.34 | 0.38 |
| 28 | 5.00 | 0.26 | 0.07 | 1.28 | 0.35 |
| 29 | 5.00 | 0.24 | 0.06 | 1.21 | 0.32 |
| 30 | 5.00 | 0.23 | 0.06 | 1.16 | 0.29 |
| 31 | 5.00 | 0.22 | 0.05 | 1.10 | 0.26 |
| 32 | 5.00 | 0.21 | 0.05 | 1.05 | 0.24 |
| 33 | 5.00 | 0.20 | 0.04 | 1.00 | 0.22 |
| 34 | 5.00 | 0.19 | 0.04 | 0.95 | 0.20 |
| Present Value | 85.96 | 53.04 | |||
| Break Even Rate = 5% + 5%*23.05/32.92 | |||||
| Break Even Rate = 8.5024% | |||||
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