You have just won the lottery. You will receive $2,440,000 today, and then recei

Question

You have just won the lottery. You will receive $2,440,000 today, and then receive 40 payments of $1,220,000 These payments will start one year from now and will be paid every sik months. A representative from Greenleaf Investments has offered to purchase all the payments from you for $26 million. The interest rate is an APR of 8 percent compounded daily. Assume there are 12 months in a year each with 30 days. What is the present value of the cash flows from your lottery winnings? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Present value

Explanation / Answer

m = 12*30 = 360 days

Thus effective rate = [1+0.08/360]^360 - 1 = 8.33%

Now the 1st payment of 1,220,000 wil be received in year 1, 2nd payment in year 1.5, 3rd payment in year 2 and so on till the 40th payment is received in year 20.5

Thus the present value = $25,364,720.25 (or $25.364 million)

Year Cash flow 1+r PVIF PV 0.00 2,440,000.00 1.0833 1.0000 2,440,000.00 1.00 1,220,000.00 0.9231 1,126,211.95 1.50 1,220,000.00 0.8869 1,082,057.36 2.00 1,220,000.00 0.8522 1,039,633.90 2.50 1,220,000.00 0.8187 998,873.71 3.00 1,220,000.00 0.7866 959,711.58 3.50 1,220,000.00 0.7558 922,084.85 4.00 1,220,000.00 0.7262 885,933.32 4.50 1,220,000.00 0.6977 851,199.16 5.00 1,220,000.00 0.6703 817,826.80 5.50 1,220,000.00 0.6441 785,762.84 6.00 1,220,000.00 0.6188 754,956.00 6.50 1,220,000.00 0.5946 725,356.97 7.00 1,220,000.00 0.5712 696,918.41 7.50 1,220,000.00 0.5488 669,594.83 8.00 1,220,000.00 0.5273 643,342.50 8.50 1,220,000.00 0.5067 618,119.42 9.00 1,220,000.00 0.4868 593,885.25 9.50 1,220,000.00 0.4677 570,601.22 10.00 1,220,000.00 0.4494 548,230.06 10.50 1,220,000.00 0.4318 526,735.99 11.00 1,220,000.00 0.4148 506,084.63 11.50 1,220,000.00 0.3986 486,242.93 12.00 1,220,000.00 0.3829 467,179.14 12.50 1,220,000.00 0.3679 448,862.78 13.00 1,220,000.00 0.3535 431,264.54 13.50 1,220,000.00 0.3396 414,356.25 14.00 1,220,000.00 0.3263 398,110.88 14.50 1,220,000.00 0.3135 382,502.43 15.00 1,220,000.00 0.3012 367,505.93 15.50 1,220,000.00 0.2894 353,097.38 16.00 1,220,000.00 0.2781 339,253.75 16.50 1,220,000.00 0.2672 325,952.86 17.00 1,220,000.00 0.2567 313,173.46 17.50 1,220,000.00 0.2466 300,895.09 18.00 1,220,000.00 0.2370 289,098.11 18.50 1,220,000.00 0.2277 277,763.65 19.00 1,220,000.00 0.2187 266,873.56 19.50 1,220,000.00 0.2102 256,410.44 20.00 1,220,000.00 0.2019 246,357.54 20.50 1,220,000.00 0.1940 236,698.77 Total 25,364,720.25

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