Question

Bowie is trying to determine the amount to set aside so that he will have enough money on hand in 6 years to overhaul the engine on his vintage used car. While there is some uncertainty about the cost of engine overhauls in 6 years, by conducting some research online, Newman has developed the following estimates.

Engine Overhaul Estimated Cash flow	probability assessment
$380	10%
450	30%
810	50%
800	10%

How much should Bowie deposit today in an account earning 6%, compounded annually, so that he will have enough money on hand in 6 years to pay for the overhaul? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

Answer 1

Expected cash flow

Expected cash flow = ($380 x 0.10) + ($450 x 0.30) + ($810 x 0.50) + ($800 x 0.10)

Expected cash flow = $38 + $135 + $405 + $80

Expected cash flow = $658

Amount to be deposited

Amount to be deposited = Expected cash flow / (1 + r)^n

Amount to be deposited = $658 / (1 + 0.06)^6

Amount to be deposited = $658 / 1.418519112

Amount to be deposited = $463.86

Therefore, the amount to be deposited will be $463.86