Question

Keith Bowie is trying to determine the amount to set aside so that he will have enough money on hand in 2 years to overhaul the engine on his vintage used car. While there is some uncertainty about the cost of engine overhauls in 2 years, by conducting some research online, Keith has developed the following estimates. Engine Overhaul Probability Estimated Cash Outflow Assessment $200 10% 450 30% 600 50% 750 10%

Instructions How much should Keith Bowie deposit today in an account earning 6%, compounded annually, so that he will have enough money on hand in 2 years to pay for the overhaul?

Short answer

The present value of the expected cash flow will be $471.7.

Step-by-step solution

Computation expected cash flow

$$\begin{gathered} \mathbf{Expected}\mathbf{}\mathbf{CashFlow}\mathbf{=}\mathbf{Cashflow}\mathbf{\times }\mathbf{Probability} \\ \mathbf{=}\mathbf{200}\mathbf{\times }\mathbf{10}\mathbf{\%}\mathbf{+}\mathbf{450}\mathbf{\times }\mathbf{30}\mathbf{\%}\mathbf{+}\mathbf{600}\mathbf{\times }\mathbf{50}\mathbf{\%}\mathbf{+}\mathbf{750}\mathbf{\times }\mathbf{10}\mathbf{\%} \\ \mathbf{=}\mathbf{20}\mathbf{+}\mathbf{135}\mathbf{+}\mathbf{300}\mathbf{+}\mathbf{75} \\ \mathbf{=}\mathbf{\$}\mathbf{530} \end{gathered}$$

Computation of present value

$$\begin{gathered} \mathbf{Present}\mathbf{}\mathbf{Value}\mathbf{=}\mathbf{Expected}\mathbf{}\mathbf{Cashflow}\mathbf{\times }\mathbf{PV}\mathbf{}\mathbf{Factor} \\ \mathbf{=}\mathbf{530}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{89000} \\ \mathbf{=}\mathbf{\$}\mathbf{471}\mathbf{.}\mathbf{7} \end{gathered}$$