Question

For each of the following, determine the expected cash flows. Cash Flow Probability Estimate Assessment (a) \( 4,800 20% 6,300 50% 7,500 30% (b) \) 5,400 30% 7,200 50% 8,400 20% (c) $(1,000) 10% 3,000 80% 5,000 10%

Short answer

The total expected value for part A will be $6,360, the total expected value for part B will be $6,900, and the total expected value for part C will be $2,800.

Step-by-step solution

Computation for part A

$$\begin{gathered} \mathbf{Total}\mathbf{}\mathbf{Expected}\mathbf{}\mathbf{Value}\mathbf{=}\mathbf{Cashflow}\mathbf{\times }\mathbf{Probability} \\ \mathbf{=}\mathbf{4}\mathbf{,}\mathbf{800}\mathbf{\times }\mathbf{20}\mathbf{\%}\mathbf{+}\mathbf{6}\mathbf{,}\mathbf{300}\mathbf{\times }\mathbf{50}\mathbf{\%}\mathbf{+}\mathbf{7}\mathbf{,}\mathbf{500}\mathbf{\times }\mathbf{30}\mathbf{\%} \\ \mathbf{=}\mathbf{960}\mathbf{+}\mathbf{3}\mathbf{,}\mathbf{150}\mathbf{+}\mathbf{2}\mathbf{,}\mathbf{250} \\ \mathbf{=}\mathbf{\$}\mathbf{6}\mathbf{,}\mathbf{360} \end{gathered}$$

Computation for part B

$$\begin{gathered} \mathbf{Total}\mathbf{}\mathbf{Expected}\mathbf{}\mathbf{Value}\mathbf{=}\mathbf{Cashflow}\mathbf{\times }\mathbf{Probability} \\ \mathbf{=}\mathbf{5}\mathbf{,}\mathbf{400}\mathbf{\times }\mathbf{30}\mathbf{\%}\mathbf{+}\mathbf{7}\mathbf{,}\mathbf{200}\mathbf{\times }\mathbf{50}\mathbf{\%}\mathbf{+}\mathbf{8}\mathbf{,}\mathbf{400}\mathbf{\times }\mathbf{20}\mathbf{\%} \\ \mathbf{=}\mathbf{1}\mathbf{,}\mathbf{620}\mathbf{+}\mathbf{3}\mathbf{,}\mathbf{600}\mathbf{+}\mathbf{1}\mathbf{,}\mathbf{680} \\ \mathbf{=}\mathbf{\$}\mathbf{6}\mathbf{,}\mathbf{900} \end{gathered}$$

Computation for part C

$$\begin{gathered} \mathbf{Total}\mathbf{}\mathbf{Expected}\mathbf{}\mathbf{Value}\mathbf{=}\mathbf{Cashflow}\mathbf{\times }\mathbf{Probability} \\ \mathbf{=}\mathbf{-}\mathbf{1000}\mathbf{\times }\mathbf{10}\mathbf{\%}\mathbf{+}\mathbf{3}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{80}\mathbf{\%}\mathbf{+}\mathbf{5}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{10}\mathbf{\%} \\ \mathbf{=}\mathbf{-}\mathbf{100}\mathbf{+}\mathbf{2}\mathbf{,}\mathbf{400}\mathbf{+}\mathbf{500} \\ \mathbf{=}\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{800} \end{gathered}$$