Question 7.EX.4.5: Calculation of expected net present value Star has a cost ...
Calculation of expected net present value
Star has a cost of capital of 12 per cent and is evaluating a project with an initial investment of €375,000. The estimated net cash flows of the project under different economic circumstances and their respective probabilities are as follows:
Table (1)
Table (2)
If economic conditions in Year 2 are not dependent on economic conditions in Year 1, what is the expected value of the project’s NPV? What is the risk that the NPV will be negative?
Table (1)
Net cash flows for Year 1
\begin{array}{|l|c|c|}\hline \text { Economic conditions } & \text { Probability } & \text { Cash flow }(€) \\\hline \text { Weak } & 0.2 & 100,000 \\\text { Moderate } & 0.5 & 200,000 \\\text { Good } & 0.3 & 300,000 \\\hline\end{array}
Table (2)
Net cash flows for Year 2
\begin{array}{|l|c|c|}\hline \text { Economic conditions } & \text { Probability } & \text { Cash flow }(€) \\\hline \text { Moderate } & 0.7 & 250,000 \\\text { Good } & 0.3 & 350,000 \\\hline\end{array}The first step is to calculate the present values of each individual cash flow.
Table (3)
The next step is to calculate the total present value of the cash flows of each combination of Year 1 and Year 2 economic conditions by adding their present values.
Table (4)
The total present value of the cash flows of each combination of economic conditions is now multiplied by the joint probability of each combination of economic conditions, and these values are then added to give the expected present value of the cash flows of the project.
Table (5)
\begin{array}{lc} & {£} \\\text { Expected present value of cash inflows } & 410,600 \\\text { Less: Initial investment } & \underline{375,000} \\\text { Expected value of NPV } & \underline{35,600} \\\end{array}The probability that the project will have a negative NPV is the probability that the total present value of the cash flows is less than €375,000. Using the column in the table headed ‘Total present value of cash flow’ and picking out values less than €375,000, we can see that the probability that the project will have a negative NPV is 0.14 + 0.06 = 0.20, or 20 per cent.
Table (3)
\begin{array}{|c|l|c|c|c|}\hline \text { Year } & \begin{array}{l}\text { Economic } \\\text { conditions }\end{array} & \begin{array}{c}\text { Cash flow } \\(€ 000)\end{array} & \begin{array}{c}12 \% \text { discount } \\\text { factor }\end{array} & \begin{array}{c}\text { Present value } \\(€ 000)\end{array} \\\hline 1 & \text { Weak } & 100 & 0.893 & 89.3 \\1 & \text { Moderate } & 200 & 0.893 & 178.6 \\1 & \text { Good } & 300 & 0.893 & 267.9 \\2 & \text { Moderate } & 250 & 0.797 & 199.2 \\2 & \text { Good } & 350 & 0.797 & 279.0 \\\hline\end{array}Table (4)
\begin{array}{|l|c|l|c|c|}\hline{\text { Year 1 }} & {\text { Year 2 }} & \text { Overall } \\\hline \begin{array}{l}\text { Economic } \\\text { conditions }\end{array} & \begin{array}{c}\text { Present value of } \\\text { cash flow (€000) }\end{array} & \begin{array}{l}\text { Economic } \\\text { conditions }\end{array} & \begin{array}{c}\text { Present value } \\\text { of cash flow (€000) }\end{array} & \begin{array}{c}\text { Total present value } \\\text { of cash flow (€000) }\end{array} \\\hline \text { Weak } & 89.3 & \text { Moderate } & 199.2 & 288.5 \\\text { Weak } & 89.3 & \text { Good } & 279.0 & 368.3 \\\text { Moderate } & 178.6 & \text { Moderate } & 199.2 & 377.8 \\\text { Moderate } & 178.6 & \text { Good } & 279.0 & 457.6 \\\text { Good } & 267.9 & \text { Moderate } & 199.2 & 467.1 \\\text { Good } & 267.9 & \text { Good } & 279.0 & 546.9 \\\hline\end{array}Table (5)
\begin{array}{|c|c|c|c|c|}\hline \begin{array}{c}\text { Total present } \\\text { value of cash flow } \\(€ 000)\end{array} & \begin{array}{c}\text { Year 1 } \\\text { probability }\end{array} & \begin{array}{c}\text { Year 2 } \\\text { probability }\end{array} & \begin{array}{c}\text { Joint } \\\text { probability }\end{array} & \begin{array}{c}\text { Expected present } \\\text { value of cash flows } \\(€ 000)\end{array} \\\hline \text { A } & \text { B } & \text { C } & \text { D = B } \times \text { C } & \text { A } \times \text { D } \\\hline 288.5 & 0.2 & 0.7 & 0.14 & 40.4 \\368.3 & 0.2 & 0.3 & 0.06 & 22.1 \\377.8 & 0.5 & 0.7 & 0.35 & 132.2 \\457.6 & 0.5 & 0.3 & 0.15 & 68.6 \\467.1 & 0.3 & 0.7 & 0.21 & 98.1 \\546.9 & 0.3 & 0.3 & 0.09 & \underline{49.2} \\& & & & \underline{410.6} \\\hline\end{array}