Question 6.EX.3: Calculation of the net present value Clement plc is evalua...
Calculation of the net present value
Clement plc is evaluating three investment projects, whose expected cash flows are given in Table 6.4. Calculate the net present value for each project if Carter’s cost of capital is 10 per cent. Which project should be selected?
Table 6.4 Three investment projects with different cash-flow profiles to illustrate the calculation of net present value
\begin{array}{|c|c|c|c|}\hline {\text { Clement plc: cash flows of proposed investment projects }} \\\hline \text { Period } & \begin{array}{c}\text { Project A } \\\text { (£000) }\end{array} & \begin{array}{c}\text { Project B } \\\text { (£000) }\end{array} & \begin{array}{c}\text { Project C } \\\text { (£000) }\end{array} \\\hline 0 & (5,000) & (5,000) & (5,000) \\1 & 1,100 & 800 & 2,000 \\2 & 1,100 & 900 & 2,000 \\3 & 1,100 & 1,200 & 2,000 \\4 & 1,100 & 1,400 & 100 \\5 & 1,100 & 1,600 & 100 \\6 & 1,100 & 1,300 & 100 \\7 & 1,100 & 1,100 & 100 \\\hline\end{array}Project A
The cash inflows of this project are identical and so do not need to be discounted separately. Instead, we can use the cumulative present value factor (CPVF) or annuity factor for seven years at 10 per cent \text{(CPVF}_{10,7}), which is found from CPVF tables (see pages 482–3) to have a value of 4.868. We have:
Project A has a positive net present value of £355,000.
Project B
Because the cash inflows of this project are all different, it is necessary to discount each one separately. The easiest way to organise this calculation is by using a table, as in Table 6.5.
Using a table to organise net present value calculations is especially useful when dealing with the more complex cash flows which arise when taking account of taxation, inflation and a range of costs or project variables. A tabular approach also aids clear thinking and methodical working in examinations. From Table 6.5, we can see that
Project B has a positive net present value of £618,000.
Project C
The cash flows for the first three years are identical and can be discounted using the cumulative present value factor for three years at 10 per cent \text{(CPVF}_{10,3}), which is found from cumulative present value factor (CPVF) tables to be 2.487. The cash flows for years 4 to 7 are also identical and can be discounted using a cumulative present value factor. To find this, we subtract the cumulative present value factor for three years at 10 per cent from the cumulative present value factor for seven years at 10 per cent.
From the CPVF tables, we have:
\begin{array}{lc}& £ 000 \\\text { Initial investment } & (5,000) \\\text { Present value of cash inflows, years } 1 \text { to } 3=£ 2,000 \times 2.487= & 4,974 \\\text { Present value of cash inflows, years } 4 \text { to } 7=£ 100 \times 2.381= & \underline{238} \\\text { Net present value } & \underline{212} \\\end{array}
Project C has a positive net present value of £212,000. If the annual cash flows are discounted separately, as in Table 6.7, the NPV is £209,000, the difference being due to rounding.
The decision on project selection
We can now rank the projects in order of decreasing net present value:
Which project should be selected? If the projects are mutually exclusive, then Project B should be undertaken as it has the highest NPV and will lead to the largest increase in shareholder wealth. If the projects are not mutually exclusive and there is no restriction on capital available for investment, all three projects should be undertaken since all three have a positive NPV and will increase shareholder wealth. However, the cash flows in years 4 to 7 of Project C should be investigated; they are not very large and they are critical to the project, since without them it would have a negative NPV and would therefore lead to a decrease in shareholder wealth.
Table 6.5 Calculation of net present value of Project B using a tabular approach This approach organises the calculation and information used in a clear, easily understood format which helps to avoid errors during the calculation process
\begin{array}{|c|c|c|c|}\hline \text { Year } & \text { Cash flow (£000) } & \text { 10\% present value factors } & \begin{array}{c}\text { Present value } \\(£ 000)\end{array} \\\hline 0 & (5,000) & 1.000 & (5,000) \\1 & 800 & 0.909 & 727 \\2 & 900 & 0.826 & 743 \\3 & 1,200 & 0.751 & 901 \\4 & 1,400 & 0.683 & 956 \\5 & 1,600 & 0.621 & 994 \\6 & 1,300 & 0.564 & 733 \\7 & 1,100 & 0.513 & 564 \\& & \text { Net present value } & 618 \\\hline\end{array}