Question 7.E.X.4.1: Application of sensitivity analysis Swift has a cost of ca...
Application of sensitivity analysis
Swift has a cost of capital of 12 per cent and plans to invest £7m in a machine with a life of four years. The units produced will have a selling price of £9.20 each and will cost £6 each to make. It is expected that 800,000 units will be sold each year. By how much will each variable have to change to make the NPV zero? What are the key variables for the project?
The relative change in each project variable needed to make the NPV zero can be calculated as:
\cfrac{\text { NPV }}{\text { Present value of cash flows linked to project variable }}Calculating the net present value of the project:
\begin{array}{lc} & £ \\\text { Present value of sales revenue }=9.20 \times 800,000 \times 3.037= & 22,352,320 \\\text { Present value of variable costs }=6.00 \times 800,000 \times 3.037= & \underline{14,577,600} \\\text { Present value of contribution } & \underline{7,774,720} \\\text { Initial investment } & \underline{7,000,000} \\\text { Net present value } & \underline{774,720}\end{array}We can now calculate the relative change needed in each variable to make the NPV zero.
Initial investment
The NPV becomes zero if the initial investment increases by an absolute amount equal to the NPV (£774,720), which is a relative increase of 11.1 per cent:
Sales price
The relative decrease in sales revenue or selling price per unit that makes the NPV zero is the ratio of the NPV to the present value of sales revenue:
100 \times(774,720 / 22,352,320)=3.5 \%
This is an absolute decrease of £9.20 × 0.035 = 32 pence, so the selling price that makes the NPV zero is 9.20 – 0.32 = £8.88.
Variable cost
Since a decrease of 32 pence in selling price makes the NPV zero, an increase of 32 pence or 5.3 per cent in variable cost will have the same effect. Confirming this:
100 \times(774,720 / 14,577,600)=5.3 \%
Sales volume
The relative decrease in sales volume that makes the NPV zero is the ratio of the NPV to the present value of contribution:
100 \times(774,720 / 7,774,720)=10.0 \%
This is an absolute decrease of 800,000 × 0.1 = 80,000 units, so the sales volume that makes the NPV zero is 800,000 – 80,000 = 720,000 units.
Project discount rate
What is the cumulative present value factor that makes the NPV zero? We have:
and so:
C P V F=7,000,000 /((9.20-6.00) \times 800,000)=2.734Using the table of cumulative present value factors on page 483, and looking along the row of values for a life of four years (as project life remains constant), we find that 2.734 corresponds to a discount rate of almost exactly 17 per cent, an increase in the discount rate of 5 per cent in absolute terms or 41.7 per cent in relative terms (100 × 5/12). Note that this is the method for finding the internal rate of return of an investment project that was described in Section 6.4.
Our sensitivity analysis is summarised in Table 7.4. The project is most sensitive to changes in selling price and variable cost per unit and so these are the key project variables.
Table 7.4 Sensitivity analysis of the proposed investment by Swift
\begin{array}{|l|c|c|c|}\hline \text { Variable } &{\text { Change to make NPV zero }} & \text { Sensitivity } \\\hline & \text { absolute } & \text { relative } & \\\text { Selling price per unit } & -32 p & -3.5 \% & \text { High } \\\text { Sales volume } & -80,000 \text { units } & -10.0 \% & \text { Low } \\\text { Variable cost per unit } & +32 p & +5.3 \% & \text { High } \\\text { Initial investment } & +£ 774,720 & +11.1 \% & \text { Low } \\\text { Project discount rate } & +5 \% & +41.7 \% & \text { Very low } \\\hline\end{array}