Question 7.EX.3.4: NPV calculation involving inflation Thorne plc is planning...
NPV calculation involving inflation
Thorne plc is planning to sell a new electronic toy. Non-current assets costing €700,000 would be needed, with €500,000 payable at once and the balance payable after one year. Initial investment in working capital of €330,000 would also be needed. Thorne expects that, after four years, the toy will be obsolete and the disposal value of the non-current assets will be zero. The project would incur incremental total fixed costs of €545,000 per year at current prices, including annual depreciation of €175,000.
Expected sales of the toy are 120,000 units per year at a selling price of €22 per toy and a variable cost of €16 per toy, both in current price terms. Thorne expects the following annual increases because of inflation:
If Thorne’s real cost of capital is 7.5 per cent and taxation is ignored, is the project viable?
Depreciation is not a cash flow: we must deduct it from total fixed costs to find cash fixed costs:
\text { Cash fixed costs per year }=545,000-175,000=€ 370,000Inflating by 4 per cent per year:
Year 1 cash fixed costs = 370,000 \times 1.04 = € 384,800
Year 2 cash fixed costs = 384,800 \times 1.04 = € 400,192
Year 3 cash fixed costs = 400,192 \times 1.04 = € 416,200
Year 4 cash fixed costs = 416,200 \times 1.04 =€ 432,848
The contribution per unit is the difference between the selling price and the variable cost per unit, inflated by their respective inflation rates. The nominal net operating cash flow for each year is then the difference between the total contribution and the inflated fixed costs for that year, as shown in Table 7.3.
NPV = 96,207 + 220,465 + 176,683 + 392,979 – 830,000 = €56,334
Investment in working capital in Year 0 = €330,000
Incremental investment in working capital:
in Year 1 = 330,000 \times 1.07 = € 353,100, an incremental investment of € 23,100
in Year 2 = 353,100 \times 1.07 = € 377,817, an incremental investment of € 24,717
in Year 3 = 377,817 \times 1.07 = € 404,264, an incremental investment of € 26,447
working capital recovered at the end of Year 4 = €404,264
We could deflate the nominal cash flows by the general rate of inflation to give real cash flows and then discount them by Thorne’s real cost of capital. It is simpler and quicker to inflate Thorne’s real cost of capital into nominal terms and use it to discount our nominal cash flows. Thorne’s nominal cost of capital is 1.075 * 1.06 = 1.1395 or 14 per cent.
The nominal (money terms) net present value calculation is given in Table 7.2.
Since the NPV is positive, the project can be recommended on financial grounds. The NPV is not very large however, so we must ensure that forecasts and estimates are as accurate as possible. In particular, a small increase in inflation during the life of the project might make the project uneconomical. Sensitivity analysis (see Section 7.4.1) can be used to determine the key project variables on which success may depend.
Table 7.3 Net operating cash flows and net present value for Thorne plc
\begin{array}{|c|c|c|c|c|}\hline \text { Year } & 1 & 2 & 3 & 4 \\\hline \text { Selling price per unit }(€) & 23.10 & 24.25 & 25.47 & 26.74 \\\hline \text { Variable cost per unit }(€) & \underline{17.12} & \underline{18.32} & \underline{19.60} & \underline{20.97} \\\hline \text { Contribution per unit }(€) & 5.98 & 5.93 & 5.87 & 5.77 \\\hline \text { Contribution per year }(€) & 717,600 & 711,600 & 704,400 & 692,400 \\\hline \text { Fixed costs per year }(€) & \underline{384,800} & \underline{400,192} & \underline{416,200} & \underline{432,848} \\\hline \text { Net operating cash flow }(€) & 332,800 & 311,408 & 288,200 & 259,552 \\\hline\end{array}\begin{array}{|l|c|c|c|c|c|}\hline \text { Year } & 0 & 1 & & {3} & {4} \\\hline \text { Operating cash flow }(€)) & & 332,800 & 311,408 & 288,200 & 259,552 \\\text { Working capital }(€)) & (330,000) & (23,100) & (24,717) & (26,447) & 404,264 \\\text { Capital }(€)) & (500,000) & (200,000) & & & \\\text { Net cash flow }(€)) & (830,000) & 109,700 & 286,691 & 261,753 & 663,816 \\14 \% \text { discount factors } & 1.000 & 0.877 & 0.769 & 0.675 & 0.592 \\\text { Present value } €)) & (830,000) & 96,207 & 220,465 & 176,683 & 392,979 \\\hline\end{array}
Table 7.2 Calculation of net cash flows and net present value for Bent plc
\begin{array}{|c|c|c|c|c|}\hline \text { Year } & \text { Capital }(£) & \text { Operating cash flows }(£) & \text { Taxation }(£) & \text { Net cash flows }(£) \\\hline 0 & (200,000) & & & (200,000) \\1 & & 65,000 & & 65,000 \\2 & & 70,000 & (3,000) & 67,000 \\3 & & 75,000 & (6,500) & 68,500 \\4 & 20,000 & 98,000 & (9,375) & 88,625 \\5 & & & (6,725) & (6,725) \\\hline\end{array}\begin{array}{|c|c|c|c|}\hline \text { Year } & \text { Net cash flows }(£) & 10 \% \text { discount factor } & \text { Present value }(£) \\\hline 0 & (200,000) & 1.000 & (200,000) \\1 & 65,000 & 0.909 & 59,085 \\2 & 67,000 & 0.826 & 55,342 \\3 & 68,500 & 0.751 & 51,444 \\4 & 88,625 & 0.683 & 60,531 \\5 & (6,725) & 0.621 & \underline{(4,176)} \\& & \text { Net present value } & 22,226 \\\hline\end{array}