- 12 Marks
FM – L2 – Q60 – Discounted Cash Flow
Question
ZQR Ltd, a manufacturing company, is considering a proposal to invest in machinery that it will use to increase its output and sales by 10,000 units in each of the next five years. The full purchase cost of the machinery would be GH¢225,000. This price includes a payment of GH¢20,000 made 12 months ago to the machinery supplier for a non-refundable down-payment for purchase of the machinery.
The company currently makes and sells a single product. This has a selling price of GH¢15 per unit and at present-day prices the direct costs per unit are GH¢3.75 for material and GH¢2.50 for labour. Incremental production overheads (all cash expenses) would be GH¢37,500 in each year, at current price levels.
Assume that all cash flows occur at the end of the year to which they relate.
ZQR’s cost of capital is 10%.
Required
(a) Calculate the NPV of the project, ignoring inflation.
(b) Calculate the NPV of the project, at a cost of capital of 10%, taking the following inflationary increases in revenues and costs into consideration:
Because of inflation, selling prices will rise by 7% in each year.
Material costs will rise by 5% each year, labour costs by 6% each year and overheads by 2% each year.
Comment on the differences in your results, compared with the NPV you calculated in part (a)
Answer
(a) NPV ignoring inflation
Contribution each year = GH¢(15 – 3.75 – 2.50) × 10,000 = GH¢87,500
Minus: Production overheads = GH¢37,500
Contribution = GH¢50,000
| Year | Cash flow (GH¢) | Discount factor (10%) | Present value (GH¢) |
|---|---|---|---|
| 0 | (205,000) | 1.000 | (205,000) |
| 1 | 50,000 | 0.909 | 45,450 |
| 2 | 50,000 | 0.826 | 41,300 |
| 3 | 50,000 | 0.751 | 37,550 |
| 4 | 50,000 | 0.683 | 34,150 |
| 5 | 50,000 | 0.621 | 31,050 |
| NPV | (15,500) |
(b) Allowing for inflation
| Year | Selling price | Materials | Labour | Overheads | Contribution | Total cash flow | Discount factor (10%) | PV (GH¢) |
|---|---|---|---|---|---|---|---|---|
| 0 | (205,000) | 1.000 | (205,000) | |||||
| 1 | 16.05 | 3.94 | 2.65 | 38,250 | 49,360 | 49,360 | 0.909 | 44,849 |
| 2 | 17.17 | 4.13 | 2.81 | 39,015 | 51,110 | 51,110 | 0.826 | 42,217 |
| 3 | 18.38 | 4.34 | 2.98 | 39,795 | 52,930 | 52,930 | 0.751 | 39,750 |
| 4 | 19.66 | 4.56 | 3.16 | 40,591 | 54,840 | 54,840 | 0.683 | 37,456 |
| 5 | 21.04 | 4.78 | 3.34 | 41,403 | 56,850 | 56,850 | 0.621 | 35,304 |
| NPV | (5,424) |
Comment: The NPV with inflation (GH¢-5,424) is higher than the NPV ignoring inflation (GH¢-15,500). This is because the selling price inflation rate (7%) is higher than the inflation rates for costs (5% for materials, 6% for labour, 2% for overheads), leading to a relatively larger increase in revenues compared to costs, which improves the NPV.
- Tags: Cost of Capital, Discounted cash flow, Inflation, investment appraisal, NPV
- Level: Level 2
- Topic: DCF: Taxation and Inflation
- Uploader: Samuel Duah