- 8 Marks
FM – L2 – Q53 – Discounted cash flow
Question
Accra-Nungua Transport Limited is considering an investment in a new machine that would be used to manufacture a new product at its existing production centre. The product and the machine are both expected to have an economic life of four years. The following estimates of revenues and costs have been made.
| Year | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Selling price per unit | GH¢8 | GH¢9 | GH¢10 | GH¢10 |
| Variable cost per unit | GH¢4 | GH¢4.50 | GH¢5 | GH¢5.50 |
| Sales volume (units) | 30,000 | 40,000 | 50,000 | 20,000 |
It has been estimated that there would be no increase at all in fixed costs, except for depreciation of the new machine. The machine would cost GH¢40,000 at the end of its four-year life it would have no residual value.
The company has a cost of capital of 9%.
Required
Calculate the net present value of the proposed project
Answer
Workings
W1 Sales and variable costs
| Year | DCF factor 9% | Sales | Variable costs | ||
|---|---|---|---|---|---|
| Actual | PV | Actual | PV | ||
| GH¢ | GH¢ | GH¢ | GH¢ | ||
| 1 | 0.917 | 240,000 | 220,080 | 120,000 | 110,040 |
| 2 | 0.842 | 360,000 | 303,120 | 180,000 | 151,560 |
| 3 | 0.772 | 500,000 | 386,000 | 250,000 | 193,000 |
| 4 | 0.708 | 200,000 | 141,600 | 110,000 | 77,860 |
| 1,050,800 | 532,480 |
NPV Calculation
- Total PV of sales: GH¢1,050,800
- Total PV of variable costs: GH¢532,480
- PV of machine cost (Year 0, DCF = 1.000): GH¢40,000 × 1.000 = GH¢40,000
- Net Present Value = PV of sales – PV of variable costs – PV of machine cost
= 1,050,800 – 532,480 – 40,000 = GH¢478,320
The NPV of the proposed project is GH¢478,320.
- Topic: Discounted cash flow
- Uploader: Samuel Duah