- 15 Marks
FM – L2 – Q61 – Discounted Cash Flow
Question
Coastline Plc is considering whether to invest in a project whose details are as follows.
The project will involve the purchase of equipment costing GH¢2,000,000. The equipment will be used to produce a range of products for which the following estimates have been made.
| Year | Average unit sales price | Average unit variable cost | Incremental fixed costs | Sales volume (units) |
|---|---|---|---|---|
| 1 | GH¢73.55 | GH¢50 | GH¢1,200,000 | 65,000 |
| 2 | GH¢76.03 | GH¢45 | GH¢1,200,000 | 110,000 |
| 3 | GH¢76.68 | GH¢45 | GH¢1,200,000 | 125,000 |
| 4 | GH¢81.86 | GH¢45 | GH¢1,200,000 | 80,000 |
The sales prices allow for expected price increases over the period. However, cost estimates are based on current costs and do not allow for expected increases in costs. Inflation is expected to be 3% per year for variable costs and 4% per year for fixed costs. The incremental fixed costs are all cash expenditure.
Tax on profits is at the rate of 30%, and tax is payable in the same year.
The cost of capital is 10%.
Required:
Calculate the NPV of the project.
Answer
NPV calculation
| Year | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| GH¢ | GH¢ | GH¢ | GH¢ | GH¢ | |
| Initial investment | (2,000,000) | ||||
| Total contribution (W) | 1,534,250 | 3,413,300 | 3,960,000 | 2,948,800 | |
| Fixed costs | (1,200,000) | (1,248,000) | (1,297,920) | (1,349,837) | |
| Taxable cash flow | 334,250 | 2,165,300 | 2,662,080 | 1,598,963 | |
| Tax (30%) | (100,275) | (649,590) | (798,624) | (479,689) | |
| Discount factor, 10% | 1.000 | 0.909 | 0.826 | 0.751 | 0.683 |
| Present values | (2,000,000) | 213,100 | 1,262,833 | 1,364,374 | 742,693 |
NPV = GH¢383,000
Workings
Contribution
| Year | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Average sales price | 73.55 | 76.03 | 76.68 | 81.86 |
| Average variable cost | 50 | 45 | 45 | 45 |
| x 1.03 | x 1.03² | x 1.03³ | ||
| 46.35 | 47.74 | 49.17 | ||
| Contribution per unit | 23.55 | 29.68 | 28.94 | 32.69 |
| Sales units | 65,000 | 110,000 | 125,000 | 80,000 |
| Total contribution | 1,530,750 | 3,264,800 | 3,617,500 | 2,615,200 |
Fixed costs:
Year 1: GH¢1,200,000
Year 2: 1,200,000 × 1.04 = GH¢1,248,000
Year 3: 1,248,000 × 1.04 = GH¢1,297,920
Year 4: 1,297,920 × 1.04 = GH¢1,349,837
- Tags: Cash Flows, Cost of Capital, Discounted cash flow, Financial management, Inflation, investment appraisal, NPV, Taxation
- Level: Level 2
- Topic: Discounted cash flow
- Uploader: Samuel Duah