- 20 Marks
FM – L2 – Q71 – Discounted Cash Flow
Question
A company, Zenith Innovations Ltd, is considering an investment in a new project to manufacture and sell a new product with a five-year lifespan. The project requires an investment of GH₵3 million in equipment. The residual value of this equipment after five years will be 30% of its original cost.
The estimates of net cash flows from operations in each year of the project are as follows:
| Year | Net Cash Flow (GH₵) |
|---|---|
| 1 | 400,000 |
| 2 | 800,000 |
| 3 | 800,000 |
| 4 | 700,000 |
| 5 | 400,000 |
These cash flows are based on estimates that the annual increase in cash spending on fixed costs will be GH₵200,000, and the contribution/sales ratio from transactions will be 40%. The company’s cost of capital is 8%.
The management of Zenith Innovations Ltd is aware that actual cash flows could be higher or lower than expected, and sensitivity analysis should be carried out to establish the extent to which costs or revenues could differ from the estimate before the project ceases to have a positive NPV.
The investment in working capital will be minimal. Inflation and taxation should be ignored.
Required
(a) Calculate the net present value of the project.
(b) Carry out sensitivity analysis on the following items:
(i) The cost of the equipment, assuming that the residual value will be 30% of cost.
(ii) The residual value of the equipment.
(iii) Sales revenue.
(iv) Variable costs.
(v) Annual fixed costs.
(c) Comment on the risk in undertaking this project.
Answer
(A). The residual value of the equipment at the end of year 5 will be 30% × GH₵3 million = GH₵900,000.
| Year | Cash Flow (GH₵) | Discount Factor at 8% | Present Value (GH₵) |
|---|---|---|---|
| 0 | (3,000,000) | 1.000 | (3,000,000) |
| 1 | 400,000 | 0.926 | 370,400 |
| 2 | 800,000 | 0.857 | 685,600 |
| 3 | 800,000 | 0.794 | 635,200 |
| 4 | 700,000 | 0.735 | 514,500 |
| 5 | 400,000 | 0.681 | 272,400 |
| 5 | 900,000 | 0.681 | 612,900 |
| Net Present Value | +91,000 |
(B). (i) Cost of equipment
The estimated PV of the cost of the equipment, allowing for a residual value of 30% of cost after five years, is:
3,000,000 − (0.681 × 0.30 × 3,000,000) = 2,387,100.
This estimate can be wrong by GH₵91,000 before the project ceases to have a positive NPV. The cost of the equipment can therefore be higher by (91,000 / 2,387,100) = 3.8%.
(ii) Residual value of equipment
The estimated PV of the residual value is GH₵612,900. This estimate can be wrong by GH₵91,000 before the project ceases to have a positive NPV. The PV of the residual value could therefore be (612,900 − 91,000) = GH₵521,900.
The residual value (without discounting) could therefore be GH₵521,900 / 0.681 = GH₵766,372. This is 25.5% of the original cost of GH₵3,000,000.
The residual value could therefore be as low as about 25% of cost before the project ceased to have a positive NPV.
((iii),(iv) and (v)) Sales revenue and annual costs
Workings
The estimated contribution/sales ratio is 40%, therefore sales revenue 100/40 = 2.5 times annual contribution. Variable costs will be 60/40 = 1.5 times annual contribution. Fixed costs are GH₵200,000 each year; therefore contribution is GH₵200,000 more than the annual net cash flow.
| Year | Contribution | PV factor at 8% | Revenue |
|---|---|---|---|
| 1 | 600,000 | 0.926 | 1,500,000 |
| 2 | 1,000,000 | 0.857 | 2,500,000 |
| 3 | 1,000,000 | 0.794 | 2,500,000 |
| 4 | 900,000 | 0.735 | 2,250,000 |
| 5 | 600,000 | 0.681 | 1,500,000 |
| Total | 4,100,000 | 10,250,000 |
PV of contribution = 4,100,000 × (0.926 + 0.857 + 0.794 + 0.735 + 0.681) = 4,100,000 × 3.993 = 16,371,300.
(iii) Sales revenue
The sales revenue could therefore be lower by 91,000 / 16,371,300 = 0.56%.
(iv) Variable costs
Variable costs = 60% of revenue = 6,150,000.
PV of variable costs = 6,150,000 × 3.993 = 24,556,950.
The variable costs could therefore be higher by 91,000 / 24,556,950 = 0.37%.
(v) Annual fixed costs
PV of fixed costs = 200,000 × 3.993 = 798,600.
The fixed costs could therefore be higher by 91,000 / 798,600 = 11.4%.
(c) The sensitivity analysis shows that the project is most sensitive to changes in sales revenue and variable costs, with only a 0.56% decrease in sales revenue or a 0.37% increase in variable costs sufficient to eliminate the positive NPV. This indicates high risk, as small deviations in these estimates could make the project unviable. The project is moderately sensitive to the cost of equipment (3.8% increase) and residual value (down to 25% of cost), suggesting some risk but with a larger buffer. Fixed costs are the least sensitive, requiring an 11.4% increase to eliminate NPV, indicating lower risk in this area. Overall, the high sensitivity to sales revenue and variable costs suggests significant risk, and management should focus on accurate forecasting and risk mitigation strategies for these variables.
- Tags: investment appraisal, NPV, Project Risk, Risk Assessment, Sensitivity Analysis
- Level: Level 2
- Topic: DCF: Risk and uncertainty
- Uploader: Samuel Duah