- 7 Marks
FM – L2 – Q84 – Discounted cash flow
Question
A company is considering whether to invest in a new item of equipment costing GH₵45,000 to make a new product. The product would have a four-year life, and the estimated cash profits over the four-year period are as follows.
| Year | GH₵ |
|---|---|
| 1 | 17,000 |
| 2 | 25,000 |
| 3 | 16,000 |
| 4 | 4,000 |
The project would also need an investment in working capital of GH₵8,000, from the beginning of Year 1.
The company uses a discount rate of 11% to evaluate its investments.
Required
Calculate the NPV of the project at the discount rate of 11%.
Using the NPV you have calculated at 11%, and the NPV at a discount rate of 15%, estimate the internal rate of return (IRR) of the project.
Answer
NPV at 11%
| Year | Cash flow (GH₵) | Discount factor (11%) | Present value (GH₵) |
|---|---|---|---|
| 0 | (53,000) | 1.000 | (53,000) |
| 1 | 17,000 | 0.901 | 15,317 |
| 2 | 25,000 | 0.812 | 20,300 |
| 3 | 16,000 | 0.731 | 11,696 |
| 4 | 12,000 | 0.659 | 7,908 |
| NPV | 2,221 |
Workings:
- Initial investment: Equipment cost GH₵45,000 + Working capital GH₵8,000 = GH₵53,000
- Year 4 cash flow: Cash profit GH₵4,000 + Recovery of working capital GH₵8,000 = GH₵12,000
NPV at 15%
| Year | Cash flow (GH₵) | Discount factor (15%) | Present value (GH₵) |
|---|---|---|---|
| 0 | (53,000) | 1.000 | (53,000) |
| 1 | 17,000 | 0.870 | 14,790 |
| 2 | 25,000 | 0.756 | 18,900 |
| 3 | 16,000 | 0.658 | 10,528 |
| 4 | 12,000 | 0.572 | 6,864 |
| NPV | (2,918) |
IRR Estimation
Using the interpolation formula:
IRR = A + [(a / (a – b)) × (B – A)]
Where:
- A = Lower discount rate (11%)
- B = Higher discount rate (15%)
- a = NPV at lower rate (GH₵2,221)
- b = NPV at higher rate (GH₵-2,918)
IRR = 11% + [(2,221 / (2,221 – (-2,918))) × (15% – 11%)]
= 11% + [(2,221 / 5,139) × 4%]
= 11% + [0.432 × 4%]
= 11% + 1.73%
= 12.73% (approximately)
- Tags: Capital Budgeting, Discounted cash flow, investment appraisal, IRR, NPV
- Level: Level 2
- Topic: Discounted cash flow
- Uploader: Samuel Duah