- 15 Marks
FM – L2 – Q52 – Discounted cash flow
Question
Dambai Energy Ltd is considering whether to invest in either of two mutually-exclusive projects, Project 1 and Project 2. Both projects involve the purchase of machinery with a life of five years.
Project 1: The machine would cost GH₵556,000 and would have a net disposal value of GH₵56,000 at the end of Year 5. The project would earn annual cash flows (receipts minus payments) of GH₵200,000.
Project 2: The machine would cost GH₵1,616,000 and would have a net disposal value of GH₵301,000 at the end of Year 5. The project would earn annual cash flows (receipts minus payments) of GH₵500,000.
Dambai Energy Ltd uses the straight-line method of depreciation. Its cost of capital is 15%.
Ignore taxation, inflation, and investment in working capital.
Required
(a) For each of the two projects, calculate:
(i) the net present value, and
(ii) the internal rate of return to the nearest one per cent.
(b) State which project, if any, you would select for acceptance.
Answer
(a) (i) Net Present Value (NPV)
Project 1
| Year | Discount factor at 15% | Cash flow (GH₵) | PV (GH₵) |
|---|---|---|---|
| 0 | 1.000 | (556,000) | (556,000) |
| 1-5 | 3.352 | 200,000 | 670,400 |
| 5 | 0.497 | 56,000 | 27,832 |
NPV = -556,000 + 670,400 + 27,832 = +GH₵142,232
Project 2
| Year | Discount factor at 15% | Cash flow (GH₵) | PV (GH₵) |
|---|---|---|---|
| 0 | 1.000 | (1,616,000) | (1,616,000) |
| 1-5 | 3.352 | 500,000 | 1,676,000 |
| 5 | 0.497 | 301,000 | 149,587 |
NPV = -1,616,000 + 1,676,000 + 149,587 = +GH₵209,587
(ii) Internal Rate of Return (IRR)
Both projects have a positive NPV at 15%. Try a higher discount rate: Try 20%
NPV of Project 1 = -556,000 + (200,000 × 2.991) + (56,000 × 0.400)
= -556,000 + 598,200 + 22,512 = +GH₵64,712
NPV of Project 2 = -1,616,000 + (500,000 × 2.991) + (301,000 × 0.400)
= -1,616,000 + 1,495,500 + 121,002 = +GH₵502
Try 25%
NPV of Project 1 = -556,000 + (200,000 × 2.689) + (56,000 × 0.328)
= -556,000 + 537,800 + 18,368 = +GH₵168
NPV of Project 2 = -1,616,000 + (500,000 × 2.689) + (301,000 × 0.328)
= -1,616,000 + 1,344,500 + 98,728 = -GH₵172,772
IRR Calculation:
For Project 1: NPV is close to zero at 25%, so IRR ≈ 25%.
For Project 2: Using interpolation between 20% and 25%:
IRR = 20% + [(502 / (502 + 172,772)) × (25 – 20)] ≈ 20%.
(b). Project 2 should be selected because it has a higher NPV (GH₵209,587) compared to Project 1 (GH₵142,232), indicating greater value creation for shareholders.
- Tags: Capital Budgeting, investment appraisal, IRR, NPV, Project Selection
- Level: Level 2
- Topic: Discounted cash flow
- Uploader: Samuel Duah