- 12 Marks
FM – L2 – Q59 – Discounted Cash Flow
Question
ZENITH LTD
(a) Calculate the NPV of an investment with the following estimated cash flows, assuming a cost of capital of 8%:
| Years | Annual cash flow |
|---|---|
| 0 | (3,000,000) |
| 1–4 | 500,000 |
| 5–8 | 400,000 |
| 9–10 | 300,000 |
| 11 onwards | 100,000 |
ZENITH LTD
(b) The cash flows for an investment project have been estimated at current prices, as follows:
| Year | Equipment | Revenue | Running costs |
|---|---|---|---|
| 0 | (900,000) | ||
| 1 | 800,000 | (400,000) | |
| 2 | 800,000 | (350,000) | |
| 3 | 400,000 | (300,000) | |
| 4 | 400,000 | (300,000) |
It is expected that the cash flows will differ because of inflation. The annual rates of inflation are expected to be:
Equipment value: 4% per year
Revenue: 3% per year
Running costs: 5% per year.
The cost of capital is 12%.
Required
(a) Calculate the NPV of the project ignoring inflation.
(b) Calculate the NPV of the project allowing for inflation.
Answer
(A). Annuity factor at 8%, years 1–8: 5.747
Annuity factor at 8%, years 1–4: 3.312
Annuity factor at 8%, years 5–8: 2.435
Annuity factor at 8%, years 1–10: 6.710
Annuity factor at 8%, years 1–8: 5.747
Annuity factor at 8%, years 9–10: 0.963
The Year 10 value of a perpetuity of GH¢100,000 each year in perpetuity from Year 11 onwards:
= GH¢100,000 × 1 / 0.08
= GH¢1,250,000
| Years | Annual cash flow | Discount factor (8%) | PV |
|---|---|---|---|
| 0 | (3,000,000) | 1.000 | (3,000,000) |
| 1–4 | 500,000 | 3.312 | 1,656,000 |
| 5–8 | 400,000 | 2.435 | 974,000 |
| 9–10 | 300,000 | 0.963 | 288,900 |
| 10 | 1,250,000 | 0.463 | 578,750 |
| NPV | 497,650 |
(b) (i) Ignoring inflation
| Year | Annual cash flow GH¢ | Discount factor (12%) | PV GH¢ |
|---|---|---|---|
| 0 | (900,000) | 1.000 | (900,000) |
| 1 | 400,000 | 0.893 | 357,200 |
| 2 | 400,000 | 0.797 | 318,800 |
| 3 | 250,000 | 0.636 | 159,000 |
| 4 | 300,000 | 0.567 | 170,100 |
| 105,100 |
(ii) Allowing for inflation
| Year | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Equipment | (900,000) | 233,972 | |||
| Revenue | 824,000 | 848,720 | 655,636 | 450,204 | |
| Running costs | (420,000) | (441,000) | (405,169) | (364,652) | |
| Net cash flow | (900,000) | 404,000 | 407,720 | 250,467 | 319,524 |
| Discount factor at 12% | 1.000 | 0.893 | 0.797 | 0.636 | 0.567 |
| Present value | (900,000) | 360,772 | 324,953 | 159,297 | 181,170 |
NPV = +126,192
- Tags: Cash Flows, Discounted cash flow, Financial management, Inflation, investment appraisal, NPV
- Level: Level 2
- Topic: DCF: Taxation and Inflation
- Uploader: Samuel Duah