- 16 Marks
FM – L2 – Q65 – DCF: Specific applications
Question
A business entity, Volta Ventures, is considering its policy for the replacement of machines. One type of machine in regular use is Machine Y. This machine has a maximum useful life of four years, but maintenance costs and other running costs rise with use. An estimate of costs and disposal values is as follows:
Machine Y: Purchase cost GH₵40,000
| Year | Maintenance costs and other running costs in the year | Disposal value at the end of the year |
|---|---|---|
| GH₵ | GH₵ | |
| 1 | 8,000 | 25,000 |
| 2 | 12,000 | 20,000 |
| 3 | 20,000 | 10,000 |
| 4 | 25,000 | 0 |
The cost of capital is 10%.
Required
Calculate the equivalent annual cost of a replacement policy for the machine of replacement:
(a) every one year
(b) every two years
(c) every three years
(d) every four years.
Recommend a replacement policy for the machine.
Answer
(a) Replace every year
| Year | Cash flow | Discount factor at 10% | PV |
|---|---|---|---|
| GH₵ | |||
| 0 | (40,000) | 1.000 | (40,000) |
| 1 | (8,000) | ||
| 1 | 25,000 | ||
| 1 | 17,000 | 0.909 | 15,453 |
| (24,547) | |||
| Annuity factor at 10%, Year 1 | 0.909 | ||
| Equivalent annual cost |
(b) Replace every two years
| Year | Cash flow | Discount factor at 10% | PV |
|---|---|---|---|
| GH₵ | |||
| 0 | (40,000) | 1.000 | (40,000) |
| 1 | (8,000) | 0.909 | (7,272) |
| 2 | (12,000) | ||
| 2 | 20,000 | ||
| 8,000 | 0.826 | 6,608 | |
| (40,664) | |||
| Annuity factor at 10%, Years 1-2 | 1.736 | ||
| Equivalent annual cost |
(c) Replace every three years
| Year | Cash flow | Discount factor at 10% | PV |
|---|---|---|---|
| GH₵ | |||
| 0 | (40,000) | 1.000 | (40,000) |
| 1 | (8,000) | 0.909 | (7,272) |
| 2 | (12,000) | 0.826 | (9,912) |
| 3 | (20,000) | ||
| 3 | (10,000) | 0.751 | (7,510) |
| (64,694) | |||
| Annuity factor at 10%, Years 1-3 | 2.487 | ||
| Equivalent annual cost |
(d) Replace every four years
| Year | Cash flow | Discount factor at 10% | PV |
|---|---|---|---|
| GH₵ | |||
| 0 | (40,000) | 1.000 | |
| 1 | (8,000) | 0.909 | |
| 2 | (12,000) | 0.826 | |
| 3 | (20,000) | 0.751 | |
| 4 | (25,000) | 0.683 | |
| Annuity factor at 10%, Years 1-4 | |||
| Equivalent annual cost |
Recommendation
The machine should be replaced every two years, because this replacement policy gives the lowest equivalent annual cost.
- Topic: DCF: Specific Applications
- Uploader: Samuel Duah