Question 5.S-TQ.1: Choi Ltd is considering buying a new photocopier that could ...
Choi Ltd is considering buying a new photocopier that could lead to considerable cost savings. There are two machines on the market that are suitable for the business. These machines have the following outlays and expected cost savings:
| Lo-tek
£ |
Hi-tek
£ |
|
| Initial outlay | (10,000) | (15,000) |
| Cost savings | ||
| 1 year’s time | 4,000 | 5,000 |
| 2 year’s time | 5,000 | 6,000 |
| 3 year’s time | 5,000 | 6,000 |
| 4 year’s time | – | 5,000 |
The business has a cost of finance of 12 per cent and will have a continuing need for the chosen machine.
Required:
(a) Evaluate each machine using both the shortest-common-period-of-time approach and the equivalent-annual-annuity approach.
(b) Which machine would you recommend and why?
Choi Ltd
(a) In evaluating the two machines, the first step is to calculate the NPV of each project over their respective time periods:
Lo-tek
| Cash flows
£ |
Discount rate
12% |
Present value
£ |
|
| Initial outlay | (10,000) | 1.00 | (10,000) |
| 1 year’s time | 4,000 | 0.89 | 3,560 |
| 2 year’s time | 5,000 | 0.80 | 4000 |
| 3 year’s time | 5,000 | 0.71 | \underline{ 3,550} |
| NPV \underline{1,110} |
Hi-tek
| Cash flows
£ |
Discount rate
12% |
Present value
£ |
|
| Initial outlay | (15,000) | 1.00 | (15,000) |
| 1 year’s time | 5,000 | 0.89 | 4,450 |
| 2 year’s time | 6,000 | 0.80 | 4,800 |
| 3 year’s time | 6,000 | 0.71 | 4,260 |
| 4 year’s time | 5,000 | 0.64 | \underline{ 3,200} |
| NPV \underline{1,710} |
The shortest common period of time over which the machines can be compared is 12 (that is, 3 × 4) years. This means that Lo-tek will be repeated four times and Hi-tek will be repeated three times during the 12-year period.
The NPV for Lo-tek will be:
Total NPV = £1,110 +\frac{ £1,110}{(1 + 0.12)^{6} }+\frac{ £1,110}{(1 + 0.12)^{9}} + \frac{£1,110}{(1 + 0.12)^{12}}
= £2,358.8
The NPV for Hi-tek will be:
Total NPV = £1,710 +\frac{ £1,710}{(1 + 0.12)^{8} }+\frac{ £1,710}{(1 + 0.12)^{12}}
= £2,840.3
The equivalent-annual-annuity approach will provide the following results for Lo-tek:
£1,110 × 0.4163 = £462.09
and the following results for Hi-tek:
£1,710 × 0.3292 = £562.93
(b) Hi-tek is the better buy because calculations show that it has the higher NPV over the shortest common period of time and provides the higher equivalent-annual-annuity value.