Question 5.S-AQ.1: The directors of Tocantins Co. are considering whether to in...
The directors of Tocantins Co. are considering whether to invest in two separate projects: one is small while the other is large. They are also trying to decide between two other competing projects. Details of all four projects are set out below.
Project 1
The directors are considering buying a new photocopier, which should lead to cost savings.
Two machines that are suitable for the business are on the market. 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 years’ time | 5,000 | 6,000 |
| 3 years’ time | 5,000 | 6,000 |
| 4 years’ time | – | 5,000 |
The business will have a continuing need for whichever machine is chosen.
Project 2
The directors are also considering building a new factory in Qingdao, China to produce clothing for the Western European market. To date, the company has invested £500,000 in researching the proposal and in obtaining the licences necessary to build the factory.
The factory will cost £16 million to build and will take one year to complete. Payments for building the factory will be paid in 12 monthly instalments during the first year of the investment project.
The factory will be operational in the second year and estimates of the likely cash flows from the factory and their probability of occurrence are as follows:
| Estimated net cash flows |
Probability of occurrence |
|
| £m | £m | |
| Year 2 | 4.5 | 0.2 |
| 5.0 | 0.4 | |
| 6.0 | 0.4 | |
| Year 3 | 5.0 | 0.3 |
| 6.5 | 0.4 | |
| 8.0 | 0.3 | |
| Year 4 | 5.0 | 0.2 |
| 7.0 | 0.6 | |
| 9.0 | 0.2 | |
| Year 5 | 2.0 | 0.5 |
| 2.5 | 0.4 | |
| 3.0 | 0.1 |
Estimates for each year are independent of each other.
Projects 3 and 4
The directors have to decide between two competing projects. Their details are as follows:
| Expected net present value |
Standard deviation |
|
| £m | £m | |
| Project 3 | 14.0 | 2.0 |
| Project 4 | 14.0 | 2.8 |
The company has a cost of capital of 12 per cent.
Required:
Project 1
(a) Evaluate each photocopier using both the shortest-common period-of-time approach and the equivalent-annual-annuity approach.
(b) Which machine would you recommend and why?
Project 2
(c) Calculate the expected net present value of the project.
(d) Calculate the net present value of the worst possible outcome and the probability of its occurrence.
(e) State, with reasons, whether or not the business should invest in the new factory.
Projects 3 and 4
(f) State, with reasons, which of the two projects should be accepted.
The answer to this question can be found at the back of the book on p. 562 .
Tocantins Co.
Project 1
(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 | Present value | |
| £ | 12% | £ | |
| Initial outlay | (10,000) | 1.00 | (10,000) |
| 1 year’s time | 4,000 | 0.89 | 3,560 |
| 2 years’ time | 5,000 | 0.80 | 4,000 |
| 3 years’ time | 5,000 | 0.71 | \underline{3,550} |
| NPV \underline{1,110} |
Hi-tek
| Cash flows | Discount rate | Present value | |
| £ | 12% | £ | |
| Initial outlay | (15,000) | 1.00 | (15,000) |
| 1 year’s time | 5,000 | 0.89 | 4,450 |
| 2 years’ time | 6,000 | 0.80 | 4,800 |
| 3 years’ time | 6,000 | 0.71 | 4,260 |
| 4 years’ 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.
Project 2
(c) Expected net cash flows
| Net cash flows | Probability of occurrence | Expected cash flows | |
| (a)
£m |
(b)
|
(a × b)
£m |
|
| 4.5 | 0.2 | 0.9 | |
| Year 2 | 5.0 | 0.4 | 2.0 |
| 6.0 | 0.4 | \underline{2.4} | |
| Expected net cash flow | \underline{5.3} | ||
| Year 5 | 5.0 | 0.3 | 1.5 |
| 6.5 | 0.4 | 2.6 | |
| 8.0 | 0.3 | \underline{2.4} | |
| Expected net cash flow | \underline{6.5} | ||
| Year 4 | 5.0 | 0.2 | 1.0 |
| 7.0 | 0.6 | 4.2 | |
| 9.0 | 0.2 | \underline{1.8} | |
| Expected net cash flow | \underline{7.0} | ||
| Year 5 | 2.0 | 0.5 | 1.0 |
| 2.5 | 0.4 | 1.0 | |
| 3.0 | 0.1 | \underline{0.3} | |
| Expected net cash flow | \underline{2.3} |
| Expected net present value | |||
| Year | Expected net cash flow | Discount rate | Expected present |
| £m | 12% | £m | |
| 1 | (16.0) | 1.00 | (16.0) |
| 2 | 5.3 | 0.89 | 4.7 |
| 3 | 6.5 | 0.80 | 5.2 |
| 4 | 7.0 | 0.71 | 5.0 |
| 5 | 2.3 | 0.64 | \underline{1.5} |
| ENPV \underline{0.4} | |||
(d) Worst possible outcome
| Year | Estimated cash flow | Discount rate | Present value |
| £m | 12% | £m | |
| 1 | (16.0) | 1.00 | (16.0) |
| 2 | 4.5 | 0.89 | 4.0 |
| 3 | 5.0 | 0.80 | 4.0 |
| 4 | 5.0 | 0.71 | 3.6 |
| 5 | 2.0 | 0.64 | \underline{1.3} |
| ENPV \underline{( 3.1 )} |
The probability of occurrence is (0.2 × 0.3 × 0.2 × 0.5) = 0.006.
(e) The ENPV of the investment is positive (£0.4 million). The decision rule is to accept projects with a positive ENPV as this will shareholder wealth. However, the investment outcome is only just in positive territory. A thorough review of critical assumptions, as well as the gathering of further information, should be undertaken before a final decision is made.
Projects 3 and 4
(f) Project 4 has the higher standard deviation and therefore the greater variability of possible outcomes. Hence, it has the higher level of risk. Using the expected value-standard deviation rule, we should accept Project 3. This is because the expected return of Project 3 is equal to that of Project 4 but the standard deviation of Project 3 is lower than that of Project 4.