Revision Answers
Revision 1 Advanced Investment Appraisal
Chapter 1 Discount Cash Flows Techniques
Answer 1
(a)
The first thing to do in this question is to determine how to correct the errors of principle.
(1) Interest should not be included as this is already accounted for in the discount rate. The annual interest charge of $4 million (less tax of 30%) should be added back to the cash flow in each year.
(2) Depreciation is NOT a cash flow and should be ignored in NPV calculations. The annual charge of $4 million (less tax at 30%) should be added back to the cash flow in each year.
(3) Indirect allocated costs are not relevant. These should be added back to the annual cash flows (net of tax). Corporate infrastructure costs are relevant to the project and should have been included. These costs should be deducted from annual cash flow figures (net of tax), as should the estimates for site clearance.
(4) Capital allowances in year 6 should be accounted for.
Corrected project evaluation
W1 Capital allowances
Sensitivity analysis of project to a $1m increase in initial capital expenditure
Extra capital expenditure will affect not only the cash outflow of the project but also the capital allowances.
This means that every additional $1 million spent on capital equipment will only cost the project $0.738 million due to tax savings resulting from capital allowances. [4]
(b)
Discounted payback and duration
The discounted payback period is approximately 4.5 years (4 years + 13.65/26.95). [2]
Project duration is the time it takes the project to recover approximately 50% of its initial investment. It is calculated by weighting each year of the project by the percentage of the present value recovered in that year.
Duration = 677.03 / 190.45 = 3.55 years [2]
l Discounted payback overcomes one of the problems of the ordinary payback technique – that is, it uses discounted cash flows rather than ignoring the time value of money.
l However the problem with payback (discounted or not) is that it ignores cash flows that occur beyond the payback period. Thus projects that have very high initial cash flows but few (if any) in later years may be favoured over those projects that might add greater value to the firm but over a longer period.
l The advantage of duration is that it considers the cash flows over the entire life of the project. It measures how long it will be before the project recovers the bulk of its present value.
l However it can be more difficult to understand the concept behind duration and for this reason it may not be widely used.
[1]
(c)
Recommendation on capital investment project
l The current project under review has a positive net present value (NPV) of $29.42m which means that the value of the business will be increased by this amount if the project is undertaken.
l It has also been found that for every additional $1m spent on capital equipment for this project, the project’s NPV will be reduced by $0.738m (due to tax savings made on the capital allowances available on capital expenditure).
l However given the size of the NPV it is expected that any variations in capital expenditure should not significantly affect the value added to the firm.
[3]
Investment appraisal techniques
l Payback is a technique that has been employed in the appraisal of this project. However, although the discounted version of payback reflects the cost of finance in the results, there is still the problem that it ignores any cash flows that occur after the payback period has been reached. This may result in vital information being missed, such as very few or no cash flows beyond the payback point.
l Duration removes this problem as it focuses on all cash flows of the project, regardless of when they occur. It is a measure of the time taken to recover 50% of the initial investment or, alternatively, earn 50% of the present value. It is a superior technique to payback and its implementation should be considered for future investment appraisal exercises.
l It is therefore recommended that simulation is incorporated into the investment appraisal in future.
[3]
Answer 2
(a)
Capital investment plan
Restrictions:
(i) Project PO801 cannot be scaled down – this project cannot be varied.
(ii) No project can be scaled up.
(iii) Capital budget is $1.2 million.
In capital rationing situations, projects should be ranked according to the profitability index (PI) which is the NPV per $ of invested capital at year zero. Before we can rank the projects, we must calculate the PI for each. [2]
Project / Initial investment / NPV / PV of Cash inflows / IRR / PI / Ranking$000 / $000 / $000
PO801 / (620) / 55 / 675 / 16% / 1.0887 / 3
PO802 / (640) / 69 / 709 / 13% / 1.1078 / 2
PO803 / (240) / 20 / 260 / 15% / 1.0833 / 4
PO804 / (1,000) / 72 / 1,072 / 13% / 1.0720 / 6
PO805 / (120) / 19 / 139 / 17% / 1.1583 / 1
PO806 / (400) / 29 / 429 / 15% / 1.0725 / 5
Now that we have established the order in which investments should be made, we have to determine how many of the projects we can afford, subject to the restrictions above.
Project / Initial investment / NPV / IRR / PI / Cumulative investment$000 / $000 / $000
PO805 / (120) / 19 / 17% / 1.1583 / (120)
PO802 / (640) / 69 / 13% / 1.1078 / (760)
PO801 / (620) / 55 / 16% / 1.0887 / (1,380)
PO803 / (240) / 20 / 15% / 1.0833 / (1,620)
PO806 / (400) / 29 / 15% / 1.0725 / (2,020)
PO804 / (1,000) / 72 / 13% / 1.0720 / (3,020)
[3]
The marginal project is PO801. Our problem is that this project cannot be scaled down – it is the supermarket project that cannot be varied. We now have two choices.
1. We can move PO801 above PO802 (which can be scaled down) in the ranking – this would allow us to undertake the supermarket project in its entirety.
2. Alternatively, we could remove PO801 from the problem completely and ignore it. This would move the other projects up the rankings. The choice with the higher overall NPV should be undertaken.
Choice 1 – move PO801 above PO802
Project / Initial investment / NPV / Cumulative investment / Proportion of project / NPV from investment$000 / $000 / $000 / $000
PO805 / (120) / 19 / (120) / 1 / 19.00
PO801 / (620) / 55 / (740) / 1 / 55.00
PO802 / (640) / 69 / (1,380) / 0.71875 / 49.59
Total NPV / 123.59
[2]
Note: the proportion of PO802 that is undertaken is calculated as follows:
Proportion = (capital budget – cumulative investment to date) / investment required
= ($1,200 – $740) / $640
= 0.71875
Choice 2 – ignore PO801
$000 / $000 / $000 / $000
PO805 / (120) / 19 / (120) / 1 / 19.00
PO802 / (640) / 69 / (760) / 1 / 69.00
PO803 / (240) / 20 / (1,000) / 1 / 20.00
PO806 / (400) / 29 / (1,400) / 0.5 / 14.5
Total NPV / 122.50
[2]
Choice 1 is preferable as it earns the higher NPV. PO801 should therefore be ranked above PO802 to allow the entire project to go ahead.
NPV per $ invested (PI) = $123.59 / $1,200 = 0.1030 [1]
Internal rate of return
IRR must be calculated on the NPV of the full projects – it cannot be calculated on proportions of projects. Therefore we must determine the IRR of the optimum investment plan on the assumption that we can invest in the whole of PO802.
Now try 14% first
[2]
Then try 17%
IRR = = 14.27% [2]
(b)
When calculating the rate for short-term financing the maximum rate which should be offered is that which generates a zero net present value on those projects which do not qualify for the current plan. The internal rate of return is not appropriate as that is the rate that would be the maximum rate for investment over the life of the projects concerned. This is however, a short-term capital rationing problem. The profitability index gives the net present value of each dollar invested. [2]
[4]
Therefore these projects could support a maximum additional finance charge of the following:
Additional finance = $1,820,000 × 0·077746 = $141,000 (round to)
Given that 10% is the rate assuming no short-term market failure for finance for this company, the maximum rate for the one year over which capital rationing is expected to hold is 17·75% (10% + 141,000 / 1,820,000). [2]
(c)
The option to delay project PO804 will have no effect on the answer to part (a) as the project would not have been undertaken as it had the lowest profitability index. It could now be undertaken in the second year when capital is not restricted, although the net present value would be lower than $72,000, as all associated cash flows would be delayed by one year.
[1 – 2 marks]
PO802 can now be delayed until the second year, which would allow the whole of project PO803 to be undertaken as well as (220/400 = 55%) of Project PO806. Again the NPV from project PO802 will be lower than $69,000 as all cash flows are delayed, but Slow Fashions Co is highly likely to generate additional overall shareholder wealth from undertaking the two extra projects. Detailed calculations would need to be performed to support this analysis.
[1 – 2 marks]
Answer 3
(a)
PDur05
Annual sales revenue = $14 × 300,000 units = $4,200,000
Annual costs = $3,230,000
Annual cash flows = $970,000
[2 marks]
PV of annual sales revenue = 4,200,000 × 7.191 × 0.731 = 22,077,808
Sensitivity of selling price = 380,922 / 22,077,808 = 1.7% [3 marks]
Selling price would fall to = $14 × (1 – 1.7%) = $13.76
Comment: The net present value of the project is very sensitive to changes in the selling price of the project. A small fall in the selling price would reduce the net present value to nil or negative and make the project not worthwhile. [1 mark]
(b)
A multi-period capital rationing model would use linear programming and is formulated as follows:
If:
Y1 = investment in project PDur01; Y2 = investment in project PDur02; Y3 = investment in project PDur03; Y4 = investment in project PDur04; and Y5 = investment in project PDur05
Then the objective is to maximize:
464Y1 + 244Y2 + 352Y3 + 320Y4 + 383Y5 [1 mark]
Given to the following constraints:
Constraint year 1: 4,000Y1 + 800Y2 + 3,200Y3 + 3,900Y4 + 2,500Y5 ≤ 9,000
Constraint year 2: 1,100Y1 + 2,800Y2 + 3,562Y3 + 0Y4 + 1,200Y5 ≤ 6,000
Constraint year 3: 2,400Y1 + 3,200Y2 + 0Y3 + 200Y4 + 1,400Y5 ≤ 5,000
And where Y1, Y2, Y3, Y4, Y5 ≥ 0
[2 marks]
(c)
Category 1: Total Final Value. This is the maximum net present value that can be earned within the three-year constraints of capital expenditure, by undertaking whole, part or none of the five projects. This amount is less than the total net present value of all five projects if there were no constraints. [1 mark]
Category 2: Adjustable Final Values. These are the proportions of projects undertaken within the constraints to maximise the net present value. In this case, all of project PDur05, 95·8% of project PDur01, 73·2% of project PDur03 and 40·7% of project PDur02 will be undertaken. [2 marks]
Category 3: Constraints utilised, slack. This indicates to what extent the constraint limits are used and whether any investment funds will remain unused. The figures indicate that, in order to achieve maximum net present value, all the funds in all three years are used up and no funds remain unused. [2 marks]
(d)(i)
Normally, positive net present value projects should be accepted as they add to the value of the company by generating returns in excess of the required rate of return (the discount rate). However, in this case, Arbore Co seems to be employing soft capital rationing by setting internal limits on capital available for each department, possibly due to capital budget limits placed by the company on the amounts it wants to borrow or can borrow. In the latter case, the company faces limited access to capital from external sources, for example, because of restrictions in bank lending, costs related to the issue of new capital and lending to the company being perceived as too risky. This is known as hard capital rationing and can lead to soft capital rationing. [2 marks]
(d)(ii)
A capital investment monitoring system (CIMS) monitors how an investment project is progressing once it has been implemented. Initially the CIMS will set a plan and budget of how the project is to proceed. It sets milestones for what needs to be achieved and by when. It also considers the possible risks, both internal and external, which may affect the project. CIMS then ensures that the project is progressing according to the plan and budget. It also sets up contingency plans for dealing with the identified risks.
[1 – 2 marks]
The benefits, to Arbore Co, of CIMS are that it tries to ensure, as much as possible, that the project meets what is expected of it in terms of revenues and expenses. Also that the project is completed on time and risk factors that are identified remain valid. A critical path of linked activities which make up the project will be identified. The departments undertaking the projects will be proactive, rather than reactive, towards the management of risk, and therefore possibly be able to reduce costs by having a better plan. CIMS can also be used as a communication device between managers charged with managing the project and the monitoring team. Finally CIMS would be able to re-assess and change the assumptions made of the project, if changes in the external environment warrant it.