Week 10 - Investment Appraisal Flashcards
What is investment appraisal?
A method for seeing how long it will take a project/investment to provide a return and what that return may be
What are the four main techniques of project appraisal?
- The accounting rate of return (ARR) method
- Average annual operating profit/average investment to earn that profit x 100 - The payback period (PP) method
- The net present value (NPV) method
- Seen as one of the best techniques to use - The internal rate of return (IRR) method
The ARR Method - Example
A company is looking to invest in some new equipment, which costs £300,000. This equipment would lead to increased profits (before depreciation) of £120,000 and would have a useful life of 12 years. It
would have no residual value after this period.
Calculate the accounting rate of return
- Calculate the depreciation expense per year:
£300,000/12 = £25,000 - Calculate the average annual profit: £120,000 –
£25,000 = £95,000 - Use the formula:
ARR = Average annual operating profit/average investment to earn that profit x 100
ARR = £95,000/£300,000 = 32%
What is the PP method?
The payback period (PP) is a quick method of establishing how long it will take a project to pay off the original investment
Consider the cash flows of the following projects
Years Project A (£) Project B (£) Project C (£)
0 -2,000 -2,000 -2,000
1 800 500 600
2 700 700 700
3 500 800 500
4 – – 200
5 – – 300
6 – – 500
Calculate the PP for each project
- To calculate the PP, we need to work out the cumulative
cash flows
Years Project A (£) Project B (£) Project C (£)
0 -2,000 -2,000 -2,000
1 -1,200 -1,500 -1,400
2 -500 -800 -700
3 Nil Nil -200
4 – – Nil
5 – – 300
6 – – 800
- Therefore, Projects A and B have a PP of 3 years, whilst project C has a PP of 4 years
- Usually projects with a quicker PP are preferable
- However, depending on the information provided we can be more precise
- Assume Project A had a cash flow of £1,000 in year 3 and not £500. Thus, it began year 3 needing £500 to pay off the original investment, but had a cash flow of £1,000
- 500/1000 = 0.5; therefore, under these circumstances the PP was 2 years and 6 months
What are the advantages and disadvantages of the PP method?
• The main advantage of the PP method is that it is
easy and quick to use
• Its disadvantages are as follows:
• It does not take into account the timing of cash
flows, i.e. two projects might have the same PP, but
one pays back a far greater amount in the earlier years
• It also ignores cash flows after the PP
• However, its main disadvantage is that is does not
take into account the time value of money
• Due to inflation, money loses its value over time
• Therefore, an amount of money promised in several
years’ time, will usually be worth less
• Thus, we need to calculate its present value
Explain the concept of PV
- Whenever anyone makes an investment they have to consider the future value of money
- For example, if I invest £1,000 in a scheme that will give me £1,100 in a year’s time, is it a good investment if interest rates for savers are 15%?
- The answer is no because I have given up the chance to earn £1,150 (e.g. 1,000 x 1.15)
- Another way to look at this is - what would the PV of £1,100 in a year’s time be?
- This is done by dividing the amount by the interest rate or discount rate - 1,100 / 1.15 = £956.52
What is the NPV method?
- Establishes the present value of future costs and revenues
- A company will normally set a discount rate or hurdle rate, which is the minimum return it is seeking
- This hurdle rate is not just the current cost of finance, and could include elements such as risk
- However, it is often referred to as the cost of capital
- All future costs and revenues are then discounted at that rate
- NPV compares the initial outlay of an investment with its total returns over a number of years. If the NPV is a positive figure then the investment is worthwhile
The NPV Method
For example, if an investment costs me £1,000, pays me £60 a year for three years and then gives me back my £1,000; is it a good investment if interest rates are likely to remain at 5%?
The sum is slightly more complicated now and is:
Year 0 (£1,000)
Year 1 £60 / 1.05
Year 2 £60 / 1.05^2
Year 3 £1,060 / 1.05^3
Fortunately to save time we can refer to a Present Value Table
Year Expenditure Revenue Net Discount PV
(£) (£) (£) rate (£)
0 (1,000) 0 (1,000) 1 (1,000)
1 0 60 60 0.952 57.12
2 0 60 60 0.907 54.42
3 0 1060 1060 0.864 915.84
NPV 27.38
In this case it would be a good investment as it returns a positive NPV; however it would be compared with the NPV of other possible investments.
The NPV Method
A company is considering disposing of part of its under utilised premises and investing in some new plant and equipment in order to boost earnings. However, given the financial restraints on the company it will have to phase in the purchase of the new non-current assets and therefore no cash will flow into the organisation as a result of these purchases until year 3. The purchase and cash flow patterns are as follows:
Purchases £ Immediate 750,000 Year 1 300,000 Year 2 215,000 Year 3 150,000 Net cash inflows Year 3 450,000 Year 4 650,000 Year 5 700,000
It should also be noted that the disposal of the premises would fetch £100,000 in the first year of the project. Given that the company has a cost of capital of 8% what is the NPV of the above project? Ignore depreciation.
Year Expenditure Revenue Net Discount PV
(£) (£) (£) rate (£)
0 (750,000) 0 (750,000) 1 (750,000)
1 (300,000) 100,000 (200,000) 0.926 (185,200)
2 (215,000) 0 (215,000) 0.857 (184,255)
3 (150,000) 450,000 300,000 0.794 238,200
4 0 650,000 650,000 0.735 477,750
5 0 700,000 700,000 0.681 476,700
NPV 73,195
How does depreciation affect NPV?
- Most capital assets will have a residual value – i.e. what they can be sold for when they are no longer of use
- Remember, depreciation does not represent cash
flowing out of the business and thus should not be
included when looking at the cash flows from a project
NPV and Depreciation
• A company is purchasing a non-current asset for
£550,000, which is expected to have a residual value
of £75,000 in five years’ time
• The net profit from this investment for each of the
five years is as follows:
Year 1 20,000 2 30,000 3 40,000 4 60,000 5 40,000
If the company has a cost of capital of 6%, what is
the NPV?
• We first have to calculate the annual depreciation
• Assuming that the straight line method is used this
will be (550,000 – 75,000)/5 or £95,000 per annum
• Therefore the NPV is as follows:
Year Expenditure Revenue Net Discount PV
(£) (£) (£) rate (£)
0 (550,000) 0 (550,000) 1 (550,000)
1 0 115,000 115,000 0.943 108,445
2 0 125,000 125,000 0.890 111,250
3 0 135,000 135,000 0.840 113,400
4 0 155,000 155,000 0.792 122,760
5 0 210,000 210,000 0.747 156,870
NPV 62,725
- In this example the revenue in years 1-4 consists of the net profit with the depreciation added back on, and the revenue in year 5 consists of the revenue with the depreciation added back on and the residual value of the non-current asset
- This project has an overall NPV of £62, 725, so appears to be worthwhile. However, it would be compared with other potential projects.
What is the IRR method of project appraisal?
• The IRR method determines the rate of interest at
which the NPV is 0. The IRR is therefore the rate of
return of an investment.
• This method will indicate that a project is viable if the
IRR exceeds the minimum acceptable rate of return
How is the internal rate of return calculated?
One way to calculate the IRR is via trial and error,
whereby interest rates (where the NPV is 0) are
estimated until a rate is found between the smallest
positive and negative NPVs that have been calculated
by using whole figures
A company is purchasing a non-current asset for
£550,000, which is expected to have a residual value of £75,000 in five years’ time
The net profit from this investment for each of the
five years is as follows:
Year 1 20,000 2 30,000 3 40,000 4 60,000 5 40,000
Year Expenditure Revenue Net Discount PV
(£) (£) (£) rate (£)
0 (550,000) 0 (550,000) 1 (550,000)
1 0 115,000 115,000 0.943 108,445
2 0 125,000 125,000 0.890 111,250
3 0 135,000 135,000 0.840 113,400
4 0 155,000 155,000 0.792 122,760
5 0 210,000 210,000 0.747 156,870
NPV 62,725
Calculate the IRR for the above project
- Using the figures from the previous NPV example we know that the IRR must be higher than 6%, as this gave us an NPV of £62, 725; therefore see what a rate of 10% would give:
Year Expenditure Revenue Net Discount PV
(£) (£) (£) rate (£)
0 (550,000) 0 (550,000) 1 (550,000)
1 0 115,000 115,000 0.909 104,535
2 0 125,000 125,000 0.826 103,250
3 0 135,000 135,000 0.751 101,385
4 0 155,000 155,000 0.683 105,865
5 0 210,000 210,000 0.621 130,410
NPV (4,555)
- The NPV is negative, but fairly close to zero, therefore we can state that the IRR appears to be around 9%.
- To work it out more accurately we would use the following calculation:
i = i1 + (P - P1)/(P2 - P1)x(i2 - i1) i = 6% + (0 - 62,725)/(-4,555-62,725)x(10%-6%) i = 9.7%
