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Investment Appraisal Techniques
Net Cash Receipt: Difference between money coming in and going out.
A) Types of Techniques
These fall into two broad categories:
Traditional techniques, including the Accounting Rate of Return (ARR) and Payback
Discounted Cash Flow (DCF) techniques, including Net Present Value (NPV) and Internal Rate of Return (IRR)
1. The Accounting (Average) Rate of Return (ARR)
Profitability is here expressed as an annual return on investment.
Two alternative projects for capital investment, Project A and Project B, both involving the purchase of a new machine, are being considered.
Project A requires an initial investment of Lm6,000. It will produce net cash receipts (net cash flow) of Lm3,000 in Year 1, Lm4,000 in Year 2; and Lm8,000 in Year 3. It will have a scrap value of Lm1,200.
Project B will cost Lm12,000. It will produce a net cash flow of Lm7,000 in Year 1; Lm8,000 in Year 2; and Lm9,000 in Year 3. It will then have a scrap value of Lm2,000.
Which project should be chosen?
Step 1: We will first add up the net cash receipts of the two projects during their life, and divide the result by the number of years each project will last.
Project A: (Lm3,000 + Lm4,000 + Lm8,000) / 3 = Lm5,000
Project B: (Lm7,000 + Lm8,000 + Lm9,000) / 3 = Lm8,000
Step 2: We work out the Average Investment. This is found by adding up the opening and closing values and dividing by 2. (Note: Some accountants and financial managers do not work on â€˜Average Investmentâ€™ but on â€˜Initial Investmentâ€™ and would therefore miss this step. Personally I do not agree with this method) Project A: (Lm6,000 + Lm1,200) / 2 = Lm3,600
Project B: (Lm12,000 + Lm2,000) / 2 = Lm7,000 Step 3: We now calculate the depreciation to be suffered by the two projects during their lives. Remember that this is an â€œAccountingâ€ rate of return, or profit, and accountants take depreciation into consideration when calculating profits. Depreciation is a â€˜
the cash flow figures given to us.
Project A: (Lm6,000 â€“ Lm1,200) = Lm4,800
Project B: (Lm12,000 â€“ Lm2,000) = Lm10,000 Step 4: Calculate the depreciation on an annual basis:
Project A: Lm4,800 / 3 = Lm1,600
Project B: Lm10,000 / 3 = Lm3,333
We can now work out the ARR on the formula ARR = Average Annual Profit Average Investment
To arrive at the â€˜annual profitâ€™ we deduct depreciation from the cash flow. The ARR for the 2 projects will therefore be as follows:
Project A: Lm5,000 â€“ Lm1,600 = 94.4% Lm3,600
Project B: Lm8,000 â€“ Lm3,333 = 66.7% Lm7,000
Note how ARR is expressed in percentage terms.
The payback period is the time it takes for the original amount invested to be recovered. In calculating the payback period, we must consider cash inflows (money in) and outflows (money out) and not accounting profit.
For illustration we shall take the previous example:
Project A (Lm)
Project B (Lm)
Y3 inflow (scrap)
The solution will be as follows:
Project A: There is an outflow of Lm6,000 in Y0. Lm3,000 of this will be recovered
in Y1, leaving a balance of Lm3,000 to be recovered in Y2.
In Y2 we get inflows for the whole year of Lm4,000 which is more than the balance
of Lm3,000 which still needs to be recovered, Assuming constant inflows during the
year, we will recover those Lm3,000 in Y2 after 9 months.
The total payback period for the project is therefore 1 year 9 months.
Project B: When you work it out in the same way you get a payback period of 1 year
Conclusion: All things being equal, you would choose Project B since it has the shorter payback period.
3. Net Present Value (Important)
Before we learn how to compute this, we must understand the concept of the Time Value of Money.
Investment means spending money now in the expectation of getting future returns. To know whether the returns are large enough to produce a profit or surplus, we need a way to compare money returns in the future with money outflows (i.e. investment now).
A given amount of money now is worth more than the same amount in the future for the following reasons:
Ability to spend it: money held now can be spent immediately to satisfy your wants.
Reduction of Risk: until the money is actually received, there is a risk that you will
not receive it.
Ability to invest: even if the money is not required now, it could be invested and earn
interest, and so accumulate to a larger sum in the future.
Let us suppose that money today can be invested at 10% interest, Then, Lm100
invested today will accumulate (compounding annually) to the following amounts:
after 1 year (Lm100 x 1.10) = Lm110.00 after 2 years (Lm110 x 1.10) = Lm121.00 after 3 years (Lm121 x 1.10) = Lm133.10
Thus, using an interest rate of 10% a year, the future value in 3 yearsâ€™ time of Lm100 now will be Lm133.10. We can say the same thing the other way round: the present value of Lm133.10 to be received in 3 yearsâ€™ time is Lm100.
In computing present values we can either use a simple formula or
P.V. = Lm133.10 x 0.751 = Lm99.96 i.e. Lm100 *
(if we use 5-figure tables the D.F. will be 0.75131, and the P.V. would be Lm99.999)
Having understood the principle of the Time Value of Money, we can proceed to understand the Net Present Value (NPV) method of Investment Appraisal.
The NPV method calculates a projectâ€™s â€˜profitâ€™ by comparing cash payments (or outflows) with cash receipts (or inflows) at the same point in time. It does this by discounting future cash flows back to the present (Y-); and then comparing the total present value of the net future cash receipts with the present value of the cash payments related to the capital invested in the project.
Alpha Ltd. is considering the purchase of a new machine. This requires an investment of Lm8,000 now, and will last for 5 years, during which it will produce goods which would be sold for Lm20,000 per year. The expected costs include wages of Lm5,000 per annum and materials of Lm11,000 per annum. The company discounts its capital projects at 10%.
Using the NPV method of investment appraisal, would you advise the company to purchase the machine?
Y0 Y1 Y2 Y3 Y4 Y5
Receipts 20,000 20000 20000 20000 20000
Wages -5,000 -5000 -5000 -5000 -5000
Materials -11,000 -11000 -11000 -11000 -11000
Flow -8,000 4,000 4,000 4,000 4,000 4,000
D.F. @ 10% 1 0,909 0,826 0,751 0,683 0,621
Value -8,000 3,636 3,304 3,004 2,732 2,484
If we add up the net cash flows from Y1 to Y5, and subtract the initial outflow in Y0, the Net Present value is found to be Lm7,160.