Methods of Appraisal
Q. Write short notes on the following:
- Pay Back Period (Dec. 97, Dec. 98, June 03)
- Accounting Rate of Return (June 03)
- Net Present Value
- Internal Rate of Return (June 98, Dec. 98, June 99)
- Profitability Index
| Pay Back Period (Dec. 97, Dec. 98, June 03) |
|
In simple terms it means the total period within which
the total amount invested will be recovered throughout net
cash flow (after tax). Suppose a sum of Rs. 5 lakh has to
be invested in a project whose expected net cash flows are
as follows:
| |
Incremental
cash Flow (Rs. 000) |
| Year |
Annual |
Annual |
Cumulative |
| 0 |
(---) 500 |
(---) |
500 |
| 1 |
185 |
(---) |
315 |
| 2 |
125 |
(---) |
190 |
| 3 |
140 |
(---) |
50 |
| 4 |
170 |
(---) |
120 |
| 5 |
180 |
|
300 |
The money invested (Rs. 5 lakh) could be recovered during
the fourth year. The payback period is 3.29 yrs. The payback
period can be calculated as:
P = E + B/C
Where P: payback period
E: no. of years immediately preceding the year of final recovery
B: balance amount still to be recovered
C: cash flow during the year of final recovery
Weaknesses
The greatest weakness of this method is that it ignores the
timing and amount of all cash inflows. It does not any cognizance
of the cash flows after the payback period. Thus, this method
is not appropriate either for absolute or comparative appraisal.
The payback method concentrates only on liquidity aspect and
ignores the overall profitability of a project.
|
| Accounting Rate of Return (June 03) |
|
This method of working out the rate of return on investment
is based on the financial accounting practices of the company
for working out the annual profits. The net annual profits
are derived after deducting depreciation and taxes. The average
of annual profits thus derived is worked out on the basis
of the period of the life of the project. Example:
| Years |
Cash Flow (after tax) |
Depreciation |
Interest |
| 1 |
13,000 |
6,000 |
400 |
| 2 |
11,000 |
6,000 |
400 |
| 3 |
9,000 |
6,000 |
400 |
| 4 |
6,400 |
6,000 |
400 |
| 5 |
6,400 |
6,000 |
400 |
| Total |
45,800 |
30,000 |
2,000 |
The investment is Rs. 30,000. Accounting rate of return will
be equal to the average of net cash flow (after depreciation,
taxes, & interest) as a percentage of investment.
| (45,800 - 30,000 - 2,000)
x 1/5 |
|
|
|
= |
9.2 |
| Rs. 30,000 |
|
|
Since the investment in this example is a depreciable asset
so it could be argued that the investment base for calculating
ARR ought to be average investment which would be one-half
of initial investment, in this case Rs. 30,000/2 = 15,000.
Now the ARR will be:
| (45,800 - 30,000 - 2,000)
x 1/5 |
|
|
|
= |
18.4 |
| Rs. 15,000 |
|
|
Weakness
This method like the Payback method ignores the time value
of cash flows since it does not give any recognition to the
timing of the generation of income. Thus ARR method suffers
from a serious drawback by neglecting the quality or pattern
of benefits and by ignoring the time value of money. It also
does not take into account the scrap value of asset (or project)
at the end of its useful life. Finally, the calculation of
profit is subject to varying practices. All these factors
make ARR a less reliable method.
|
| Net Present Value |
|
Calculation of the net present value of future income
is related to the understanding of the compounded rate of
interest or the general formula of compounding. Suppose a
sum of Rs. 100 (P) is invested for a period of one year at
a rate of interest (r) of 10% per annum. The investment at
the end of one year will be equal to
= 110
It can also be stated that Rs. 110 in one year's time is
worth only Rs. 100 today. Applying the compounding formula
over a number of years to work out the present value (PV)
of a future flow of income will be reconstructed as
Where P is the amount to be received in future (number of
years = n). Example: Suppose we want to know cash flow of
Rs. 500 to be received at the end of five years discounted
at 10% rate of interest. The PV will be:
The following table shows the discount factor for 10% over
a period of 5 years in respect of the present value of one
rupee.
| Years |
Amount Rs. |
Present value factor |
Present value Rs. |
| 1 |
1,000 |
.909 |
909 |
| 2 |
1,000 |
.826 |
826 |
| 3 |
1,000 |
.751 |
751 |
| 4 |
1,000 |
.683 |
683 |
| 5 |
1,000 |
.621 |
621 |
| |
|
|
3790 |
By adding the PV of the annual inflow of cash for each year
of the expected life of the project we come to know the PV
of the aggregate of inflows. This can easily be compared with
the cash outflow needed today for investment. The proposal
is acceptable is the aggregate PV of cash inflow is more than
the current outflow.
Internal Rate of Return: The Internal Rate of return is a
method under the discounted cash flow technique which is used
for appraising the investment proposals. Under this method,
we derive the discounting rate at which the aggregate of the
PVs of all future cash inflows equals the present cash outflows
for the proposal.
Weakness
Compared to pay back period or ARR methods, the NPV method
is difficult to calculate. What discount rate is to be used
in calculating net present values may be difficult to decide.
The selection of discount rate has a significant effect on
the desirability of the project. With a change in rate, a
desirable project may become undesirable and vice versa. Moreover,
NPV is an absolute measure. For projects involving different
outlays the NPV method may not give dependable results. It
may also not give satisfactory results where the projects
under competition have different lives.
|
| Internal Rate of Return (June 98, Dec.
98, June 99) |
|
The internal rate of return is another method under the
Discounted cash Flow technique that is used for appraising
the investment proposals. Under this method, we derive the
discounting rate at which the aggregate of the PVs of all
future cash inflows equals the present cash outflows for the
proposal.
Mathematically
Where:
IRR is the internal rate of return
LRD is the Lower rate of discount
NPVL is the net present valus at lower rate of dicount
PV is the difference in present values at lower and higher
discount rates
R is the difference between two rates of discount
Advantages & Limitations
IRR, like NPV, takes into consideration time value of money
and also the total cash inflows & outflows over the entire
life of the project. For managers it is easier to understand
as the calculation is always a % and not an absolute value.
Another advantage is that it does not require discounting
rate. The method itself provides a rate of return.
However, IRR require tedious calculations. Under IRR method,
it is assumed that cash flows are reinvested at the same rate
of IRR. This also implies that if IRR of two projects is 16%
and 20%, the cash flows arising from these two projects will
also be reinvested at their respective rates, i.e., 16% &
20%
|
| Profitability Index |
|
It is also known as benefit-cost ratio. The profitability
index is the relationship between the present value of net
cash inflows and the present value of cash outflows. It can
be worked out either in unitary or in percentage terms. The
formula is:
Profitability Index = Present value of cash inflows/present
value of cash outflows
|
|
Accounts
Home Page
