# PRESENT VALUE METHOD - Accounts and Finance for Managers

Under this method, the initial outlay or initial investment available in terms of present value is compared with the present value of future earnings of the enterprise.
Why the present value of the future earnings are found out?
The ultimate reason to find out the present value future earnings is that the comparison in between inflows and outflows should be meaningful as well as effective. The present value of the initial outlay cannot be converted into the future value for comparison, even otherwise the conversion takes place, the comparison cannot be meaningful. To be meaningful comparison, the future earnings are converted into the present value which is known as discounting process through the discount rate. The rate at which the future earnings are discounted is known as required rate of return.
Selection criterion of Net present value method.If the present value of future cash inflows are greater than the present value of initial investment; the proposal has to be accepted.
If the present value of future cash inflows are lesser than the present value of initial investment; the proposal has to rejected.

Initial Outlay <Present value of Benefits=> +ve NPV:- Project can be accepted
Initial Outlay>Present value of Benefits=>-ve NPV:-Project can be rejected

What is present value index?

The major lacuna of the Net present value method is unable to rank the projects one after the another, only due to the volume of the investment involved. To rank the projects meaningfully, the present value index method is adopted. The present value index of the investment can be calculated with the help of following formula:

Present value index method=
Present value of the cash inflows
Present value of the cash outflows

Selection criterion

If the present value index is greater than one, accept the proposal; otherwise vice versa
Present value index>1:- Accept the investment proposal
Present value index<1:-Reject the investment proposal

What is internal rate of return method?

IRR is the rate at which initial investment is equal to the Present Value of future case in -flows. Under this method, while matching, these two are known but the rate which is taken for equation not given or known. The rate of discounting for matching should be determined through trial and error method.

Once the Internal rate of return is found out, the found IRR should be compared with the required rate of return.

Decision criterion

If the IRR is more than the Required rate of return, the project has to be accepted
If the IRR is less than the Required rate of return, the project has to be rejected

Illustration:

Project ABC Ltd. costs Rs 1,00,000. It produces the following cash flows

The investment proposal has to be accepted only due to positive Net present value.
It means that the present value of the cash inflows are greater than the present value of the outlay. It means the discounted future earnings are greater than the present initial investment outlay.

Illustration :

The Alpha Co Ltd., is considering the purchase of a new machine. Two alternative machines (A and B) have been suggested, each having an initial coast of Rs.4,00,000 and requiring of Rs.20,000 an additional working capital at the end of 1st year. Earnings after taxation are expected to be follows

In the above problem, among the given machines, the firm is required to chose only one machinery. To chose the ideal machinery among the given two, the net present value should be ranked.

The Machine B has been considered as preferable over the machine A due to higher net present value. The ranking of the machines do not indulge any difficulties. Why it so ? The main reason is that both machines are having equivalent volume of investment outlay. Out of the same initial outlays, we can rank that both machines one after the another based upon the net present value.

Illustration :

The initial cost of an equipment is Rs.50,000. Cash inflows for 5 years are estimated to be Rs.20,000 per year. The management's desired minimum rate of return is 15%. Calculate Net present value and Excess present value index.

At the end of every year, the firm expects to earn Rs.20,000. The amount expects to earn Rs.20,000 on every year is nothing but future value of money. The future value of money should be converted into the present value for having comparison with the initial investment.

On every Rs.20,000 expected to receive forms a series of future cash inflows which should be converted into present value.

This conversion process i.e the process of converting the future value into present value is known as discounting process. For discounting, the rate which is used for the process pronounced as discount rate or minimum rate of return. The conversion process can be done in two different ways.
Discounting process :- PV= FV/ (1+r)n
For first year cash inflow Rs.20,000:-
PV=20,000/(1.15)=20,000×.870 =Rs.17,400
For second year cash inflow Rs.20,000;-
PV=20,000/(1.15)2 =20,000×.756 =Rs.15,120
For third year cash inflow Rs.20,000:- Capital Budgeting
PV=20,000/(1.15)3=20,000×.658 =Rs.13,160
For fourth year cash inflow Rs.20,000:-
PV=20,000/(1.15)4=20,000×.572 =Rs.11,440
For fifth year cash inflow Rs.20,000:-
PV=20,000/(1.15)5=20,000×.497 =Rs.9,940
Rs.67,060
OR
Alternately, the discounting can be done as follows
Being Rs.20,000 is nothing but as common cash inflow throughout 5 years of the
project, considered to be a series of cash inflows
Rs.20,000(.870+.756+.658+.572+.497) =Rs.67,060
Net present value = Present value of cash inflows - Present value of cash outlay
=Rs.67,060- Rs.50,000= Rs.17,060
The net present value of the project is +ve. Hence, the project can be accepted.

Illustration :

A project costs Rs.36,000 and is expected to generate cash inflows of Rs.11,200 annually for 5 years. Calculate the IRR of the project.
First step is to find out the fake pay back quotient

Pay back=
Initial Investment
Annual average return
=
Rs.36,000
Rs.11,200
=3.214

The next step is to locate the pay back quotient in the table M-4. The present value of 1 Re should be computed for 5 number of years.
The location of the pay back quotient is in between the values of table M-4
The value 3.214 which lies in between 3.274 of 16% and 3.199 of 17%
The next step in the IRR calculation is that locating the maximum rate of return which equates the initial outlay with the cash inflows of various time periods.

While equating the initial outlay with discounted cash inflows at certain percentage will derive the original rate of return. The process may be started from two different angles viz

• Low discount rate
• High discount rate

The computation of IRR can be had through either low discount rate or high discount rate. This is further extended to different methods of calculation., which are as follows

• On the basis of values extracted from the table
• On the basis of volume

Calculation on the basis of discount rate table value

On the basis of Lower % of discount rate

Alternately, on the basis of volume, the methodology to be adopted for the determination of IRR
The cash inflows of Rs.11,200 for 5 years are discounted @ 16% which amounted Rs.36,668.8. Like wise the cash inflows of the same should be discounted at the rate of 17% which amounted Rs.35,828.8

The next step is to find out the IRR. The IRR can be found out either on the basis of lower discounted cash inflows or higher discounted cash inflows.

Merits of DCF methods

• It is only the best method incorporates the timing of benefits - time value of money
• It consider s the economic life of the project
• It is a best method for both even and uneven cash inflows

Demerits of DCF methods

• It involves with tedious method of computation
• It is very difficult to locate or identify the exact discounting factor
• It never performs functions of discounting to the tune of accounting concepts

Illustration :

XYZ company is considering an investment proposal to install new drilling controls at a cost of Rs.1,00,000. The facility has a life expectancy of 5 years and no salvage value. The tax rate is 35%. Assume the firm uses straight line depreciation and the same is allowed for tax purposes. The estimated cash flows before depreciation and tax formthe investment proposal are as follows:

Calculate the following

1. Pay back period
2. Average rate of return
3. Net present value at 10 percent discount rate
4. Profitability index at 10 percent discount rate

The first and foremost step is to find out the Cash Flows After Taxation
For finding out the Cash flows after taxation, the amount of depreciation i.e non recurring expenditure should be appropriately considered for calculation. The depreciation has to be computed in accordance with the stipulation given in the problem. The depreciation charged by the firm is nothing but straight line method.

Straight line method of depreciation=
Initial Investment -Scrap value
Economic life period of the machine
=
Rs.1,00,000
5 Years
= Rs.20,000

The depreciation has to be deducted initially from the cash flows before taxation, after the deduction of taxation, the earnings after taxation should be added with the depreciation which was already deducted in order to find out the total cash flows after taxation. The purpose of deducting the depreciation is nothing but an amount to be charged under the Profit & Loss account against the total revenue. Being as a non-recurring expenditure not created any outflow cash resources. When there is no cash outflow, the amount of depreciation should be added finally to derive CFAT(Col 7)

Pay back period method: Under this, method most important step is to identify the nature of the cash flows after taxation. Are they uniform ? No, they are not even cash flows. Hence, the cumulative cash flows after taxation has to be found in order to find out the pay back period of the investment.

Average rate of return (ARR):

ARR=
Average Income*100
Average Investment

Average Income is the average of earnings after taxation of the entire duration.
Why earnings after taxation has to be taken into consideration ? Why not the cash flows after taxation to be taken for consideration ?
The main purpose of considering the earnings after taxation is that the amount extracted from the book of accounts and taken for the computation of ARR, and immediately after the payment of taxation.
Average investment is the average of opening and closing investment. If the depreciation charge given is nothing but straight line method, automatically final value of the asset will become equivalent to zero. The closing balance of the asset / investment is zero.

How the closing balance of the investment could be adjudged as equivalent to zero?

At the end of the year, the closing balance amounted Rs.0 after charging the depreciation year after year constantly in volume

Net present value method:

Under this method, the future cash flow after taxation should be discounted at the rate 10%

The net present value is negative due to excessive investment more that of the present value of future earnings of the enterprise. Under this method, the investment is not advisable to procure for the firm's requirements.

Profitability Index

The profitability index method is more useful in the case of more number of investments, having uneven investment outlays, but this problem comes with only one investment proposal It is much easier to assess even in the case of Net present value method.

Profitability Index (PI)=
Present value of cash inflows
Present value of cash outflows
=
Rs.90,704
Rs.100,000
= .90704

The present value index quotient is less than that of the norms which should be greater than one but it secures only 90704. It means that the present value earnings are not sufficient to meet the initial cost of the machine.