# METHODS OF CAPITAL BUDGETING - Accounts and Finance for Managers

The methods are the nothing but the instruments of the capital budgeting to study the quality of the investments/fixed assets. The investments are studied by the firms in the following angles:

• Based on the number of years taken for getting back the investment – Pay Back Period Method
• Based on the profits accrued out of the investment – Accounting Rate of Return/ Average Rate of Return
• Based on the timing of benefits – Present value of future benefits of the investment

–Discounted cash flow methods
Based on the comparison in between the cash outlay and receipts discounted with the help of minimum rate of return - Net present value method
Based on the identification of maximum rate of return, in between the initial cash outlay and discounted expected future receipts - Internal Rate of return method
Based on the ration in between the present values of cash inflows and outflows
– Present value index method

The classification of methods are generally in two categories:

• Traditional methods
• Pay Back Period method
• Accounting Rate of Return
• Discounted cash flow methods
• Net present value method
• Internal Rate of Return method
• Present value index method
• Discounted pay back period method

Pay Back Period Method

What is pay back period?

The pay back period is the period taken by the firm to get back the investment. The pay back period is nothing but number of years/months/days required by the firm to get back its investment invested in the project.

To find out the pay back period, the following are two important covenants required:

• Initial outlay / Initial investment / Original investment
• Cash inflows

How the pay back period is calculated?

The pay back period is calculated by way of establishing the relationship between the volume of investment and the annual earnings

While calculating the pay back period, the nature of annual earnings should be identified. The nature of the annual earnings can be classified into two categories:

• Cash flows are equivalent or constant
• Cash flows are not equivalent or constant

If the cash flows are equivalent, How the pay back period is to be calculated ?

The cost of the project is Rs.1,00,000. The annual earnings of the project is Rs.20,000. Calculate the pay back period.

Pay back period =
Initial Investment
Average Annual Earnings
=
Rs.1,00,000
Rs. 20,000
= 5years

It is obviously understood that, Rs.20,000 of annual earnings (cash inflows) requires 5 years time period to get back the original volume of the investment.
If the cash flows are not equivalent, How the pay back period is to be calculated ?

The cost of the project is Rs.1,00,000. The annual earnings of the project are as follows The ultimate aim of determining the cumulative cash inflows to find out how many number of years taken by the firm to recover the initial investment.
The next step under this method is to determine the cumulative cash flows The uncollected portion of the investment is Rs,10,000. This Rs.10,000 is collected from the 4th year Net income / cash inflows of the enterprise. During the 4th year the total earnings amounted Rs.20,000 but the amount required to recover is only Rs.10,000. For earning Rs.20,000 one full year is required but the amount required to collect it back is amounted Rs.10,000. How many months the firm may require to collect Rs.10,000 out of the entire earnings Rs.20,000? Pay back period consists of two different components

• Pay back period for the major portion of the investment collection in full course -E.g.: 3 years
• Pay back period for the left /uncollected portion of the investment
For the second category =
Rs.10,000
Rs. 20,000
= 0.5 years

Total pay back period= 3 Years +.5 year = 3.5 years

Criterion for selection: If two or more projects are given for appraisal, considered to be mutually exclusive to each other for selection, the pay back period of the projects should tabulated in accordance with the ascending order. The project which has lesser pay back period only to be selected over the other projects given for scrutiny.
Why lesser pay back has to be chosen?

The reason behind is that the project which has lesser pay back period got faster recovery of the initial investment through cash inflows/Net income.
Selection criterion
Lesser the pay back period is better for acceptance of the project

Illustration :A project costs Rs.2,00,000 and yields and an annual cash inflow of Rs.40,000 for 7 years. Calculate pay back period. First step is identify the nature of the annual cash inflows In this problem, the annual cash inflows are equivalent throughout life period of the project

Pay Back Period=
Initial Investment
AnnualCash Inflows
=
Rs. 2,00,000
Rs. 40,000
=
5 years

Illustration :Calculate the pay back period for a project which requires a cash outlay of Rs.20,000 and generates cash inflows of Rs 4,000 Rs.8,000 Rs. 6,000 and Rs. 4,000 in the first, second, third, and fourth year respectively
First step is to identify the nature of the cash inflows
The cash inflows are not equivalent/constant Cost of the project is to be recovered Rs.20,000. The project takes 3 full years time period to recover the major portion of the initial investment which amounted Rs.18,000 out of Rs.20,000.

The remaining amount of the initial investment is recovered only during the fourth year. The left portion Rs.2,000 has to be recovered only from the fourth year cash inflows of Rs.4,000.

Pay Back Period = Pay Back period of the major portion + Pay Back period of the remaining portion
Pay Back period of the major portion = 3 years

Pay Back period of the remaining portio: For the entire earnings of Rs.4,000, the firm consumed one full year/12 months time period. How many number of months required to recover Rs.2,000 ?

Rs.2,000
Rs. 4,000
= 0.5

Total pay back period = 3 years + 6 months = 3 years 6 months

Illustration :A project cost of Rs.10,00,000 and yields annually a profit of Rs.1,60,000 after depreciation and depreciation at 12% per annum but before tax 50% calculate pay back period.

Pay Back Period=
Initial Investment
Annual Cash inflow

In this problem, the initial investment is given which amounted Rs.5,00,000.
The annual cash inflow is not given directly; to determine the cash inflow; what is meant by the cash inflow ?
Cash inflow = Profit after tax + Depreciation
Profit Before taxation = Rs.1,60,000
(-)Taxation = Rs. 80,000
Profit after taxation = Rs. 80,000
(+)Depreciation 12% on = Rs. 10,00,000
= Rs. 1,20,000
Annual Cash Inflow = Rs. 2,00,000

Pay Back Period
Rs.10,00,000
Rs. 2,00,000
=5years

Illustration :A company proposing to expand its production can go in either for an automatic machine costing Rs.2,24,000 with an estimated life of 5 ½ years or an ordinary machine costing Rs.60,000 having an estimated life of 8 years. The annual sales and costs are estimated as follows: Compute the comparative profitability of the proposals under the pay back period method. Ignore Income Tax

The first step is to find out the Annual profits of the two different machines
The next step is to find out the pay back period of the two different machines respectively The pay back period method highlights that the ordinary machine is more ideal than the automatic machine due to lesser pay back period i.e., 3 years. It means that the ordinary machine is bearing the faster rate in getting back the investment invested than the automatic machine.
The another method to discuss is post pay back impact of the two different machines
Post pay back profit is the profit of the two different machines after the recovery of the initial investment. The machine which has greater post pay back profit construe. Post pay back profit of the Automatic machine is higher than the Ordinary machine; which amounted Rs.1,28,000. It means that the profit of the automatic machine after the recovery of the initial investment is greater than that of the ordinary machine.

Illustration : A company has to choose one of the following two mutually exclusive projects. Investment required for each project is Rs 30,000. Both the projects have to be depreciated on straight line basis The tax rate is 50%. Calculate pay back period
First step is to find out the depreciation under the straight line method
The next step is to determine the pay back period of the both projects A and B respectively
The next step is to compare both pay back periods of two different projects.
The depreciation under the straight line method is as follows

For Project A

=
Initial Investment
Life of the Project
=
Rs. 30,000
5 years
=
Rs.6,000

For Project B

=
Initial Investment
Life of the Project
=
Rs. 30,000
5 years
=
Rs.6,000 Pay back period = Pay back period of a major portion + Pay back period for remaining
Pay back period of the major portion= the firm has recovered a major portion of the initial investment of Rs.25,000 within 3 full years out of Rs.30,000

The second half of the equation is that pay back period for the remaining i.e., Rs.5000 of initial investment which is to be recovered during the fourth year out of Rs.10,000

If Rs.10,000 earned throughout the year /12 months, how many months taken by the firm in recovering Rs.5,000 out of rs.10,000

=
Rs.5,000
Rs.10,000
=6months

Pay back period (Project A) = 3.6 years
The next stage to find out the pay back period of the project B Pay back period of the project B= = 4 years +.02 × 365 days = 4 years + 8 days
= 4 years and 8 days
Pay back period of the project B is greater than that of the earlier Project A. It means that the Project A is bearing the faster rate in getting back the investment invested.

Merits

• It is a simple method to calculate and understand
• It is a method in terms of years for easier appraisal

Demerits:

• It is a method rigid
• It has completely discarded the principle of time value of money
• It has not given any due weight age to cash inflows after the pay back period
• It has sidelined the profitability of the project.

Accounting or Average Rate of Return:

Under this method, the profits are extracted from the book of accounts to denominate the rate of return. The profits which are extracted are nothing but after depreciation and taxation and not cash inflows.

Selection criterion of the projects:
Highest rate of return of the project only is given appropriate weightage.
The Accounting rate of return can be computed as follows

Accounting Rate of Return (ARR)=
AnnualReturn*100
Original Investment
Accounting Rate of Return (ARR)=
Average Annual Return*100
Average Investment

Average annual return= Average profit after depreciation and taxation of the entire life of project i.e. for many number of years

Average Investment=
Opening Investment + Closing Investment
2
=
Opening Investment - Scrap
2

Illustration :

Calculate the average rate of return for Projects X and Y from the following If the required rate of return is 10% which project should be undertaken?

Accounting Rate of Return (ARR)=
Average Annual Return*100
Original Investment

The first step is to find out the average annual income of the two different projects X and Y

The next step is to find out the Average rate of return :

Both the projects are lesser than the given required rate of return. These two projects are not advisable to invest only due to lesser accounting rate of return.

Illustration :

The alpha limited is considering the purchase of a machine to replace a machine which has been in operation in the factory for the last 5 years. First step is to consider that few assumptions to proceed the problem without any technical difficulties.

First assumption is that there is no closing stock i.e. what ever goods produced are sold out in the market.

Second assumption is that the volume of the sales is expected to be remain throughout the life of the period.

Third assumption is that the depreciation charged by the firm is on the basis of straight line method.

Steps involved in the computation of the accounting rate of return
The first is to compute the total number of units expected to produce
Total number of units of production = Total machine hours per annum * Units per hour
For old machine = 2,000 Hrs* 24= 48,000 units
For new machine = 2,000 Hrs * 36= 72,000 units
The second step is to determine the volume of annual sale of units:
Total volume of sales = Total number of units * Selling price per unit
For old machine = 48,000 units * Rs 1.25= Rs.60,000
For new machine = 72,000 units* Rs.1.25= Rs.90,000

According to the second assumption, the volume of sales is known as unaffected throughout the life period of the projects.
The next step is to find out the volume of the wages
Total wages = wages per hour * Machine running hours
For old machine = Rs.3* 2000 Hrs= Rs.6,000
For new machine = Rs5.25* 2000 Hrs=Rs.10,500
The next step is to find out the total material cost
Total material cost per unit = Total number of units * Material cost per unit
For old machine = 48,000 * .5= Rs.24,000
For new machine = 72,000 * .5=Rs.36,000
The last step is to find out the depreciation

Depreciation under straight line method=
Initial investment
Economic life period of the asset

For old machine = Rs.8,000
For new machine = Rs.12,000

The next step is to draft the profitability statement of the enterprise under the head of two different machine viz old and new. To find out the annual income of the enterprise under two different machines  Merits

• It is simple method to compute the rate of return
• Average return is calculated from the total earnings of the enterprise through out the life of the firm
• The entire rate of return is being computed on the basis of the available accounting data

Demerits

• Under this method, the rate of return is calculated on the basis of profits extracted from the books but not on the basis of cash inflows
• The time value of money is not considered
• It does not consider the life period of the project
• The accounting profits are different from one concept to another which leads to greater confusion in determining the accounting rate of return of the projects

Discounted Cash Flows Method The discounted cash flows method is the only method nullifies the drawbacks associated with the traditional methods viz Pay back period method and Accounting rate of return method. The underlying principle of the method is time value of money. The value of 1 Re which is going to be received on today bears greater value than that of 1 Re expected to receive on one month or one year later. The main reason is that "Earlier the benefits better the principle". It means that the benefits whatever are going to be accrued during the present will be immediately reinvested again to maximize the earnings, so that the earlier benefits are weighed greater than the later benefits. The later benefits are expected to receive only during the future which is connected with the future i.e., future is uncertain. It means that there is greater uncertainty involved in the receipt of the benefits connected with the future.

Why the time value of money concept is inserted on the capital budgeting tools?

The main reason is that the capital expenditure is expected to extend the benefits for many number of years. The 1 Re is expected to receive one year later cannot be treated at par with the 1 Re of 2 years later. This is the only method considers the profitability as well as the timing of benefits. This method gives an appropriate qualitative consideration to the benefits of various time periods.
The time value of money principle is used for an analysis to study about the quality of the investments in receiving the future benefits.

There are general classifications which are as follows

• Net present value method
• Present value index method
• Internal rate of return method
Accounts and Finance for Managers Topics