#3 Average Rate of Return (ARR) - Investment Decision - Financial Management ~ B.COM / BBA / CMA

Summary

This video tutorial introduces the Accounting Rate of Return (ARR) technique for capital budgeting. It explains how to calculate the average profit and investment by considering the project's total cash inflows, depreciation, and taxes. The ARR formula is presented, and viewers are guided through a step-by-step example, emphasizing the importance of understanding accounting profits and comparing the ARR percentages of different projects to select the most profitable one.

Takeaways

• 📈 The video discusses the Average Rate of Return (ARR) technique, an important method in capital budgeting for evaluating investments.
• 💡 ARR focuses on the accounting profits earned from an investment over its entire life, which includes profits after tax and depreciation.
• 🔢 The formula for ARR is Average Profit divided by Average Investment, where Average Profit is calculated by dividing the total profit by the project's life span.
• 💼 The script explains that cash inflows are not the same as profits; profits are derived after accounting for depreciation and taxes.
• 📊 To calculate total profit, the script details a step-by-step process: sum all cash inflows, subtract total depreciation, and then subtract taxes based on the residual value after depreciation.
• ⏱ The script provides a clear example of how to calculate ARR, including the addition of all cash inflows over a project's life, the calculation of annual depreciation, and the application of a tax rate to the residual value.
• 💹 The ARR is expressed as a percentage, which is used to compare different investment projects, with the project having the highest ARR being potentially the most profitable.
• 💡 The script emphasizes that the ARR method is also known as the Accounting Rate of Return, highlighting its focus on accounting profits.
• 📝 The video script also mentions that the ARR method is simple to calculate and understand, making it a useful tool for comparing the profitability of various investment projects.
• 🔍 The video concludes with a problem-solving example, demonstrating the practical application of the ARR technique in evaluating an investment project with given cash inflows, depreciation, and tax rate.

Q & A

What is the main focus of the third video in the investment decision chapter?

The third video focuses on explaining the Accounting Rate of Return (ARR) technique of capital budgeting, which takes into account the earnings from the investment over its whole life.

What are the two names for the technique discussed in the video?

The technique discussed in the video is known as both the Accounting Rate of Return (ARR) and the Average Rate of Return.

How is the Average Rate of Return (ARR) calculated?

The Average Rate of Return (ARR) is calculated by dividing the average profit by the average investment.

What is considered when calculating the average profit in the ARR technique?

The average profit in the ARR technique is calculated by considering the total cash inflows, subtracting the total depreciation, and then the tax on the residual value after depreciation.

How is the average investment calculated in the ARR technique?

The average investment is calculated by adding the initial investment and the scrap value, dividing by 2, and then adding any additional working capital if given.

What is the formula for calculating the depreciation of an asset in the ARR technique?

The formula for calculating the depreciation is the initial investment minus the scrap value, divided by the number of years of the project's life. If there is no scrap value, the initial investment is considered the total depreciation.

What is the significance of considering the whole life of the project when calculating ARR?

Considering the whole life of the project allows for a comprehensive evaluation of the investment's profitability over its entire duration, taking into account all cash inflows and the full depreciation of the asset.

Why is it incorrect to calculate tax directly on the cash inflows in the ARR technique?

Calculating tax directly on the cash inflows would not account for the impact of depreciation on the project's profitability. Instead, tax should be calculated on the residual value after deducting depreciation.

What is the purpose of comparing the ARR percentages of different projects?

Comparing the ARR percentages of different projects helps in selecting the project with the highest average rate of return, which indicates the most profitable investment option.

How does the script illustrate the calculation of ARR with an example?

The script provides a step-by-step example, starting with the initial investment, calculating cash inflows, depreciation, tax, and then using these figures to find the average profit, average investment, and finally the ARR percentage.

What is the next topic the video series will cover after the ARR technique?

The next topic the video series will cover is the Net Present Value (NPV) technique of capital budgeting.

Outlines

00:00

💼 Introduction to Accounting Rate of Return (ARR)

This segment introduces the concept of the Accounting Rate of Return (ARR), also known as the Average Rate of Return, as a technique in capital budgeting. The ARR method considers the earnings from an investment over its entire life, focusing on accounting profits. The formula for ARR is presented as the average profit divided by the average investment. The video explains the importance of understanding how to calculate average profit and average investment, which involves accounting for cash inflows, depreciation, and taxes. The process of calculating profits by deducting depreciation and taxes from cash inflows is emphasized, setting the stage for a deeper dive into the ARR technique.

05:02

📊 Calculating Average Profit and Investment

The second paragraph delves into the specifics of calculating average profit and average investment. It explains that average profit is derived from total cash inflows minus total depreciation and taxes. The calculation of depreciation is detailed, emphasizing that if there is no scrap value, the entire initial investment is considered for depreciation. The tax calculation is also discussed, highlighting that it should be based on the residual value after depreciation. The process of determining average investment is outlined, which involves averaging the initial investment and scrap value (if any), and adding any additional working capital. The paragraph concludes by demonstrating how to calculate the ARR percentage by dividing the average profit by the average investment and multiplying by 100.

10:02

🔢 Practical Application of ARR Calculation

This segment provides a practical example to illustrate the ARR calculation. It walks through a scenario with an initial investment of 1 lakh sixty thousand, no scrap value, and cash inflows for five years. The depreciation is calculated on a straight-line basis over five years, with a tax rate of 40 percent. The process involves summing up the cash inflows, calculating the total depreciation (considering the entire initial investment since there's no scrap value), and then determining the profit after tax. The average profit is then calculated by dividing the total profit by the project's life (five years). The average investment is calculated by taking half of the initial investment, as there's no scrap value or additional working capital. Finally, the ARR is computed by dividing the average profit by the average investment and converting it to a percentage.

15:04

📚 Conclusion and Preview of Future Topics

The final paragraph wraps up the discussion on ARR by summarizing the steps involved in calculating it. It reiterates the importance of considering cash inflows, depreciation (especially when there's no scrap value), and taxes in the profit calculation. The paragraph also previews upcoming topics, such as the Net Present Value method, and hints at the possibility of solving combined problems in future videos. The summary serves as a conclusion to the ARR discussion and a teaser for further learning in capital budgeting techniques.

Keywords

💡Investment Decision

Investment Decision refers to the process of choosing between different options for allocating funds with the expectation of generating a profit. In the video, it is the overarching theme as the presenter discusses various techniques for evaluating the viability of investment opportunities.

💡Payback Period Technique

The Payback Period Technique is a capital budgeting method that calculates the time it takes for an investment to generate an amount of income or cash equal to the cost of the investment. It was mentioned in the script as a previously discussed technique, indicating the progression from one method to another within the series.

💡Accounting Rate of Return (ARR)

Accounting Rate of Return, also known as the Average Rate of Return, is a financial metric that calculates the percentage profit of the investment over its lifetime. The video focuses on this technique, explaining its formula and application in evaluating investment options.

💡Capital Budgeting

Capital Budgeting is the process of evaluating the profitability of long-term investments. The script discusses it as the context in which the ARR technique is applied, emphasizing its importance in financial decision-making.

💡Earnings

Earnings, in the context of the video, refer to the income or profits generated from an investment. The ARR technique takes into account the earnings over the life of the investment, which is a key factor in determining the investment's success.

💡Cash Inflows

Cash Inflows are the streams of cash generated by an investment. The script uses the term to describe the expected future cash receipts from an investment, which are essential for calculating profits and ARR.

💡Depreciation

Depreciation is the systematic allocation of the cost of a tangible asset over its useful life. In the script, depreciation is a factor subtracted from cash inflows to determine the accounting profit, illustrating its impact on the investment's financial performance.

💡Tax

Tax, in the context of the ARR technique, is the portion of profit that must be paid to the government. The script explains that tax is calculated on the residual value after depreciation, which affects the final profit and thus the ARR calculation.

💡Average Profit

Average Profit is the total profit from an investment divided by the number of years the investment is expected to generate earnings. The script describes how to calculate it, emphasizing its role in determining the ARR.

💡Average Investment

Average Investment is calculated by adding the initial investment and the scrap value (if any), then dividing by two. The script explains this formula and its importance in the ARR calculation, noting that additional working capital can also be included.

💡Net Present Value (NPV)

Net Present Value, while not the main focus of the video, is mentioned as a technique to be discussed in the next video. It is a method used to determine the profitability of an investment project by discounting cash inflows to their present value.

Highlights

Introduction to the Average Rate of Return (ARR) technique in capital budgeting.

Explanation of how ARR takes into account the earnings from an investment over its entire life.

Description of the ARR formula: Average Profit divided by Average Investment.

How to calculate average profit by dividing total profit by the project's life span.

The process of calculating total cash inflows by adding up all cash inflows over the project's life.

Details on calculating depreciation, especially when there is no scrap value involved.

Clarification on calculating tax based on the residual value after depreciation, not on cash inflows.

The method to determine the Average Investment by using the initial investment and scrap value.

Importance of considering additional working capital in the calculation of average investment.

How to compare ARR percentages of different projects to select the one with the highest return.

The significance of ARR in focusing on accounting profits, hence its alternative name, Accounting Rate of Return.

A step-by-step guide to solving an ARR problem, starting with writing the formula.

Instructions on adding up all cash inflows for the entire life of the project.

The approach to calculating annual depreciation when there is no scrap value.

How to calculate tax on the residual value after accounting for depreciation.

The final steps to determine the average rate of return in percentage form.

Emphasis on the simplicity of the ARR method once the cash inflows, depreciation, and tax are understood.

Preview of the next video covering Net Present Value and the possibility of a combined problem.

Transcripts

hi everyone this is the third video of

investment decision chapter and in the

previous video we have seen the payback

period technique of capital budgeting

right we have seen this payback period

now in this video what are we going to

do is in this video we are going to see

another technique of capital budgeting

that is accounting rate of return or you

can also call it as average rate of

return okay it has two names fine an

average rate of return or accounting

rate of return fine let's get into it

now let's try to understand this average

rate of return technique of capital

budgeting see here I have written the

meaning over here this method takes into

account the earnings from the investment

over its whole life see this is very

important earnings from the investment

whatever earnings the investment that

investment will fetch us right those

earnings those accounting profits are

taken into account in this average rate

of return technique what here in this

technique of a are our average rate of

return profits accounting profits are

taken into account earning from the

investment suppose if company is

considering right these three

investments and they're evaluating these

investment right then the initial

investment of this project a would be 50

lakh right it is 50 lakh so if company

invest 50 lakh in this then what all

cash inflows it will have in the future

right those cash inflows are not profits

are those profits no they are not they

are not profits profits are something

that after deducting the tax and the

depreciation right depreciation and tax

after deducting depreciation and tax

that would be profits so those

accounting profits are taken into

account here in average rate of return

okay so the formula of this technique is

a RR see here this is the average rate

of return a RR is equal to average

profit divided by average investment

okay this is the formula of this

technique a RR is equal to average

profit divided by average investment so

now the main thing is how do we

calculate average

profit and how do we calculate average

investment because obviously it will not

be given into the question right if it

is given in the question then there is

nothing to do just divide right so

that's not the focus here here you have

to calculate the average profit and

averaging less than so how do you go

about that see you to calculate profit

as I said simple in the cushion cash

inflows will be given cash inflows will

be given if invest in any project right

the estimate will be there that this

project will fetch us this much cash

flows cash inflows in the year one it

would be ten lag in the year it would be

fifteen lag in the year three it would

be twenty like like that estimates will

be there so on the basis of those

estimates only we evaluate the project

right because this is something that

will happen in the future it's uncertain

right so yeah so those cash inflows are

added up okay all the cash inflows of

the whole life okay whatever life is

there of that project all the cash

inflows will be added and then

depreciation the whole depreciation of

that project will be subtracted right

for example if this is ten lakh

depreciation is two lakh then what is

the residual value eight like then tax

percentage would be given in the

question you have to calculate tax on

not on the cash inflow not on the ten

lakh you have to calculate tax on the a

eight lag that residual value the value

after deducting the depreciation fine

okay so that is how you will get the

profit the total cash inflows add them

up altogether minus depreciation and

then minus PACs and calculate tax after

deducting the depreciation okay don't

calculate tax directly on the cash

inflows no okay all right

then once you get the profit then easily

you can calculate the average profit

that is profit whatever profit you got

here profit divided by number of years

that would fetch you the average profit

now what is this number of years the

years that is estimated that project

will continue okay that is the number of

years the life of the project fine

yeah then your first thing is done the

average profit is done right first work

is done the second average investment

how do you calculate a

investment see to calculate average

investment there is a simple formula see

here average investment is equal to

initial investment initial investment

means the outflow the first outflow

whatever money we invest right whatever

money the company invests that is the

initial investment right initial

investment plus scrap value the scrap

value means the value which you would

fetch at the last the termination value

of the project that is the scrap value

so you will add those two together and

then divided by 2 okay you are

calculating average investment so you

are dividing it by 2 and then at last if

there is any additional working capital

given in the question at last add it up

ok at last add this additional working

capital

what is additional working capital

sometime what will happen sometime in

the project they would need some funds

in between in between of the project

right so if they estimate that some

working capital would be required then

the working capital will be given to

reading the question and you have to add

it to this at last

then you will get average investment

this simple technique is first do this

ok initial investment plus craft value

divided by 2 and then whatever answer

you get added with the additional

working capital okay don't add this

first add this at last okay add the

additional working capital at last fine

so this is how you will you calculate

the average profit and then average

investment and once you divide that you

will get average rate of return it will

be in form of of course percentage write

rate it is rate so it will be in form of

percentage and then you will compare the

compare the percentages the AR are of

different different projects and you

will select the project which has the

highest AR are the highest average rate

of return fine so that is what is there

in average rate of return here you focus

on the accounting profits so that is why

this method is also known as accounting

rate of return okay this method is also

known as this technique is also known as

accounting rate of return fine so this

is it now let's see the problem let's

solve the problem of this AR AR and you

will get more okay you will understand

more fine

okay then let's go to the

now let's solve this problem see here

here's the question

initial investment 1 lakh sixty thousand

right initially in this project we are

going to invest how much 1 lakh sixty

thousand fine and then they have said no

scrap value right so we have to ignore

the scrap value if you have to consider

there is no scrap value and we have to

take scrap value s nil

fine and then they have given us the

cash inflows see here cash inflows here

and here the amount here 156 thousand

year to 48 thousand year three thirty

thousand a year for sixty four thousand

and year five eighty thousand right and

then they have said depreciation is on

straight-line basis tax rate forty

percent right now we have all we need

now let's start and solve this problem

see here first what are we going to do

first we are going to write the formula

because we need to know what we need to

find right so average rate of return is

equal to average profit divided by

average investment that is the formula

we need average profit and we need

average investment now we have the

formulas over here right how do we

calculate profit to calculate average

profit first we need profit cash inflows

minus depreciation and then minus tax

right that is what we do so let's do

that first

see here to calculate that first let's

add up all the cash inflows because here

we are considering the whole life of the

project right whole life of the project

so we have to add up all the cash

inflows so cash inflows fifty six

thousand forty eight thousand thirty

thousand sixty four thousand eighty

thousand we have to add them up okay we

have to add all of them right so

ignoring the zeros let's add them up 56

plus ya 56 plus then 48 plus 30 plus and

what is the 64 plus 80 that is equal to

278 isn't it it is equal to 278 so it is

2 lakh 78,000 that is the total cash

inflows right total cash inflow right so

we have got total cash inflow now now

use that profit formula right cash

inflows minus depreciation minus tax use

that profit is equal to cash inflows the

total cash inflows

- the whole depreciation -

right now we have the total cash inflow

that is 278 we just added that up right

so 278 to like 78,000 and then

depreciation now how do we calculate

depreciation now I have said that here

we are considering the whole

depreciation how much whole depreciation

whole depreciation so that is why that

is why here here how many years are

there of this project five years are

they right how many years five years and

the cost of the investment the initial

investment is one like fifty thousand so

now you will have to depreciate this

right right so what would be the

depreciation of one year the one year

depreciation is one like sixty thousand

right cost what is the formula of

depreciation cost minus scrap value

divided by the number of years that is

the that is a formula right but we don't

have any scrap value so minus zero that

is one last 80,000 only and then divided

by the number of years that is five

right so that is 32,000 the depreciation

of one year is 32,000 but here we are

considering the whole life of the

project so we have to take the whole

depreciation that is into five that is

one last 50,000 but you don't have to do

all this you don't have to do that you

just have to directly take the initial

investment as the depreciation because

this whole amount will be depreciated in

the five years whole amount because

there is no scrap value if there had

been scrap value then what would be the

depreciation let's say scrap value was

twenty thousand this for an example

scrap value was twenty thousand then

that whole depreciation would be 160

minus twenty thousand this was the hold

appreciable amount the whole

depreciation would be 140 right so that

is what you have to take whole here

because entire thing will be depreciated

in the period of five years okay that is

what so you have to take the whole

deposition that is one like thirty

thousand the entire initial investment

the entire cost would be depreciated in

the five years so you have to take the

entire depreciation we are considering

the whole life of the project in this

average rate of return so whole

depreciation you have to take okay

okay so don't get confused in that okay

how do you calculate that symbol if

there is scrap value just subtract the

scrap value from the initial investment

okay 160 if there is scrap value let's

say 10 so minus 10 right 150 would be

the depreciation if the scrap value

would have been 50 50 thousand then the

depreciation would have been 1 lakh 60

minus 50 thousand right so one lakh 10

would be the depreciation this is how

you have to do it okay don't worry

so cash inflows minus depreciation 1

lakh 60,000 in the higher thing would be

depreciated okay entire thing would be

depreciated because there is no scrap

value so entire thing would be

depreciated so you have to take that

whole thing and then you have to

calculate tax okay so 278 yeah - like 78

thousand - 160 thousand that is a

depreciation when the residual value get

us one lakh 18000 now on this one like

eighteen thousand you have to calculate

the tax and the tax percentage is given

in the question as forty percent isn't

it it is given as 40 percent so on this

you have to calculate 40 percent in to

40 percent that is equal to 40 7200 so

the tax is 40 7200 right you have to

calculate the tax on the residual value

not on the cash inflow fine you saw

right how we did that yes and then this

is a tax 40 7200 write that down and

then do it again - 78 yeah - 160 minus

40 7200 the tax you will find 70

thousand 800 as the profit now this is

the total profit this is the total

profit okay after considering the

depreciation and after considering the

tax after deducting them up this is the

total profit of the five years now you

have to find annual average profit you

have to find average profit so to find

out average annual profit what do you do

you just divided by the life of the

project the number of years to calculate

average profit divided by number of

years just do that number of years so if

you do that you would get fourteen

thousand one hundred and sixty right

let's try that 70 thousand eight hundred

divided by five

would fetch us 14,000 160 this is the

average profit so one thing is done

right we have calculated the average

profit now we have to calculate the

average investment isn't it now how do

we go about that how do we calculate

average investment the formula is

initial investment plus scrap value

divided by 2 plus additional working

capital but here in this question do we

have scrap value

no no scrap value no additional working

capital nothing so what are they going

to do be able to ignore this completely

ignore this right because there is no

scrap value with no working capital

given no additional working capital

given only initial investment we have so

that is all we are going to take initial

investment yeah one lakh 60,000 divided

by two that would fetch us 80,000 80,000

is the average investment if there would

have been scrap value an additional

working capital then we would have taken

them here but now there is nothing so we

have to only take initial investment

okay so one lakh 60,000 divided by 2

that is 80,000 fine so we have got we

have got the average investments so once

we get average profit and average

investment then it's very simple right

just divide it up right just divide them

up and find out the average rate of

return right so that is what we are

going to do 14,000 160 divided by 80,000

yeah so and then you have to multiply it

by 100 because here we are finding out

in terms of percentages so in 200 that

gives you 17.7 percentage right 17.7

percentage that is how you do it it's

very simple right what do you do first

first you have to add up all the cash

inflows right you can also do it in the

table form also k1 by 1 you can take the

cash inflows and then calculate the

depreciation first and to calculate

depreciation it's very simple okay

if there is no scrap value whatever cost

is there the entire thing would be the

depreciation keep that in mind and then

the tax right and if there is scrap

value here then just subtract the scrap

value that whole thing would be the

depreciation the entire depreciable

amount whatever that would get

depreciated right that is what you have

to take over here and then

tax tax calculate it on the residual

value so that is how you do it and then

average investment is initial investment

plus scrap value divided by two and if

there is any additional working capital

then after calculating this then add it

with the additional working capital okay

so that is how you go about it it's very

very simple okay all right then in the

next video we are going to see net

present value and if you want we can

also do a combined problem okay