There are several ways to measure investment returns. Which method is the best?

You will surprised to note the number of methods we have, to establish return on investment (ROI).

The **method** that can be used to measure investment returns depends on the type of cash-flow we are dealing with.

Yes, investment is not always about two transactions (buying low and selling high).

At times, there can be multiple cash flows like:

- Several cash outs, one cash in.
- One cash out, several cash ins.
- Several cash-in happening at random times.

Even in investment, there is a lot of variety, right?

Undoubtably, it is very important to use a right method to calculate our ROI.

Correct calculation of investment returns will quantify how an **investment is performing**.

Hence it is no surprise why, 99% of all investment decisions are based on its potential to generate the “desired returns”.

And to figure out the desired returns, one has to calculate (estimate) the potential ROI.

## #1. The concept of investment returns

In the process of investment, following two actions come into play:

- Cash-out ($) > Buying.
- Cash-in ($) > Selling, dividends, interest, annuity etc.

Investment return is measured by the amount of “cash-in generated for every dollar ($) of cash-out”.

In simple words we can also say:

*Investment return is measured by the profit generated for every dollar which is invested.*

Broadly speaking, return on investment can be classified into 3 categories:

**Break even**– When cash-in minus cash-out is zero.**Loss**– When cash-in minus cash-out is negative.**Profit**– When cash-in minus cash-out is positive.

But the real utility of measuring investment returns comes into play in “*quantifying*” the the **level** of loss and profit.

Quantifying an investment returns is a part of investment process itself.

Unless the return on investment (loss / profit) is quantified, investment cannot be considered complete.

Why quantification is important?

We invest money to make our money grow.

Hence it is only logical to ask, how fast the invested money is growing?

If one does not get an answer to this vital question, the whole essence of investment will eventually fade.

It is very important for investors to know how to measure investment returns.

### #1.1 Why quantification of investment returns is important?

Suppose we are living in a world where we do not know how to measure investment returns.

In such a world, which of the following investment will be considered best?

- Cash out of $50,000 & Cash in of $55,000.
- Cash out of $4,000 & Cash in of $4,550.

In case 1, the amount of profit is $5,000.

In case 2, the amount of profit is $550

Hence, case 1 is deemed as a better option as it is generating bigger volumes.

But put this question to an investor of today.

Before announcing the result, below calculation will be performed:

- Case 1 – Profit/Cash-out = 0.1 (5000/50000*100=10%)
- Case 2 – Profit/Cash-out = 0.1375 (500/4000*100=13.75%)

The case 1 is generating a profit of $0.1 for every dollar of invested money.

Case 2 is generating a profit of $0.1375 for every dollar of invested money.

Hence, case 2 is a more profitable investment.

This kind of clarity can be achieved only when the investor knows how to quantify investment returns.

It sounds very basic, right?

But in more complicated examples, where calculating returns is not as simple, people may get confused and skip this step all together.

Hence one must know all common methods of calculating investment returns.

## #2. Absolute returns vs annualised returns

In real life investments, the use of absolute returns is limited. It is generally used to quantify returns when holding period is almost a year.

The formula for absolute returns is as below:

(Profit or loss) / Cash-out x 100

The problem with the usage of absolute return is that, it does not give a clear picture.

It only gives a “superficial idea” of which investment is likely performing better (we will see an example below).

But to know a correct answer, one must resort to calculation of annualised returns.

Use of annualised returns is more useful.

It exactly quantifies and confirms which investment is performing how.

The formula for anualised returns is as below:

(Profit or loss) / Cash-out x 100 X (1/number of years)

or

(Profit or loss) / Cash-out x 100 X (365/total number of days)

The annualised returns are often denoted as % p.a.

Lets take a simple example for better understanding:

- Stocks worth $110 was purchased a year back. Today it has been sold for $115.
- Stocks worth $110 was purchased 1.5 years back. Today it has been sold for $115.

What is the absolute return and annualised return for the above investments?

- Case 1:
- Absolute Return = 4.5% [(115-110)/110 * 100]
- Annualised Return = 4.5% p.a [(115-110)/110 * 100 * (1/1)]

- Case 2:
- Absolute Return = 4.5% [(115-110)/110 * 100]
- Annualised Return = 3.0% p.a. [(115-110)/110 * 100 * (365/547)]

The difference between absolute and annualised returns is as follows:

- Absolute Returns does not consider the impact of holding period of the investment.
- Annualised Returns consider the impact of holding period of the investment.

For the same profit, longer will be the holding period lower will be the annualised returns.

### #2.1 Another example of annualised returns

Take example of a shares investment.

- Share buy price: $25/share.
- Holding time 3 years.
- Dividend paid: $1, $1.2, & $1.3 per share in 3 years.
- Share selling price: $30/share after 3 years (1095 days).

Total profit = $1+$1.2+$1.3 (Dividend) + $5 (capital appreciation) = $8.5/share.

Annualised return = 11.33% p.a [8.5/25 * 100 * (365/1095)].

## #3. Compounded annual growth rate (CAGR) vs annualised return

We often use the terms “CAGR” and “annualised returns” as if they are same.

They are similar, but are not identical.

The formula for CAGR is as below:

[(Cashout+Profit) / (Cashout)]^(1/n) -1

or

[End value / Beginning Value] ^(1/n) – 1

Lets use the above example to calculate CAGR:

- Share buy price: $25/share.
- Holding time 3 years.
- Dividend paid: $1, $1.2, & $1.3 in 3 years.
- Share sell price: $30/share after 3 years (1095 days).

Total profit = $1+$1.2+$1.3 (Dividend) + $5 (capital appreciation) = $8.5/share.

CAGR = **10.25%** { [(25+8.5)/25]^(1/3) -1 }

For the above example, the annualised return was **11.33%**

Though the difference between CAGR and annualised return is not big, but they are not mathematically identical.

As an investor which is more useful, CAGR or annualised return?

*CAGR is a more realistic representation of the true growth rate happening every year.*

### #3.1 Use XIRR function in Excel to calculate CAGR

If you do not want to bother yourself calculating the CAGR using the above mathematical formula, there is an easier way out.

Use the XIRR function in excel.

Consider an example of stocks purchase.

- Cash-out : $20 (01-Jan-12) –
*buying* - Cash-in : $52 (02-Jan-15) –
*selling*

What is the CAGR of the above investment?

CAGR is 37.43% per annum.

XIRR is particularly useful in those cases where cash-in has happened on multiple dates over a period of time.

Consider an example of stocks purchase.

- $20 (01-Jan-12) : Cash-out.
- $0.50 (02-Jan-13) : Cash-in (dividend).
- $0.42 (02-Jan-14) : Cash-in (dividend).
- $0.48 (02-Jan-15) : Cash-in (dividend).
- $52 (08-Jan-15) : Cash-in (Capital appreciation).

What is the CAGR of the above investment?

CAGR is 38.95% per annum.

## #4. Internal Rate of Return (IRR)

There is a simpler way of calculating CAGR using Excel functions.

XIRR is a more advanced form of CAGR calculation.

Consider a simple case where:

- Invested amount : Rs.15,000.
- Cash-in : Rs.8,000 (at end of 1st year).
- Cash-in : Rs.9,000 (at end of 3rd year).

What is the “compounded return” on this investment?

In this case we can use the IRR function of Excel.

IRR function of excel works on a theory which states that:

*Present Value of all future cash flows = Investment Amount*

The “discounting rate” that must be applied to satisfy the above equation becomes IRR.

Not clear?

Lets try to understand it using the above example:

What are the future cash-ins?

- 17,000 [Rs.8,000 (1st year), Rs.0 (2nd year), and Rs.9,000 (3rd year)].

What is the investment amount?

- 15,000

Applying the above equation:

*Present Value of Rs.17,000, time horizon 3 years = Rs.15,000*

In this case the IRR of the above investment is 6.4%.

What does it mean?

If we discount the below cash-in @6.4%, their total sum will be equal to Rs.15,000

- #1. Cash in number 1 – Rs.8,000 received in 1st year, when discounted at 6.4%, has a present value of Rs.7,521.19.
- #2. Cash in number 2 – Rs.0 received in 2nd year, when discounted at 6.4%, has a present value of Rs.0.
- #3. Cash in number 3 – Rs.9,000 received in 3rd year, when discounted at 6.4%, has a present value of Rs.7,478.81.

Present value of all future cash flows is, Rs.7521.19+Rs.0+Rs.7478.81 = Rs.15,000.

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