 # Five important formulas to calculate returns on investments

Familiarize yourself on five important formulas that are used to calculate returns.

1) Holding Period Return (HPR)

2) Post Tax Returns

4) Compounded Annual Growth Rate (CAGR)

5) Effective Annual Rate

Let us understand each of these formulas in detail.

#### 1) Holding Period Return (HPR)

Holding period return is the total return received from holding a Financial Asset. It is calculated as income plus price appreciation during a specified time period, divided by the cost of investment.

When we are looking at the return that we earn on our investments, one of of the first measures that we will look at is the Holding period of return. This return includes income from all sources like dividends, interest, periodic receipts and the change in the price of the asset.

Holding Period return is also known as, Absolute return (or) Total Return (or) Historic Return.

HPR = ( Periodic Receipts +(Sale price – Purchase price)) / Purchase        price

Example : Mr. Sinha invested Rs 1,00,000 in stock market . After 2 months he received a dividend amount of Rs 2,000. He sold the shares after 8 months and received Rs 1,12,000. What is the holding period return in this case?

HPR = (2000 + (1,12,000-1,00,000)) / 1,00,000

HPR = 14%

#### 2) Post Tax Returns

Different financial instruments attract different tax rates. It is important to factor in the taxes while calculating your returns on investments. It is used to calculate the actual returns from any investment after paying applicable taxes.

Post-tax returns = Pre-Tax retuns * { (100-Tax Rate) / 100 }

Example : Continuing with the above example, Mr Sinha had to pay 15% as Short Term Capital Gains Tax. So, what is the actual returns (in percentage) after accounting for taxes?

Post-tax returns = 14 * { (100-15) / 100 }

Post – tax returns = 11.9%

This formula can be used to find out the actual returns after adjusting nominal returns to change in prices or inflation. This is mainly used during ‘withdrawal phase’ of your investments. This is also known as ‘Real Rate of Return.’ It is used to determine the actual worth of an investment after adjusting for inflation rate.

Inflation adjusted returns = { [( 1+nominal return ) / ( 1+inflation rate )] – 1 } * 100

Example : Mr. Gupta (Age 59 years) received Rs 25,00,000 as his retirement benefits. He invested  this amount in Bank Fixed Deposit. He plans to withdraw the interest amount periodically. The interest rate offered is 9.5%. The average inflation rate is 8%. What is the Real rate of return?

Real rate of return = { [ ( 1 + .095) / (1+.08) ]-1 } * 100

Real rate of return = 1.39%.

4) Compounded Annual Growth Rate (CAGR)

CAGR is the year-over-year growth rate of an investment over a specified period of time. It is known as Annualized returns. Is is mainly used to compare performances of mutual funds, stocks etc.,

CAGR = [ { ( 1+ r )^ 1/n } – 1 ] * 100

(r = Holding period or total return and n = Time)

Example : Mr. Iyer invested Rs 1,00,000 in a mutual fund scheme. After 4 years, he sold the mutual fund units and received Rs 1,35,000. Calculate Holding period return and CAGR?

HPR = (135000 -100000) / 100000

HPR = 35%

Whereas, CAGR = [ { ( 1+.35)^1/4 } -1 ] *100

CAGR = 7.79%

Holding period return is 35% for 4 years. The annual growth rate will not be 35/4 = 8.75%. But, it will be less than this figure which is 7.79% as growth is compounded.

If the holding period is 1 year then CAGR and HPR will be the same. If the holding period is more than 1 year then the CAGR will be less than the HPR.

#### 5) Effective Annual Rate

The formula for converting the nominal return into an effective annual rate is as below:

Effective Annual Rate = { ( 1 + r )^n  – 1 } * 100

( r = nominal return divided by no of compounding in a year)

(m = no of compounding in a year. 12,4,2 and 1 for monthly, quarterly, half-yearly and annually respectively.)

Example: Mr. Gowda invests some amount in a bank fixed deposit. The interest rate offered is 9% pa, compounded quarterly. What is the effective annual rate in this case?

Effective Annual rate = { ( 1 + .09/4) ^ 4 -1 } * 100

Effective Annual rate = 9.3%

Hope this post is useful to you. Make use of these formulas while analyzing your investments. You may execute these formulas using financial calculator or on MS excel. Kindly share your views.

( Image courtesy of Stuart Miles at FreeDigitalPhotos.net)

• Sreekanth Reddy says:

Dear Abhik,
Wonderful question!

For quick calculation, an individual may choose to approximate the real rate of return by using the simple formula of nominal rate – inflation rate. This is casual way of calculating!

Both, Inflation & Returns have long term impact of compounding effect, thus simple difference might give you a wrong information.

Related article : What is Time Value of Money?

• ts ghosh says:

Hi,

How can I calculate inflation-adjusted CAGR for a fixed deposit (term 5 years), Help me with a good example like the ones listed in the blog?

thanks

• Sreekanth Reddy says:

Dear Mr ghosh,
You can first calculate the inflation adjusted rate and then use this rate (as R) in CAGR formula for the required period.
You may go through this article @ Why you should not invest in Fixed Deposits & Recurring Deposits for long-term

• ts ghosh says:

Thank you Sreekanth.

• Tudor says:

Hi Srikant, please tell me the monthy returns post tax if I invest 1 lakh in DHFL NCD issue. I opt for monthly payout. Thanks

• Sreekanth Reddy says:

Dear Tudor,
It depends on the interest rate and your tax slab bracket.
Post-tax returns = Pre-Tax retuns * { (100-Tax Rate) / 100 }

• SHRIKANT says:

1. Good inputs wrt calculating returns.
2.How are returns calculated when u are investing a fixed amount annualy- say 25000/ for 7 years n then at the end of 7 yrs u get Rs 2 lac.

• Sreekanth Reddy says:

Dear SHRIKANT,
• Prabhudas says:
• Sreekanth Reddy says: