IRR, XIRR : Calculating investment return

Calculating return on investment is an important aspect of any investment review. Whether investment mode is stock, mutual fund, debts, savings account etc. you need tools to calculate the return on investment so that relative effectiveness of different investments can be ascertained. Herein we will discuss two formulas which are very effective in calculating return on investment.

Calculating Annuity return : Back to basics

An annuity is a series of equal payments made in a specific interval over a period of time frame. This formula helps to calculate the future value of an annuity.

Formula:

        A = P * [ {(1+ i) ^ n - 1} / i ] * (1 + i )  -  when payment is made at the start
                                          or
       A = P * [ ((1+ i) ^ n - 1) / i ]       -   when payment is made at the end

      where
              A = final amount
              P = each equal payment
              i  =  interest rate for the interval ( in decimal)
              n =  the number of total payment made over the period.

Usage scenario:

• Return on PPF deposits made over 15 years.
• Return for mutual fund SIP done for a period of time.

Examples:

• What is the final return at the end of 15 years if Rs. 10000 is deposited every year?

          Here  P = 10000, i = .08, n =15

          Thus final amount, A = 10000 * [ {(1+.08)^15-1}/.08] * (1+.08)
                                         = 10000 * 27.15 * 1.08
                                         = 293242.8

• What is the final return for a Rs. 2000 monthly mutual fund SIP at the end of 3 years if annual return of the mutual fund is 15% ?

          Herein,  P = 2000
                       i  =  (15/12) = 1.25 % ~ 0.0125
                       n =  (12*3) = 36

           Thus final amount, A = 2000 * [ {(1 + .0125)^36-1}/0.0125] * (1 + 0.0125)
                                           = 2000 * 45.16 * 1.0125
                                           = 91358.9                   

Compound Annual Growth Rate (CAGR) : Back to basics

CAGR provides the year-over-year growth rate of an investment over a specific time. It provides a rate at which an investment would have grown if it had a steady growth rate. It is a mean annual growth rate.

Formula:
        CAGR = (A/P)^(1/n) -1
    
        where,

                 CAGR = Compound annual growth rate ( in decimal)

                         A = Final amount

                         P = Initial amount

                         n =  number of years

Example: If Rs. 10000 was invested in a mutual fund 3 years back and the current value is Rs. 15000, then CAGR is:
                        = ((15000/10000)^(1/3))-1
                        = 0.1447
                        ~ 14.47 %

A few usage scenario:

• Return generated by mutual funds. Return of mutual funds for more than 1 year is expressed in CAGR.
• Compare return for different investment instruments over a time period.
• Growth of companies

Compound Interest: Back to basics

Main concept of compound interest is that interest paid adds to and becomes part of the principal that accrues interest during the next period. Thus principal keeps increasing continuously with time and interest accrued on it also increases.

Formula:
             A = P * (1+ r/n) ^ (t*n)

             where,
                      P = Principal amount
                      r  = annual rate of interest (in decimal)
                      n = number of times interest is compounded per year
                      t = time in years
                     A = amount at the end of t years

Example:
There are many investment instruments that returns compound interest. One of them is PPF wherein interest rate is 8% compounded yearly. An amount of Rs. 20000 invested in PPF for 15 years which return:                 
                     = 20000(1+.08/1)^(15*1)
                     = 63443