IRR Formula

http://mksnotes.blogspot.com 3 comments
Calculation of IRR (Internal Rate of Return) is bit tedious so i have tried to break the steps in simpler and easy to understandable form. For understanding IRR in detail, please refer to my separate post on this.

There could be two scenarios, either future cash flows are equal or it would be different. Please check the steps below for both the case.
Scenario 1: When future cash flows are equal
Steps
1. Rough estimation: To start with, calculate the payback period and search for value nearest to payback period in PVAF table (present value annuity factor). Take out two rates nearer to payback period.
2. Precise estimation: Find out the NPV (Net Present Value) of the project by considering both the rates which we got through rough estimation.
3. Interpolation: Find out the exact IRR by interpolating between two rates. Formula for interpolation is mentioned below.
IRR = L + {A/ (A-B)} X (H-L)
Where,
L = Lower Discount Rate
H = Higher Discount Rate
A = NPV at Lower Discount Rate
B = NPV at Higher Discount Rate

Example
Cash outflow         = $ 1, 00,000
Annual Inflows = $ 25,000 at the end of every year
No. of years           = 6
Salvage Value = 0

Step 1: Rough Estimation
a. Calculate payback period: Payback period for this project would be (Cash Outflow / Life of project) i.e. $1, 00,000 / $ 25,000 = 4 years
b. Look for value nearest to payback period i.e. 4 in the row of 6th year of the PVAF (present value annuity factor) table. You would find 4.11 @ 12% & 3.99 @ 13%. This gives us a rough idea that IRR would be lying between these two rates only. 
Step 2: Precise Estimation
Calculate NPVs at both the rates i.e. 12% & 13%
NPV @ 13% = {($ 25,000 X PVAF (13%, 6yr)) - $ 1, 00,000}
= {($25,000 X 3.998) - $ 1, 00,000}
= $ (50)
 NPV @ 12% = {($ 25,000 X PVAF (12%, 6yr)) - $ 1, 00,000}
= {($25,000 X 4.11) - $ 1, 00,000}
= $ 2,775
Step 3: Interpolation
IRR = L + {A/ (A-B)} X (H-L)
Where,
L = Lower Discount Rate i.e. 12%
H = Higher Discount Rate i.e. 13%
A = NPV at Lower Discount Rate i.e. $ 2,775
B = NPV at Higher Discount Rate i.e. $ (50)
Hence,
IRR = 12% + {$2,775 / ($2,775 – (-50)} X (13-12) = 12.98%

Scenario 2: When future cash flows are not equal
Steps
1. Calculate weighted average: Assign weights to Cash inflows & find out the weighted average of cash inflows. Maximum weight to be awarded to inflow which came earliest. If inflows are coming in 5 years then weights for 1st year would be 5, 2nd year would be 4, 3rd year would be 3 & so on. Multiply the weights with cash inflow & divide by sum of weights to arrive at weighted average.
Example, 
So, weighted average would be   $ 1,698,000 / 28 = $ 60,642.86
Rest calculation remains same as discussed in Scenario 1
2. Calculate Payback period by dividing the total outflow by weighted average.
3. Rough estimation: search for value nearest to payback period in PVAF table (present value annuity factor). Take out two rates nearer to payback period.
4. Precise estimation: Calculate the NPV for both the rates.
5. Interpolation: Find out the exact IRR by interpolation method (see formula of interpolation above).

In case of any suggestions, do post on the comment section so that we can discuss and make these steps more easier.

3 comments :

  1. SUDERSHAN TIWARI18 October 2019 at 22:08

    Excellent.... On one hand it is complete covering all the scenarios.On the other , it is lucid and clear.
    This is an example of good knowledge and penetrative explanation.

    ReplyDelete
  2. eFinancial Models15 April 2020 at 09:23

    Very useful and informative post. Thanks for sharing with us.
    Break Even Analysis Excel
    Discounted Payback Period Formula

    ReplyDelete
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