13 June 2010

Tutorial: Basic Internal Rate of Return, IRR, Calculation and Explanation

First of all, let's assume

P = present
F = Future
A = Annual
W = Worth
N = number of year


Basically, two equations are involved in this tutorial
1. PW = FW (P|F, IRR , N)
2. (P|F,IRR, N) = 1/(1 + IRR)^N

(1 + IRR)^N means (1 + IRR) to power N.

 Example 1:

1. Let present worth, PW in a six years cash flow is:
present worth, PW = -(capital) + (annual return)(P|A,IRR,6) + (book value)(P|F,IRR,6).

2. Let's say in trial and error approach with different value of IRR, you found that,
PW1 = positive value when IRR = 20%
PW2 = negative value when IRR = 25%

therefore, obviously, IRR is between 20% to 25%

3. Now, one can using a linear interpolation to find approximation of IRR since the IRR is between 20% to 25%.


Example 2:

What is the IRR for the case of PW is $180,000.00, period is 30years, and the return is $455996 after the end of period?

First method : Manually calculation

1.  present worth, PW =  (FW)(P|F,IRR,N).

PW = $180,000.00
N = 30
FW =  $455,996.00

2. (P|F,IRR,N) = PW / FW = 0.3947

3. (P|F,IRR,30) = 1/(1 + IRR)^30 = 0.3947

4. (1 + IRR)^30 = 2.5336

5. IRR = 0.03147 or 3.147%

Second Method: Trial and Error + reference table

1. (P|F,IRR,30) = PW / FW = 0.3947

2. From reference table, we can found that,

(P|F,3%,30) = 0.4120
(P|F,4%,30) = 0.3083

Therefore, IRR is between 3% and 4%.

3. Using linear interpolation,

we have (3% - 4%) / (0.4120 - 0.3083) = (IRR - 4%) / (0.3947 - 0.3083)

As a result, the IRR from second method approach is 3.1668%

Note: The first method is limited to simple calculation like example 2. The second method is more popular since it is workable almost every question.

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Written by: Xaivier Chia


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4 comments:

Mozart said...

ya i know IRR is return rate...but i cant understand is at First method...PW / FW = u get this answer>> 0.3947...but how come>>
3. (P|F,IRR,30) = 1/(1 + IRR)^30 = 0.3947 ?? due at IRR there u no put any % rate so how u count it??
4. (1 + IRR)^30 = 2.5336 this 1 also i can understand how u get 2.5336...due at IRR there also no put out % rate so how to count it...
sry maybe i got misunderstanding some parts..i will try to read..if really cant understand will wait u post up the solution...
i check back my excel that was find out 0.03147 the answer same like u...but show out is 3%...maybe excel not show the decimal point...
thank you very much for ur answer...

Xaivier Chia said...

1.
PW = $180,000.00
N = 30
FW = $455,996.00

PW/FW = $180,000.00/$455,996.00 = 0.3947

2.(P|F,IRR,30) = PW/FW = 0.3947 ---(1)//First equation

3.(P|F,IRR,30)= 1/(1 + IRR)^30 ---(2)//second equation

From 2 and 3, (P|F,IRR,30) = PW/FW = 0.3947 = 1/(1 + IRR)^30

or 0.3947 = 1/(1 + IRR)^30

Next, IRR is in term of percentage, so, not need to mention. In other words, if you get IRR = 0.02, it means 2%.

Again, from above, 0.3947 = 1/(1 + IRR)^30

(1 + IRR)^30 = 1/0.3947 = 2.5336

Yes, you can adjust your Excel to display 4 decimal for accuracy purpose.

Mozart said...

ok...wat i understand is 0.3947 = PW180000/FW455996...

so in this fomular>>1/(1 + IRR)^30 = we count like this>>PW/FW fight?

and after that going 2nd step on fomular is (1 + IRR)^30 = 1/0.3947>>this is a fixed rule right?

so that mean in here>> 4. (1 + IRR)^30 = 2.5336
we count like this>>1/0.3947(no need look at ^30)right??

n finally is how we get this>> 5. IRR = 0.03147 or 3.147%??
2.5336 got any use at here? the mean is use 2.5336 count out 0.03147?? so how is it...i hv blur in here...

this>>(3% - 4%) / (0.4120 - 0.3083) = (IRR - 4%) / (0.3947 - 0.3083) need to Using linear interpolation to find out?? i try to learn linear interpolation at wikipedia if hv no understand i ask u ok??

and u havent post it how to count about this >>(if at first year put in 180000 until end of the year return 455996 the IRR 3% is difference with annual payment with 6000per yrs until end of the year return 455996 IRR 5%...)

thank you so much...

Xaivier Chia said...

Actually there are a lot of methods. But I'm used to using this method.

From equation (1 + IRR)^30 = 2.5336

You should get IRR after using some mathematics calculation. Hmm... For example, you can use log to solve this mathematics equation to get IRR.

The new topic is posted. Click here

If you still cannot get "linear interpolation", I will try to prepare a post about it when you require next time.

You are welcome.

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