IRR (calculation)

[babboo]

I have quite some problems with calculating the IRR:

Project	0	1	2	3	4	5	6
A	-20'000	8'000	7'000	6'000	0	0	0
B	-20'000	3'500	3'500	3'500	3'500	3'500	3'500
C	-	-10'000	2'500	2'500	2'500	2'500	2'500

What I have calculated so far for Project A:

0=-20'000+8'000/(1+IRR)+7'000/((1+IRR)^2)+6'000/((1+IRR)^3) (multiply everything with ((1+IRR)^3)


0=-20'000*((1+IRR)^3)+8'000*((1+IRR)^2)+6'000 (divide through -1'000)


0=20*((1+IRR)^3)+8*((1+IRR)^2)+6 (calculate so no brackets)


0=20*(1+IRR)*(1+IRR)*(1+IRR)+8*(1+IRR)(1+IRR)+6

0=20*(x^3+3x^2+3x+1)*8*(x^2+2x+1)+6

and now, how do I get IRR (=x)???

Would really appreciate if sbdy could help mer

 

[Deleted member 4993]

I have quite some problems with calculating the IRR:

Project	0	1	2	3	4	5	6
A	-20'000	8'000	7'000	6'000	0	0	0
B	-20'000	3'500	3'500	3'500	3'500	3'500	3'500
C	-	-10'000	2'500	2'500	2'500	2'500	2'500

What I have calculated so far for Project A:

0=-20'000+8'000/(1+IRR)+7'000/((1+IRR)^2)+6'000/((1+IRR)^3) (multiply everything with ((1+IRR)^3)


0=-20'000*((1+IRR)^3)+8'000*((1+IRR)^2)+6'000 (divide through -1'000)


0=20*((1+IRR)^3)+8*((1+IRR)^2)+6 (calculate so no brackets)


0=20*(1+IRR)*(1+IRR)*(1+IRR)+8*(1+IRR)(1+IRR)+6

0=20*(x^3+3x^2+3x+1)*8*(x^2+2x+1)+6

and now, how do I get IRR (=x)???

Would really appreciate if sbdy could help mer

You have a quintic (x⁵) equation - there is no closed form solution. You can use numerical methods - e.g. Newton's method - to estimate the solution.

 

[Ishuda]

I have quite some problems with calculating the IRR:

Project	0	1	2	3	4	5	6
A	-20'000	8'000	7'000	6'000	0	0	0
B	-20'000	3'500	3'500	3'500	3'500	3'500	3'500
C	-	-10'000	2'500	2'500	2'500	2'500	2'500

What I have calculated so far for Project A:

0=-20'000+8'000/(1+IRR)+7'000/((1+IRR)^2)+6'000/((1+IRR)^3) (multiply everything with ((1+IRR)^3)


0=-20'000*((1+IRR)^3)+8'000*((1+IRR)^2)+6'000 (divide through -1'000)<--Typo?


0=20*((1+IRR)^3)+8*((1+IRR)^2)+6 (calculate so no brackets)<--error


0=20*(1+IRR)*(1+IRR)*(1+IRR)+8*(1+IRR)(1+IRR)+6

0=20*(x^3+3x^2+3x+1)*8*(x^2+2x+1)+6

and now, how do I get IRR (=x)???

Would really appreciate if sbdy could help mer

Your initial equation is correct but see above and let's correct your typo (dropping the 7 part) and error (you need minus signs for all but the 20) and start from there
0=20*((1+IRR)^3)-8*((1+IRR)^2)-7*(1+IRR)-6
What I would do is let x = 1+IRR but there is certainly nothing wrong with expanding it out and letting x = IRR so I will do that [for the other problems though I would suggest you do the x=1+IRR since it might be easier to solve for x and just subtract 1 to get IRR]
0=20*(x^3+3x^2+3x+1) - 8*(x^2+2x+1)-7(1+x)-6
Collect terms
0=20 x³ + (60-8) x² + (60-16-7) x +(20-8-7-6)
or
0=20 x³ + 52 x² + 37 x - 1
You now have a cubic to solve or possibly you might try some sort of guestimate/correct method like Newton's formula or what ever. Looking at this, I might be try a guestimate/correct method of
x_i+1 = (-20 x_i³ - 52 x_i² + 1) / 37
Note that if xi+1 = xi, then out equation is satisfied. If we start out with x₁=0, we get

0

0.027027

0.02599

0.026068

0.026062

0.026063

0.026063

Edit: Fix typo which changed answer

 

[babboo]

Amazing, thank you very much for your help!
I will look into that cubic equation!

 

[DexterOnline]

I have quite some problems with calculating the IRR:

Project	0	1	2	3	4	5	6
A	-20'000	8'000	7'000	6'000	0	0	0
B	-20'000	3'500	3'500	3'500	3'500	3'500	3'500
C	-	-10'000	2'500	2'500	2'500	2'500	2'500

and now, how do I get IRR (=x)???

Would really appreciate if sbdy could help mer

Cash flows = -20,8,7,6
Actual IRR = 2.61%
Abraham A's IRR formula = 2.64%


Cash flows = -20,3.5,3.5,3.5,3.5,3.5,3.5
Actual IRR = 1.41%
Abraham A's IRR formula = 1.44%


Cash flows = 0,-10,2.5,2.5,2.5,2.5,2.5
Actual IRR = 7.93%
Abraham A's IRR formula = 7.91%

 

[DexterOnline]

You have a quintic (x⁵) equation - there is no closed form solution. You can use numerical methods - e.g. Newton's method - to estimate the solution.

Closed form formula to solve n-degree polynomial to find IRR.

\(\displaystyle i=\left(\frac{B}{C}\right)^{\frac{1}{t}}-1\)

Hallelujah! Praise Coke

Imagine if I doubled the daily dosage of recreational worship, what else may become possible

Recall Dexter's theorem 2.1

Nothing is impossible

 

[mmm4444bot]

Praise Coke

Imagine if I doubled the daily dosage of recreational worship, what else may become possible

I'm imagining a fatal cardiac episode.

Or are you worshipping high-fructose corn syrup?

 

[DexterOnline]

I'm imagining a fatal cardiac episode.

Or are you worshipping high-fructose corn syrup?

It's a bit hard to kill a perpetuity so is my life story.

\(\displaystyle \frac{B}{C}\) in the IRR formula may refer to one of the following:

\(\displaystyle \frac{Before}{Christ}\)

\(\displaystyle \frac{Bible}{Christ}\)

\(\displaystyle \frac{Bible}{Christian}\)

\(\displaystyle \frac{Bible}{Christianity}\)

If Sir Denis were to discover the same IRR formula, he would have used different variable according to his disbelief, for example

\(\displaystyle \frac{F}{C}\)

standing for

\(\displaystyle \frac{Fible}{Cartoon}\)

But then openly portraying Cartoon these days may pose a health hazard.

 

[stapel]

Geezzzz...what a mess DO NOT use format 1'000 again!

If the original poster is from, say, Switzerland, then this format may be what was taught. (reference)

 

[mmm4444bot]

It's a bit hard to kill a perpetuity

...

openly portraying Cartoon these days may pose a health hazard.

I don't see why. Denis' perpetuity differs not from yours or mine. :cool:

 

[DexterOnline]

I don't see why. Denis' perpetuity differs not from yours or mine. :cool:

The last thing I would worry about is turbanators, I had been through a lot worse in the time period 1992-1993, they tried every thing that was written in the death manual. Yet I am here talking to you!

 

[DexterOnline]

This forum was brought to my attention when I landed on a post by someone whom I consider my virutal online friend namley Sir Jonah v2.0

That's his second reincarnation whereas my own history of living through time puts me in between a Rock and Hard place where I tend to forget who I am, where I came from and where I am heading next.

The time I spent in New York between 1986-1993, I recall watching a TV show called "Quantum Leap" may be that's a more accurate description of how I went through my long life in past, at present and in the future.

In any case, I told you Sir Jonah that I have nothing at present to make a living. The only job in the past 24 years was the one with a US company for 6 months between October 2014 and March 2015.

I gave you my best this time with IRR formula, previously I gave you 60 TVM formulas on MHF. I have roughly 9,000 new financial formulas in my head that are explained at the end of this note. Yet if I don't even have money to buy food, cigarettes, and my favorite Coke then there in ROI. The IRR is -100%

How long can I go on like this, not long I suppose.


------------------

Notes from digital diary

------------------


Over the years that I have spent time investigating numerical methods for financial analysis, I have come to a conclusion that the "value" or "price" of an investment of any sort (such as a single sum investment in a savings account or one time lending for fixed term, or an investment into any financial instrument such as certificate of deposit, commercial paper, corporate or treasury bill, note and bond, money market fund or anything for that matter) is determined by the same mathematical equation albeit very complex one that when broken down to its parts explodes into myriads, literally thousands, of individual financial formulas.

Such formula then help an analyst or an investor determine the following attributes or metrics of the investment.

1) Price
2) Modified Duration
3) Macaulay Duration
4) Convexity
5) Dollar Modified Duration
6) Dollar Macaulay Duration

In each such measure of investment, there are number of variables involved such as payment amount "A", interest rate "i" aka Yield, number of periods "N"

Solving for each such variable in combinations of the above and below listed measures amounts to a large number of financial formulas, my current count is around 9,000 formulas.

1) Price or the Value at any time from the settlement date to it's maturity date, it is even possible to go back in past. Therefore, the time horizon for valuation of investment is [-8<t<8]

This then leads to following time values of money:

a) Past value
b) Present value
c) Intermediate value
d) Horizon value
e) Future value

All such 5 valuations apply to almost any type on investment as explained below

I) A lump-sum lending or borrowing for fixed term
II) A periodic payment or receipt for limited period
III) A periodic payment or receipt forever

These payments in II and III are classifies as either

A) Ordinary annuity or ordinary perpetuity
B) Annuity due or perpetuity due

Both types of payments in A and B may further be categorized in terms of their timings

I) On-time payment
II) Deferred payment
III) Early payment

Such payments may be either in

A) constant amounts
B) grow/shrink by a rate
C) increase/decrease by a constant money amount

The payment period and the growth period may either

I) coincide
II) are different from each other

All 3 types of payments may pay or earn

1) compound interest
2) simple interest

For compound interest, the frequency of compounding may be almost of any type

a) annual
b) semi-annual
c) quarterly
d) monthly
e) fortnightly
f) weekly
g) daily
h) hourly
i) infinite aka continuous
j) biennial
k) triennial
l) year-and-halfly
m) anything else you can imagine

The payment period or the length of the period for payment may be almost of any duration

a) year
b) semi-year
c) quarter
d) month
e) fortnight
f) week
g) day
h) hour
i) biennial
j) triennial
k) year-and-half
l) anything else you can imagine

The day count convention for payments earning compound or simple interest may be of any type

I) 30/360
II) 30/365
II) 30/Actual
III) Actual/360
IV) Actual/365
V) Actual/366
VI) Actual/Actual
VII) anything else you can imagine e.g. 30/400


That wraps up the feature of our SINGLE time value of money equation upon which our many financial calculations will be based.

 

[DexterOnline]

Phewwww...glad to see I can still make
a monthly payment...

Know why JC walked on water?

Because he couldn't swim...

So how do you explain the following

1) Walking on quick sand
2) Walking on thin air
3) Surviving a night in a gas chamber
4) Surviving an acid shower
5) Surviving a lethal injection
6) Surviving after consuming Pepsi Crystal
7) And many other episodes...

 

[DexterOnline]

Phewwww...glad to see I can still make
a monthly payment...

Know why JC walked on water?

Because he couldn't swim...

Alright, let us go back to Abraham A's IRR formula and see if you could notice any signs of heavenly intervention in finding the solution for "t" when "i" is set to zero.

\(\displaystyle i=\left(\frac{B}{C}\right)^{\frac{1}{t}} - 1\)

\(\displaystyle 0=\left(\frac{B}{C}\right)^{\frac{1}{t}} - 1\)

\(\displaystyle 1=\left(\frac{B}{C}\right)^{\frac{1}{t}}\)

\(\displaystyle ln(1)=\frac{1}{t} \times ln \left(\frac{B}{C}\right)\)

Given that \(\displaystyle i=0\) when \(\displaystyle B=C\)

\(\displaystyle ln(1)=\frac{1}{t} \times ln(1)\)

\(\displaystyle \frac{1}{ln(1)}= t \times \frac{1}{ln(1)}\)

\(\displaystyle t = \frac{ln(1)}{1} \times \frac{1}{ln(1)}\)

\(\displaystyle t = \frac{0}{1} \times \frac{1}{0}\)

\(\displaystyle t = \frac{0}{0} \)

\(\displaystyle t = ?\)

 

[DexterOnline]

STOP right here: t = anything you want except 0

Always wondered why everybody cries blue murder
when they see n/0 : in my drinking days, if I had
n bottles of beer and divided them with 0 people,
(in other words drank 'em all myself!), was I doing
something illegal?

Alright, then solving for "t" by setting \(\displaystyle i=0\) given \(\displaystyle B=C\) further \(\displaystyle B=0\) suggesting \(\displaystyle C=0\)

\(\displaystyle i=\left(\frac{B}{C}\right)^{\frac{1}{t}} - 1\)

\(\displaystyle 0=\left(\frac{B}{C}\right)^{\frac{1}{t}} - 1\)

\(\displaystyle 1=\left(\frac{B}{C}\right)^{\frac{1}{t}}\)

\(\displaystyle ln(1)=\frac{1}{t} \times ln \left(\frac{B}{C}\right)\)

\(\displaystyle ln(1)=\frac{1}{t} \times [ln(B)-ln(C)] \)

\(\displaystyle ln(1)=\frac{1}{t} \times [ln(0)-ln(0)] \)

\(\displaystyle [ln(0)-ln(0)]\) would only be \(\displaystyle 0\) when you know the value of \(\displaystyle ln(0)\)

They did kill the S.O.B at that time in history, didn't they?

 

[Otis]

if I had n bottles of beer and divided them with 0 people

If zero people present, where were you? In the ether?

 

[Otis]

They did kill the S.O.B at that time in history, didn't they?

Not "really".

His perpetuity continues -- as will yours and mine. :cool: