Thank problem deals with present value given annuity. Alright I\'ll try to artic

Question

Thank problem deals with present value given annuity.
Alright I'll try to articulate it briefly.

So, I'm given
IC=400k, annuity 200k over 4 years. Find Incremental Rate of return. Or IRR, I am confused about the diff between Internal and incremental. Maybe someone can take a stave at that one too.
The real q;
IRR(-400k{200k<1,1,1,1>})=3.49%
However when I solve this problem algebraicly I'm left with a bizarre finding;
400=200[((1+rr)^4)-1)/(rr*(1+rr))]
Solve rr= -1.69, and 0.349.

So my q is this; in future problems, can I simply take the 0.349 and move the decimal over one space, or is this just a coincidence?
Also, can someone explain why these numbers exist the way they do; like, Logically/graphically speaking what does that -1.69 stand for? Y?
Does this have something to do with linear interpolation? Or is that what it essential is? Or is this just a shortcut?
Thanks for your time.

Thank problem deals with present value given annuity.
Alright I'll try to articulate it briefly.

So, I'm given
IC=400k, annuity 200k over 4 years. Find Incremental Rate of return. Or IRR, I am confused about the diff between Internal and incremental. Maybe someone can take a stave at that one too.
The real q;
IRR(-400k{200k<1,1,1,1>})=3.49%
However when I solve this problem algebraicly I'm left with a bizarre finding;
400=200[((1+rr)^4)-1)/(rr*(1+rr))]
Solve rr= -1.69, and 0.349.

So my q is this; in future problems, can I simply take the 0.349 and move the decimal over one space, or is this just a coincidence?
Also, can someone explain why these numbers exist the way they do; like, Logically/graphically speaking what does that -1.69 stand for? Y?
Does this have something to do with linear interpolation? Or is that what it essential is? Or is this just a shortcut?
Thanks for your time.

Thank problem deals with present value given annuity.
Alright I'll try to articulate it briefly.

So, I'm given
IC=400k, annuity 200k over 4 years. Find Incremental Rate of return. Or IRR, I am confused about the diff between Internal and incremental. Maybe someone can take a stave at that one too.
The real q;
IRR(-400k{200k<1,1,1,1>})=3.49%
However when I solve this problem algebraicly I'm left with a bizarre finding;
400=200[((1+rr)^4)-1)/(rr*(1+rr))]
Solve rr= -1.69, and 0.349.

So my q is this; in future problems, can I simply take the 0.349 and move the decimal over one space, or is this just a coincidence?
Also, can someone explain why these numbers exist the way they do; like, Logically/graphically speaking what does that -1.69 stand for? Y?
Does this have something to do with linear interpolation? Or is that what it essential is? Or is this just a shortcut?
Thanks for your time.

Thank problem deals with present value given annuity.
Alright I'll try to articulate it briefly.

So, I'm given
IC=400k, annuity 200k over 4 years. Find Incremental Rate of return. Or IRR, I am confused about the diff between Internal and incremental. Maybe someone can take a stave at that one too.
The real q;
IRR(-400k{200k<1,1,1,1>})=3.49%
However when I solve this problem algebraicly I'm left with a bizarre finding;
400=200[((1+rr)^4)-1)/(rr*(1+rr))]
Solve rr= -1.69, and 0.349.

So my q is this; in future problems, can I simply take the 0.349 and move the decimal over one space, or is this just a coincidence?
Also, can someone explain why these numbers exist the way they do; like, Logically/graphically speaking what does that -1.69 stand for? Y?
Does this have something to do with linear interpolation? Or is that what it essential is? Or is this just a shortcut?
Thanks for your time.


Alright I'll try to articulate it briefly.

So, I'm given
IC=400k, annuity 200k over 4 years. Find Incremental Rate of return. Or IRR, I am confused about the diff between Internal and incremental. Maybe someone can take a stave at that one too.
The real q;
IRR(-400k{200k<1,1,1,1>})=3.49%
However when I solve this problem algebraicly I'm left with a bizarre finding;
400=200[((1+rr)^4)-1)/(rr*(1+rr))]
Solve rr= -1.69, and 0.349.

So my q is this; in future problems, can I simply take the 0.349 and move the decimal over one space, or is this just a coincidence?
Also, can someone explain why these numbers exist the way they do; like, Logically/graphically speaking what does that -1.69 stand for? Y?
Does this have something to do with linear interpolation? Or is that what it essential is? Or is this just a shortcut?
Thanks for your time.

Explanation / Answer

Incremental rate of return is used when there are two different projects or investment opportunities having different time period, initial investment and cash inflows. In this situation difference of cash outflows and inflows are identified and then incremental rate of return is calculated just as we calculate internal rate of return.

In case of single investment opportunity, we calculate internal rate of return (IRR) only. It is the rate at which present value of cash inflows will be equal to the present value of cash outflows. Once, IRR is identified then we match it with our own expected return. If IRR is bigger than the minimum expected return then we accept the project otherwise we reject the project.

In the given scenario,

Initial cost= $400

Cash inflows (P) $200 per year for the 4 years

n= 4 years

Above case is the case of present value of annuity that will be used to calculate IRR.

There is an error in the present value of annuity formula. Correct formula is as follows:

Initial cost = P*(1-1/(1+R)^n)/R

400 = 200*(1-1/(1+R)^4)/R

Here, R = IRR

Now, we will get the value of R with the use of trial and error method and interpolation.

At R = 40%

PV of cash inflows = $369. 845

At R = 30%

PV of cash inflows = $433.248

Thus,

IRR = R = 30% + ((PV of cash inflows at 30% - 400)/( PV of cash inflows at 30% - PV of cash inflows at 40%)) * (40%-30%)

R = 30% + ((433.248 - 400)/( 433.248 - 369. 845)) * (40%-30%)

R = .35 or 35 % approx.

Thus, answer is correct though there is error in the mathematical formula mention by you in explanation.

It is a particular case, where we got 35% as the IRR but with the change of data in terms of cash inflows , years, or initial cost , IRR will change.

To solve IRR, interpolation is the very useful technique as it is very easy to implement.

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