Iterative solving using VBA ...

[M100C]

All,
This is more of a general programming question, but I am posting to this
group to see if I can get help with the answer.

I have a public function that sums the future values (fv) of investments,
using a given rate of return (r). For example, the syntax is "fv(r)", where
"fv(0.03)" would return the future values at an annual growth rate of 3%.

Now, suppose the value returned is 30,000 but the actual value I was
expecting was 50,000 (val). I need a procedure to: 1) increment r, 2) pass
it to fv, and 3) iterate through 1 and 2 until the fv function returns a
value "close to" val.

What I have so far (see below) works well, but is ugly. Is there a more
elegant way to do this iteration?

Thanks,
Chris

VBA:
'Start by guessing at 3%
s = 0.03

If fv(s) < val Then
Do
'increment by whole percents
s = s + 0.01
Loop Until fv(s) > val

'oops ... too far ... back out a percent
s = s - 0.01

Do
'increment by a tenth percent
s = s + 0.001
Loop Until fv(s) > val

'oops ... too far ... back out a tenth percent
s = s - 0.001

Do
'increment by a hundredth percent
s = s + 0.0001
Loop Until fv(s) > val

'oops ... too far ... back out a hundredth percent
s = s - 0.0001

Else
' Code here if guess is too high
End If

 

[Carim]

Hi Chris,

Why bother when IRR() does the job ?

Cheers
Carim

 

[Niek Otten]

But if you still like to do similar iterations, take the function below,
just as an example.

--
Kind regards,

Niek Otten

' ===================================================================
Option Explicit
Function Backward(ValueToBeFound As Double, MoreArguments As Double, _
Optional ReasonableGuess, Optional MaxNumberIters, _
Optional MaxDiffPerc) As Double
' This example function goalseeks another function,
' called Forward. It works for almost any continuous function,
' although if that function has several maximum and/or minimum
' values, the value of the ReasonableGuess argument becomes
' important.
' It calculates the value for ReasonableGuess and for
' 1.2 * ReasonableGuess.
' It assumes that the function's graph is a straight line and
' extrapolates that line from these two values to find the value
' for the argument required to achieve ValueToBeFound.
' Of course that doesn't come out right, so it does it again for
' this new result and one of the other two results, depending on
' the required direction (greater or smaller).
' This process is repeated until the maximum number of calculations
' has been reached, in which case an errorvalue is returned,
' or until the value found is close enough, in which case
' the value of the most recently used argument is returned

Dim LowVar As Double, HighVar As Double, NowVar As Double
Dim LowResult As Double, HighResult As Double, NowResult As Double
Dim MaxDiff As Double
Dim NotReadyYet As Boolean
Dim IterCount As Long

If IsMissing(ReasonableGuess) Then ReasonableGuess = 1.5 ' use default
Values
If IsMissing(MaxNumberIters) Then MaxNumberIters = 20 ' that make sense in
the
If IsMissing(MaxDiffPerc) Then MaxDiffPerc = 0.001 ' context of the function

MaxDiff = ValueToBeFound * MaxDiffPerc
NotReadyYet = True
IterCount = 1
LowVar = ReasonableGuess
LowResult = Forward(LowVar, MoreArguments)
HighVar = LowVar * 1.2
HighResult = Forward(HighVar, MoreArguments)

While NotReadyYet
IterCount = IterCount + 1
If IterCount > MaxNumberIters Then
Backward = CVErr(xlErrValue) 'or some other
errorvalue
Exit Function
End If

NowVar = ((ValueToBeFound - LowResult) * (HighVar - LowVar) + LowVar _
* (HighResult - LowResult)) / (HighResult - LowResult)
NowResult = Forward(NowVar, MoreArguments)
If NowResult > ValueToBeFound Then
HighVar = NowVar
HighResult = NowResult
Else
LowVar = NowVar
LowResult = NowResult
End If
If Abs(NowResult - ValueToBeFound) < MaxDiff Then NotReadyYet = False
Wend

Backward = NowVar

End Function
Function Forward(a As Double, b As Double) As Double
' This is just an example function;
' almost any continous function will work
Forward = 3 * a ^ (1.5) + b
End Function
' ===================================================================

 

[Rock]

Hi Chris,

Some how, the increament of s should be related to fv(s)-val.
For example:

....
s=s+(fv(s)-val)/val
Loop until ABS(fv(s)-val) < 0.001 'This is tolerance

Note:
1- Pay attention to the sign (+ or -) of the fv(s)-val related to s so
that when fv(s)>val the s will be increased or reduced accordingly.
2- The above expression will help to speed up the convergence
3- The tolerance will be defined up to you

Regards

All,
This is more of a general programming question, but I am posting to
this
group to see if I can get help with the answer.

I have a public function that sums the future values (fv) of
investments,
using a given rate of return (r). For example, the syntax is "fv(r)",
where
"fv(0.03)" would return the future values at an annual growth rate of
3%.

Now, suppose the value returned is 30,000 but the actual value I was
expecting was 50,000 (val). I need a procedure to: 1) increment r, 2)
pass
it to fv, and 3) iterate through 1 and 2 until the fv function returns
a
value "close to" val.

What I have so far (see below) works well, but is ugly. Is there a
more
elegant way to do this iteration?

Thanks,
Chris

VBA:
'Start by guessing at 3%
s = 0.03

If fv(s) < val Then
Do
'increment by whole percents
s = s + 0.01
Loop Until fv(s) > val

'oops ... too far ... back out a percent
s = s - 0.01

Do
'increment by a tenth percent
s = s + 0.001
Loop Until fv(s) > val

'oops ... too far ... back out a tenth percent
s = s - 0.001

Do
'increment by a hundredth percent
s = s + 0.0001
Loop Until fv(s) > val

'oops ... too far ... back out a hundredth percent
s = s - 0.0001

Else
' Code here if guess is too high
End If