Imagine you had just finalised the budget for a project and that it started in Period 3 and ended in Period 8, as pictured below.
Suddenly, your boss told you the amounts needed to be reallocated on a “similar basis” but for periods 4 to 15. That’s fairly straightforward, as this duration is double the original project length, so you would just attribute half of each period’s amount to the new periods, as shown below.
But what about a general solution? How would you cope with project advancements or delays and changes in duration at the same time? It sounds pretty horrible, but truth be told, finance staff face these types of challenges day in, day out.
Assuming no inflationary factors to consider (eg, time value of money), the problem boils down to prorating the original numbers across the new number of periods. The revised start and end dates tell you when the calculations begin, but in essence it is the number of periods in the revised forecast that drives the calculations.
You can follow our explanation in this Excel file.
Now, where would a financial model be without some good old-fashioned algebra? Let’s assume our original forecast has x periods going from start period t1 to end period tx, and the revised forecast has y periods going from revised start period r1 to revised end period ry. Please note that in the illustration below, tx-1 and ry-1 simply represent the periods prior to their respective end periods. Also, in this illustration, r1 occurs after t1, but this does not have to be true necessarily.
Regardless of start and finish dates (which simply govern when the calculations are made), basically three scenarios can occur:
- x > y, ie, the revised forecast duration is shorter than the original one.
- x < y, ie, the revised forecast duration is longer than the original one.
- x = y, ie, the durations of both forecast periods are equal (this effectively simply moves the forecast period).
Let’s focus on the first scenario for a moment as it brings into focus how we could go about calculating the revised forecast. If the original duration were longer, then the revised forecast would consider the effects of more than one original period in each period, as suggested in the graphic below.
In this graphic, the red boxes with yellow shading represent original periods, and the blue boxes with borders denote a revised period. If x > y, then the blue box must straddle at least two red boxes. It could be more though, which is what is depicted here, where we have:
- A start period, where this is the proportion of the earliest original period considered.
- middle (or full) period(s), which (when x > y) are original periods that must be fully included. There could be more than one. Further, if x < y, then the middle (full) period is not defined.
- An end period, which is the proportion of the final original period considered.
Sound confusing? Let’s explain with an example laid out in the screenshot below:
In the original forecasts, the cash flows of $1 to $8 (big spenders here!) were allocated across the first eight periods for a total of $36. However, the revised forecast wanted the same profile over just periods 4 to 6 (three periods). That is, the start date t1 is period 1, x is 8, and the final period tx (t8) is period 8.
The start and end dates (r1 and r3, periods 4 and 6, respectively) for the revised forecast just denote when the forecast starts and stops. The key information is that there are only three (y) periods. This means that each period in the revised forecast includes 8/3 (known as the Period Factor in the attached Excel file), which equals two and two-thirds (2.67) periods of the old forecast data, as follows.
- Revised Period 4 = Old Period 1 + Old Period 2 + 2/3 of Old Period 3 = 1 + 2 + (2x3)/3 = 5
- Revised Period 5 = 1/3 of Old Period 3 + Old Period 4 + Old Period 5 + 1/3 of Old Period 6 = (1x3)/3 + 4 + 5 + (1x6)/3 = 12
- Revised Period 6 = 2/3 of Old Period 6 + Old Period 7 + Old Period 8 = (2x6)/3 + 7 + 8 = 19.
The aforementioned Excel file identifies which original periods are used in each revised period,
what the start, middle (full), and end periods are,
and what proportions to use of each.
These then cross-multiply the original forecast numbers for the appropriate periods using the SUMIF and SUMIFS functions to get the values explained above.
When the revised forecast period is longer than the original one (ie, x<y), the problem is slightly simpler, as there are no middle (full) periods (ie, no period of original data is ever in just one revised period). Otherwise, the logic remains the same.
For those who are interested or are insomniacs, the detail is discussed below …
The devil is in the detail
Let’s use the aforementioned Excel file to talk through the formulas we used. For this example, we’ll go with a scenario where x < y (the original period is shorter than the revised period).
The first section captures the original forecast (inputs) in cells J13:Q13 and automatically computes the start and end period using the array formulas for MIN(IF) and MAX(IF) (cells G16 and G17, respectively). LU_Original_Forecast_Data represents the inputs in row 13, and LU_Periods denote the counters in row 12; the prefix “LU” means nothing more than “Look Up” to highlight that these range names are created to ease referencing. These formulas must be entered using Ctrl+Shift+Enter, as IF will not work across a range (an array) of cells otherwise.
The next section is the Revised Forecast assumptions.
This collects the required start and end periods in cells G27 and G28, together with an error check in cell H28 to ensure that the end period is not before the start period.
The first part of the next section simply collates all of the data to be used:
The key calculation here is the Period Factor (cell H55), which divides the original forecast duration by the revised forecast duration. This represents the number of original periods in each revised period, and this is pivotal to all of the calculations.
The next part of this section works out how the original periods are reallocated to the revised periods.
The Revised Flag (row 63) uses the formula
to check that the period counters in row 62 are greater than or equal to the revised start period (H50) and less than or equal to the revised end period (H51). The value is 1 if these assumptions are true and zero (0) otherwise.
The formula for the Start (row 64)
is a simple formula that takes the previous period’s closing balance (as long as the flag is active) but also accounts for the fact that the original forecast may not have occurred in Period 1 (ie, it sets the first period t1 of the original forecast period).
The final formula for the End (row 65)
simply adds the Period Factor to the Start period as long as the flag is active. This gives us ultimately the beginning and the end of the blue section in our graphic from before (pictured again below):
The next section starts working out which original periods need to be considered for the start, middle (full), and end:
The Start Part Period uses the formula
Essentially, if Start (row 64) is an integer, it uses that period number; otherwise, it uses the next period. (ROUNDUP(z,0) rounds z up to zero decimal places, ie, the next whole number.)
Rows 68 and 69 establish the beginning and the end of the middle (full) period — sort of. Row 69, the calculation for the Start Part Period
adds one to the Start Part Period (row 67) (as long this is not zero) to avoid any double count. Row 69’s formula for the End Full Period
takes the “beginning of the end”, that is, up to but not including the End period. Therefore, the way these two dates are calculated it is possible that the Start Full Period could be a period prior to the End Full Period. That is actually pictured in our example (above) and is acceptable — it simply means there is no middle (full) period in that instance.
The final formula here (row 70) for End Part Period
uses the same logic as per the Start Part Period. This means we now have the relevant original periods identified!
Next, we need to know what percentages should be used for Start and End Part Periods.
The Full Part % is also calculated, as it ensures the End Part % is not overstated.
The formula in row 72 for the Start Part %
looks horrible, but isn’t as bad as it seems (honest)! J67-J64 calculates the proportion Start Part Period less Start (ie, this formula computes the proportion of the first red box that is blue).
ROUND is used to prevent rounding errors, and MOD is incorporated to ensure this proportion is less than 100% (I’ve discussed MOD in a previous article).
The second formula is not pleasant either. The Full Part % (row 73) is given by
Erm, lovely … Again, once you get your head wrapped around it, it’s not so bad. The two IF conditions required (inside the AND expression) check that the periods are not zero and that the end is not before the beginning (as discussed above). If this test is passed, it takes the MIN(Period_Factor,1) (you cannot count more than the forecast amount in an original period) and multiplies this by the number of full original periods in the revised period. This is then restricted so that the sum of the Start Part % and the Full Part % cannot exceed the Period_Factor. This number is calculated only to keep the End Part % honest. Talking of which …
The End Part % (row 74)
just mops up the rest of the Period_Factor where the flag is active. This is equal to the section highlighted below:
This concludes the percentages needed. We now have identified which periods are the Start, Middle, and End and what proportions we require for the Start and End. All we have to do is multiply it out:
I say all because we’ve left the best to last …
Again, it’s really not that bad! There are three calculations here: one each for the start, middle, and end. The first one
locates the original period to be used for Start and multiplies it by the appropriate proportion (SUMIF only sums the original range LU_Original_Forecast_Data where the counter in LU_Periods is equal to the value in cell J67, ie, the correct original period to be used).
The last formula
performs a similar operation for the End period. This just leaves
SUMIFS is used here, as we need to sum based on two conditions, not one (that the full periods meet the conditions for the Start and End Full Periods). Here, you can clearly see that if the End Full Period precedes the Start Full Period, no amounts will be summed. The factor MIN(Period_Factor,1) is required when the number of revised periods is greater than the original number of forecast periods (so only the correct proportion) is used and to ensure the amount in a full period is never multiplied by a factor greater than 1 also.
These three added together give us our total.
Word to the wise
Anyway, apologies for this article being a little heavier than usual, but this is a common problem when revising forecasts in Excel. The solution may be a little involved, but I hope you will agree you can always “steal” my template and figure out the formulas at your leisure. This is the curse of modelling sometimes — not every essential calculation is simple!
— Liam Bastick, FCMA, CGMA, FCA, is director of SumProduct, a global consultancy specialising in Excel training. He is also an Excel MVP (as appointed by Microsoft) and author of Introduction to Financial Modelling. Send ideas for future Excel-related articles to him at email@example.com. To comment on this article or to suggest an idea for another article, contact Jeff Drew, an FM magazine senior editor, at Jeff.Drew@aicpa-cima.com.