6.3 Mathematics of the Indirect Method

The way Cash Flow from Operations is calculated does not affect its amount. That may or may not be obvious to you, so just in case, here is a proof:

The total cash flow is equal to the change in cash.

Total Cash Flow = CashEND - CashBEG.

We have seen that the Cash Flow Statement breaks this change in cash down into three categories:

  1. Changes due to operating activities (CFO)
  2. Changes due to investing activities (CFI)
  3. Changes due to financing activities (CFF)

Total Cash Flow = CashEND - CashBEG = CFO + CFI + CFF.

Rearranging, we get:

CFO = CashEND - CashBEG - CFI - CFF

CFO = Total Cash Flow - CFI - CFF

If we know the Total Cash Flow (we know this from our work preparing the balance sheet), Cash Flow from Investing (we know that from our work in the previous module) and Cash Flow from Financing (again, we know this from our work in the previous module), then we know Cash Flow from Operations.

So the indirect method for showing Cash Flow from Operations will show the same amount for Cash Flows from Operations as the direct method, but it does so in a roundabout way. The indirect method starts with Net Income and shows all the adjustments required to go from there to Cash Flow from Operations.

At a high level, there can be two basic sources of these adjustments:

  1. Amounts in net income that are not operating cash flows.
  2. Operating cash flows that are not in net income.

The indirect method involves identifying these items and laying them out in detail.

We also know that the change in cash is related to the changes in all the other balance sheet accounts. To see this, first write the balance sheet identity in a way that emphasizes cash:

Cash + Non Cash Assets = Liabilities + Equities

Cash = Non Cash Assets - Liabilities – Equities

Write the beginning and ending balance sheets this way and subtract them to get the change in cash (NCA stands for Non Cash Assets, L denotes Liabilities and E denotes Equities):

ΔCash = ΔL + ΔE - ΔNCA

ΔCash = ΔCashO + ΔCashI + ΔCashF

Where we have partitioned the changes in Cash, NCA, L and E by whether they were due to operating activities, investing activities or financing activities:

ΔCashO = change in cash due to operating activities

ΔCashI = change in cash due to investing activities

ΔCashF = change in cash due to financing activities

ΔLO + ΔEO -ΔNCAO = changes due to operating activities

ΔLI + ΔEI - ΔNCAI = changes due to investing activities

ΔLF + ΔEF - ΔNCAF = changes due to financing activities.

Defining operating activities as any activity that is not investing or financing guarantees that all activities of the entity fall into one of the three categories: investing, financing and operating.

Now let’s focus on Cash Flow from Operations and define it as:

That is, the Cash Flow from Operations equals the change in Non Cash Assets from operations minus the change in Liabilities from operations minus the change in Equities from operations.

Now focus on the change in equity: ΔEO. Changes in equity in general come from one of two places, contributed capital accounts (Common Stock and Additional Paid-in Capital) or Retained Earnings. Let CS&APIC denote Common Stock and Additional Paid-in Capital and RE denote Retained Earnings. We have:

Now note that ΔREO = Net Income. That is, the Retained Earnings account works like this:

Declaring dividends is a financing activity, so only the earning of Net Income is a change in Retained Earnings due to operations.

Combining our results, we have:

CFO = NI + ΔLO + ΔCS&APICO - ΔNCAO

In words, Cash Flow from Operations equals Net Income plus the change in Liabilities due to operations plus the change in Common Stock and Additional Paid-in Capital due to operations minus the change in Non Cash Assets due to operations.

The good news is that we know a couple of these things already. We know Cash Flow from Operations and we know Net Income. What we don’t know are the changes in Liabilities, Common Stock, Additional Paid-in Capital, and Non Cash Assets due to operations.

Figuring out all those things will require that we take a systematic approach and have a worksheet to help us structure and organize the task.