Capital Budgeting - Yearly Cash Flows (Depreciation).

CFA Level II
#1

Hi,

In terms of calculating yearly cash flows, the formula I have been using is

After Tax Operating Cash Flow: (S-C) (1-T) + (TxD).

However, going through the EOC CFA Questions, I notice that sometimes small twists in the wording of the question changes this. Sometimes the Depreciation is just added straight back without being multiplied with the tax rate first. Why? Could anyone please help explain this? Feel free to really dumb it down, thanks a lot for the help.

First Example:

  • Invests $400 000 of fixed capital. Depreciated straight line over 10 year life.
  • Annual Sales: 240 000, operating cash expenses: 110 000
  • Tax Rate: 30%
  • After Tax Operating Cash Flow: ( $240 000 - $110 000) ( 1 - 0.3) + ( $40 000 * 0.3) =$103 000
  • Correct Answer according to curriculum.

Second Example:

  • Investment in project: 100, depreciated straight line for 2 years with no salvage value.
  • Earnings before Interest and tax: 50 per year.
  • Tax Rate 30%
  • After Tax Operating Cash Flow: 50(1-0.3) + 50 = 85
    • This I do not understand? Why is it not 50(1-0.3) +(50x0.3) = 50, like the original formula and the previous example?

Third Example:

  • Operating Income after taxes: 20 000
  • Depreciation: 40 000
  • Tax Rate: 30%
  • After Tax Operating Cash Flow: 20 000 + 40 000 = 60.000
    • This I do not understand? Why is not 20 000 + (40 000x0.3) = 32.000

So my question is, why is the depreciation sometimes not multipled by the tax rate before it gets added back?

Thanks a lot for the help.

#2

First example you have (Sales - Cost of Sales) x (1-T) … you haven’t accounted for depreciation yet, which will lower your taxable income, and therefore lower your cash taxes, there’s a tax shield benefit so you have to account for it by taking Depreciation x T, or $40K x 30%. In this case the investment is $400k which will depreciate over 10 years (depreciation being $40K).

Second example you have (EBIT) x (1-T) … depreciation has already been fully deducted in EBIT, but because depreciation is a non-cash expense, you add back the full amount $50. In this case the investment is $100 which will depreciation over 2 years

Third example you have earnings after tax … depreciation has been deducted, and taxes have been accounted for, but just like example two, because depreciation is a non-cash expense, you add back the full amount $40K.

Be careful about what information you are given… Sales & Cost of Sales aka Gross Profit, or EBIT.

The “formula” is the same, it’s just manipulated algebraically depending on the information you are given.

#3

The original formula:

Operating Cash Flow = ( Sales - Cost of Sales - Depreciation ) x (1-T) + Depreciation

You add back full Depreciation amount because it’s a non-cash expense

Now manipulate the formula by taking Depreciation out of the brackets

Operating Cash Flow = (Sales - Cost of Sales ) x (1-T) - Depreciation + [Depreciation x T] + Depreciation

The two Depreciation amounts cancel each other out

Operating Cash Flow = (Sales - Cost of Sales ) x (1-T) - Depreciation + [Depreciation x T] + Depreciation

and you are left with:

Operating Cash Flow = (Sales - Cost of Sales ) x (1-T) + Depreciation x T

Same formula… except this one has gross profit in the brackets, and the original has EBIT in brackets

#4

Kblade, Thank you very much for your reply. Much appreciated and very helpful.

Can I use it as a rule, that if they give me:

  • “Sales or Revenue and costs” I will use the full formula and add back ( D x T).
  • EBIT I will add back just Depreciation.
  • Operating Income after tax I will add back just Depreciation
  • Operating Income before tax I will add back just Deprecation?

Is that rule correct?

Also, any other way they could formulate this type of question to look out for? Thanks for great help on this.

#5

bullet point #4: Operating Income before taxes is basically the same as EBIT so yes you add back full depreciation amount.

I wouldn’t advise you to think of it as “rules”. All you have to do is follow the basic structure of an income statement. Understand the structure and it will be easier to understand what calculation to perform

  • Sales - Cost of Sales = Gross Profit - G&A = EBITDA - Depreciation & Amortization = Operating Income before taxes (EBIT) - Interest Expense = Income or Earnings before taxes (EBT) - Tax = Net Income
#6

Please understand that D x T is a shortcut calculation after manipulating the original formula:

Operating Cash Flow = ( Sales - Cost of Sales - Depreciation ) x (1-T) + Depreciation

Plug the numbers from Question #1 into this formula and you will see that you get to the correct answer by adding full amount of depreciation

Operating Cash Flow = ( 240 - 110 - 40 ) x (1 - 0.3) + 40 = 103

Conversely, the manipulated formula ( Sales - Cost of Sales ) x (1-T) + (D x T) gives the same answer

Operating Cash flow = ( 240 - 110) x (1 - 0.3) + ( 40 x 0.3 ) = 103

#7

Thanks a lot Kblade - much appreciated. That is very helpful!