Capital Costs: Capitalization, Depreciation a nd

Taxation

February 23. 2004

(Rev. Feb. 25, 2004)

From an accounting perspective, there are two categories of costs:

• ‘ Expensed’ costs

– I tems that are used up quickly; costs recovered out of current revenues

• ‘ Capitalized’ costs

– L ong lifetime items; costs recovered progressively throughout the e xpected lifetime

Depreciatio n Example : Pizz a Deliver y Business

Definitions

Operating R evenues: revenues that a company receives as a r esult o f its operation (sales for instance.) Operating Expenses: labor expenses, supp ly purchases, utility costs etc.

Operating Income: Operating Revenues - Operating Expenses.

Net Cash F low: Total Cash Inflow - Total Cash Outflow = Operating Income – Capital expenditures Net I ncome: Operating Income – Depreciation Allowance

Income Statements

I: Expensing the car purchase

	Yea r 1	Yea r 2	Yea r 3	Yea r 4
Operating Revenues	20,000	20,000	20,000	20,000
Operating Expenses	10,000	10,000	10,000	10,000
Car Purchase	6 ,000	- -	- -	- -
Operating Income (=operating revenues – operating expenses)	4,000	10,000	10,000	10,000

Net Cash Flow 4,000 10,000 10,000 10,000

II: Capitalizing the car purchase & straight-line depreciation

	Yea r 1	Yea r 2	Yea r 3	Yea r 4
Operating Revenues	20,000	20,000	20,000	20,000
Operating Expenses	10,000	10,000	10,000	10,000
Operating Income	10,000	10,000	10,000	10,000
Depreciation allowance	1500	1500	1500	1500
Net income (before taxes) = Operating	8,500	8,500	8,500	8,500
income – depreciation
allowance
Net cash flow	4000	10,000	10,000	10,000

Income statements (III): Expensing the car purchase; taxe s included

	Yea r 1	Yea r 2	Yea r 3	Yea r 4
Op. Revenues (OR)	20000	20,000	20,000	20,000
Op. Expenses (OE)	10000	10,000	10,000	10,000
Car Purchase	6000
Op. I ncome (OI)	4000	10000	10000	10000
Taxable Income (TI)	4000	10000	10000	10000
(= OR-OE-‘other
deductible items’)
Taxes (T= TI*  )	1200	3000	3000	3000
(  = 30%)
Net I ncome After Taxes	2800	7000	7000	7000
(=TI – T)
Net Cash Flow	2800	7000	7000	7000
(= Total cash in –
total cash out)

Income Statements (IV): Capitalizing and depreciating the car purchase; taxe s included

(Straight-line depreciation assumed)

	Yea r 1	Yea r 2	Yea r 3	Yea r 4
Op. Revenues (OR)	20000	20,000	20,000	20,000
Op. Expenses (OE)	10000	10,000	10,000	10,000
Op. I ncome (OI)	10000	10000	10000	10000
Depreciation	1500	1500	1500	1500
Allowance (D)
Taxable Income	8500	8500	8500	8500
(TI = OR-OE-D)
Taxes (T= TI*  )	2550	2550	2550	2550
(  = 30%)
Net I ncome After Taxes	5950	5950	5950	5950
(ATNI =TI – T )
Net Cash Flow	1450	7450	7450	7450
(NCF = Total cash in
– total cash out)

Expensing the car cost D epreciating the car cost

Yea r 1 Yea r 2 Yea r 3 Yea r 4

Op. Revenues (OR) 20000 20,000 20,000 20,000

Op. Expenses (OE) 10000 10,000 10,000 10,000

Car Purchase 6000

Yea r 1 Yea r 2 Yea r 3 Yea r 4

Op. Revenues (OR) 20000 20,000 2 0,000 20,000

Op. Expenses (OE) 10000 10,000 1 0,000 10,000

Op. I ncome (OI) 10000 10000 10000 10000

Op. I ncome (OI) 4000 10000 10000 10000

Depreciation Allowance (D)

1500 1500 1500 1500

Taxable Income (TI) (= OR-OE-‘other deductible items’)

Taxes (T= TI*  ) (  = 30%)

4000 10000 10000 10000

1200 3000 3000 3000

Taxable Income (TI = OR-OE-D)

Taxes (T= TI*  ) (  = 30%)

8500 8500 8500 8500

2550 2550 2550 2550

Net I ncome After

Taxes (=TI – T)

2800 7000 7000 7000

Net I ncome After

Taxes

(ATNI =TI – T )

5950 5950 5950 5950

Net Cash Flow

(= Total cash in –

2800 7000 7000 7000

Net Cash Flow

(NCF = Total cash in

1450 7450 7450 7450

tota l cas h out ) – total cash out)

Total taxes = $10200 Total taxes = $10200

Expensing the car cost D epreciating the car cost

Yea r 1 Yea r 2 Yea r 3 Yea r 4

Op. Revenues (OR) 20000 20,000 20,000 20,000

Op. Expenses (OE) 10000 10,000 10,000 10,000

Car Purchase 6000

Yea r 1 Yea r 2 Yea r 3 Yea r 4

Op. Revenues (OR) 20000 20,000 2 0,000 20,000

Op. Expenses (OE) 10000 10,000 1 0,000 10,000

Op. I ncome (OI) 10000 10000 10000 10000

Op. I ncome (OI) 4000 10000 10000 10000

Depreciation Allowance (D)

1500 1500 1500 1500

Taxable Income (TI) (= OR-OE-‘other deductible items’)

Taxes (T= TI*  ) (  = 30%)

4000 10000 10000 10000

1200 3000 3000 3000

Taxable Income (TI = OR-OE-D)

Taxes (T= TI*  ) (  = 30%)

8500 8500 8500 8500

2550 2550 2550 2550

Net I ncome After

Taxes (=TI – T)

2800 7000 7000 7000

Net I ncome After

Taxes

(ATNI =TI – T )

5950 5950 5950 5950

Net Cash Flow

(= Total cash in –

2800 7000 7000 7000

Net Cash Flow

(NCF = Total cash in

1450 7450 7450 7450

tota l cas h out ) – total cash out)

Conclusion : On an after-tax NPV basis, the business would prefer to expense the car cost. But this is not permitted by the IRS!

Example : Capitalizin g an d depreciatin g th e car ; debt financing

Incom e Statement : Capitalizatio n an d (straigh t line ) depreciatio n o f the ca r + deb t financing

	T=0	En d o f Yea r 1	En d o f Ye a r 2	En d o f Yea r 3	En d o f Yea r 4
Operating Revenue (OR)		20000	20000	20000	20000
Operating Costs (OC)		10000	10000	10000	10000
Operating Income (OI = OR-OC)		10000	10000	10000	10000
Depreciation allowance (D)		1500	1500	1500	1500
Interest payment (IP)		400	300	200	100
Taxable income (TI = OI – D – IP)		8100	8200	8300	8400
Taxes (@ 30% of TI)		2430	2460	2490	2520
After-tax net income		5670	5700	5730	5760
Principal repayment (PR)		1000	1000	1000	1000
Net cash flow (NCF = OR – OC – I P – PR)	-2000	6170	6240	6310	6380

Sales & other oper ating rev enue			$303,000
Less s ales return & a l low ances			(3,000)
Cost of goods sold			300,000
La bor	120,000
Materials	60,000
Ov erhea d	8,000
D epreciation	20,000
T ota l			(208,000)
Gross p rofit			92,000
Oper ating e xpenses
Selling	15,720
Gener al administr ation	29,000
Lea se pa yments	14,000
T ota l	58,720		(58,720)
Net o per ating p rofit			33,280
Nonoper ating r ev enues			0
Nonoper ating e xpenses
Interest p a yments			(5,200)
Net i ncome before tax es			28,080
Income tax es (30%)			(8,424)
Net i ncome			$19,656
Sta tement of retained earnings
Cash d ividends
Preferred stock (per share, $6)			600
Common stock (per share, $.95)			9,45 6
T ota l d ividends			$10,056
Retained ea rnings Beginning of y ear (1/1/20xx)			32,800
Current y ear			9,600
End of y ear			$42,400

2/25/04

12

Nuclear Energy Eco no mics and

Policy Analysis

Derivation of composite income tax rate: Non -deductibility of federal taxes from state taxes

Let:

 = c omposite t ax rate

 F = federal tax rate

 s = state tax rate

T F = federal taxes due T s = state ta xes due R = revenues received

X = operating and maintenance e xpenses B = bond interest due

D = depreciation allowance

hen:

Thus,

T F =  F (R – X – D – B – T s )

T s =  s ( R – X – D – B ) \

T F =  F (1-  s )(R – X – D – B )

A nd total t axes, T = T F + T S = (R – X – D – B)[  F (1-  s ) +  s ] A nd if we define the t ot al tax rate,  , a s

T =  ( R – X – D – B )

W e have t hat

Recap

• Two reasons for depreciation

– F inancial reporting

– T ax calculations

• D epreciation allowance is a non-cash expense -- fictitious -- but if companies don’t make adequate provision for depreciation, their income s tatements won’t r eflect actual loss o f value of capital assets over tim e.

• D ifference between net income(NI) and net cash flow (NCF)

– N CF: Actual flows of money associated with investment

– NI: ‘ T heoretical’ financial result of the investm e nt

• D eductible items for purposes of computing taxable income include, in addition to operating expenses and depreciation, interest payments on debt, but not principal repayments or dividends on stock

Let:

Depreciatio n Methods

I 0 = i nitial investment c ost I N = net salvage value

N = depreciation lifetime (specified by tax authorities)

D n = depreciation allowance in year n

BV n = book value (or accounting value) at end of year n

= initial value - accumulated depreciation charges

= I 0 -  D i

market value(in general)

A. Straight-lin e d epreciatio n m ethod D n = (I 0 - I N )/N

Depreciatio n Method s ( contd .)

B. Sum-of-the-years ’ -digit s (S YD ) method

N

Sum of digits 1, 2, . . . .N = 

n  N(N  1)

2

Then,

D 1  N(N  1)/2  I 0  I N 

n  1

D  N  1  ˘

2 N(N  1)/2  I 0  I N  

and,in general,

D  N  n  1  I

 I 

n N(N  1)/2 o N

Depreciatio n Methods (cont.)

C. Declinin g B alanc e Method

Depreciation charge = f ixed fraction of BV at end of previous year i.e., i n y ear n,

D n =  BV n-1

Usually,  = 1 .5/N or 2.0/N

If  = 2 /N, t he method is referred to as the ‘double-declining balance’ (DDB) method.

Note t hat the f ormula doesn’t include a t erm for t he salvage value i.e.,

D n =  (1-  ) n-1 I o

yields an ‘ implied’ salvage value after N years, which i n general will differ from I N .

D. Modifie d Accelerate d Cos t R ecover y S ystem (MACRS)

– I ntroduced by Tax Reform Act of 1986 (last major overhaul of tax code)

– S ee handout

Taxe s complicat e th e economi c analysi s o f projects

• I n th e absenc e o f taxes , it is straightforward to set up a cash flow diagram for a project and solve the present worth balance equation

– W e can solve the balance equation to calculate (a) the N P V, or

(b) the rate of return, or (c) an unknow n cash flow given the required rate of return and all other cash flow s.

– N ote: In this simple case, depreciation -- a non-cas h expense

-- isn’t included in the cash f low diagram.

• W ith taxes, there are several complications:

– The taxes in each year depend on all other cash flow s in that year.

– F or projects with capitalized costs, w e must s pecify the depreciation allowance in each year in order to calculate the taxes.

– T he taxes also depend on the financing structure -- i.e., debt and equity capital is treated different from a tax point of view.

Wh y bothe r wit h taxe s a t all ?

Comparison of two alternatives, identical except for net salvage value *

ALTERNATIVE A A LTERNATIVE B

Investment cost	$120,000	Same as A
Net salvage value	$60,000	Zero
Project life	30 years	S ame as A
Financing	100% by equity	Same as A
Income tax rate	50%	Same as A
Before-tax operating income	$22,000/yr	Same as A
Depreciation method	Straight-line	Same as A
Required rate of return	10%/yr	Same as A
* From: G.W. Smith, Engineering Economy

Comparison of alternatives A and B, with taxes

Alternativ e A Alternativ e B

22

120

T A  [22000  ( 120000  60000) / 30]  0 . 5

 10000

NP V A   120000  [22000  10000]( P / A ,10 % , 30)

 60000( P / F ,10%, 30 )

  $ 3438

120

T B  [22000  120000 / 30]  0. 5

 9000

NP V B   120000  [ 22000  9000 ]( P / A ,10 % ,30)

  $ 2551

Summary

1 . Depreciation is an accounting procedure, not a cash expense.

2 . Depreciation is supposed to re flect in the income statement the loss of value of capital assets with time.

3 . Depreciation schedules only r eally m atter for tax calculations. Possible depreciation schedules for a given class of investment are determined by law.

4 . In a given year, higher depreciation allowances mean lower taxes. Since companies prefer to pos tpone taxes, they prefer depreciation schedules with high depreciation allowances during the early years of the project.

5 . Companies are r equired by law to capitalize their capital investments. They can (and do) expense any other expenditure.

6. Net cash f lows describe the actual flows of money associated with the investment during a given period, whereas net incomes describe the "theoretical" financial result of the investment during this period, by taking depreciation into account.