Massachus etts Ins titu te o f Technology Departm e nt of Nuclear Engineering

22.812 NUCLEAR E N E R GY E C ONOMICS AND POLICY ANAL YSIS

Spring 2004

A n Illustratio n o f th e Us e o f Depreciation

The f o llowing exam ple is intended to illus t r ate h o w deprecia tion is u sed to calcu late incom e taxes. It com p ares the income statem ents and net cash flows of a sim p le f irm in two cases: A) w h en the in itial inve stm ent is ex pensed, and B) when it is capitalized. A few accounting term s first need to be defined. Note that these should not be taken as precise accounting definition s. Also note th at each of th ese item s is defined for a given year (or quarter. )

Operating R e venues: revenues that a com p any rece ives as a result of its operation (sales for instan ce.)

Operating E xpenses: labor exp e ns es, s upply p u rchases, u t ility costs etc. Operating Incom e : Operating R e venues - O perating Expenses.

Taxable Incom e : Incom e from which to calcu late tax es (the re lati onship betw een taxable incom e and operating incom e is described below.)

Taxes Taxable Incom e * Co rporate Income Tax Rate.

Net Incom e : Taxable Incom e - Taxes.

Incom e Statem ent: Description of the com p any' s operation. Net Cash Flow: Total Cash I n f l ow - Total Cash Outf low.

A Pizz a Deliver y Business

We consider a pizza d e livery business about to b e started by a certain Mr. Sm ith. Mr. Sm ith wants to buy pizzas from the local pizzeria, and deliv er them to custom ers. Assum e that Mr. Sm ith has enough personal savings to purchase a $6,000 car at the beginning of year 1. Also assum e that Mr. Sm ith wants to operate his busine ss for four years and then retire. The car value at the end of the 4 years is assum e d to be zer o. Mr. Sm ith expects to sell $ 20,000 of pizzas per

year. He believes his gas expenditures and pi zza purchases from the pizzeria will am ount to

$10,000 per year. The incom e tax rate is assum e d to be 30%.

W e want to build th e inc o m e statem ent of Mr. Sm ith' s business f o r years l to 4. W e will first consider the case of expensing the car purchase, and then the case of capitalizing it.

A) EXPENSING THE CAR PURCHASE

We first ass u m e that the car purchas e is treated as a regular o perating exp e nse, jus t as pizza o r gas purchases. W e will say that th e ca r purchas e i s expensed . In this sim ple case, taxable incom e is by definition equal to operating inco me. Following the accounti ng relationships given above, the incom e statem ents of Mr . Sm ith' s bus in ess for year l to 4 are then given by table 1.

The tota l cas h inf l ows f o r Mr. Sm ith's com p any a r e equal to the operating revenues. T he tota l cash ou tf lows are e qual to the s u m of the operating expenses (including the car purchase), plus the incom e taxes paid to the governm ent. It is then easy to check that for any given year net cash flow is equal to net incom e .

Op. Revenues		Year 1 20,000		Year 2 20,000		Year 3 20,000		Year 4 20,000
- Op. Expenses		10,000		10,000		10,000		10,000
- Car Purchase		6,000		-		-		-
- Op. Incom e		4,000		10,000		10,000		10,000
- Taxable Inc.		4,000		10,000		10,000		10,000
- Taxes		l,200		3,000		3,000		3,000
- Net Incom e		2,800		7,000		7,000		7,000

Table l

Th e ca r purchas e i s exp e nsed

B) CAPITALIZING THE CAR PURCHASE

Purpos e o f capita liz ation

Because of the car pu rch a se, the n e t incom e of year 1, as giv e n by table 1, is strikin g ly different from those of years 2 to 4. This re flects the true cash flows affe cting Mr. Sm ith.

However, it does not truly reflect the econom ics of the business: from the incom e statem ent of table 1, it takes $16,000 of expenses to produ ce $20,000 of revenues during year 1, but only

$10,000 during years 2 to 4. Yet the operation of th is delivery business did not change at all between year 1 and year 2. To correct this "dis tortion”, the car purchase should be "spread" m ore evenly over the 4 years of the car operation, so that the income st atem ent better reflects the true "health" of the firm' s activities. This is the purpose of capitalization. Companies are required by law to cap ita lize those of their im portant expenditures that cover several years of operation (such expenditu res are ca lled c apita l i nvestm e nts or capital expenditures. ) In the case of Mr. Sm ith' s com pany, the car purchase is a capital expenditure and it has to be capitalized. This means that the car purchase item of table 1 is replaced by so m e "Depreciation Allowances". The series of depreciation allowances is calle d depreciation schedule. Deprecia tion allowances are usually not included in the calculation of the operating inco me (see table 2), but are deducted from it to obtain the taxable income. Hence:

Taxable Incom e - Operating Inco m e - Depreciation Allowances

The total su m of the depreciation allowances over the 4 years of operation has to equal the car purchase price (rem e mber that we assumed no car salvage value at the end of year 4.) But there are nu m e rous ways to "sp r ead" the purch as e cost over the 4 years. The law pro poses severa l of th em , the simplest b e ing known as straight line depr eciation : depreciation allowances are constant over the lif e of the investm e nt. Note that de preciation calculat ions are accounting procedures. As such they usually do not consider inflation or tim e value of m oney.

Capitalizatio n o f th e ca r purchase

We assum e that the car p u rchase is capita lized with stra ight lin e depreciation over the four year period. The deprecia tion allowances per year is then: 6,000/4 - 1,500, and the incom e statem ents for years 1 to 4 are given by table 2.

	Year 1	Year 2	Year 3	Year 4
Op. Revenues	20,000	20,000	20,000	20,000
- Op. Expenses	10,000	10,000	10,000	10,000
- Op. Incom e	10,000	10,000	10,000	10,000
- Depr. Allow.	1,500	1,500	1,500	1,500
- Taxable Inc.	8,500	8,500	8,500	8,500
- Taxes	2,550	2,550	2,550	2,550
- Net Incom e	5,950	5,950	5,950	5,950

Tabl e 2

Th e ca r purchas e i s capitalized

Ne t cas h flow s vs , ne t incom e

The net cash flows are now different from wh at they were (b ecause taxes changed), and are also different from the new net incom e s. Dur i ng the first year, Mr. S m ith sells $20,000 of pizzas, pu rchases $10,0 00 of gas and pizzas, p a ys $2,550 of taxes (see table 2), and purchases the car for $ 6,000. The net cash flow of year 1 is then:

NCF - 20,000 - 10,000 - 2,550 - 6,000

- 1,450

The net incom e of year 1, by contrast, is $5,950 (a s reported in table 2.) During year 2 to 4, Mr. Sm ith sells $20,000 of pizzas, pu rch a ses $10,00 0 of gas and pizzas, and pays $2,550 of taxes (see table 2.) His net cash flow for years 2 to 4 is therefore:

NCF - 20,000 - 10,000 - 2,550

- 7,450.

The corresponding net incom e is $5,950. For any given year, it is easy to verif y that:

NCF - Net Incom e + Depreciation A llowances - Capital Exp enditu re.

Note that this is not a definition but only a property of net cash flow. Depreciation allowances are added b a ck because they were su btracted fro m the operating incom e to calcu late the net incom e . This sim p le accounting formula is im portan t becau se it allows us to re late the concept o f accounting depreciation that we just developed w ith that of econom i c depreciation, def i ned as the loss of v alue of a cap ita l asse t with tim e.

To see this, consider the case where there is no capital expenditure (year 2, 3 or 4). W e then have:

Net Cash Flow - Net Incom e + Depreciation Allowances.

The net cash flow is what Mr. Sm ith actually pays or receives at the end of each year as a result of his delivery business. The depr eciation allowances can be seen as am ounts of m o ney that are put aside in a separate account, and that corres pond to the loss of ca r value during the year considered. If the car is believed to lose $1,500 in value in a given year, Mr. Sm ith could conceptually put $1,500 of the m one y he m a kes dur ing th is y ear in this sp ecial accoun t. The rem ainder would be his net incom e. The cum u la tive am ount of m oney put aside this way would reach $6,00 0 at the end of year 4, an d could then be used to replace the car. Note th at this separate account would be a pure accountant' s artifice, and w ould not earn interest.

It is im portant to rem e mber that Mr. Sm ith is never required to set aside this m oney (even if he indeed wanted to replace the car at the end o f year 4.) He can put all the net cash flow in his personal bank account and use it the way he wants. In this sense, depreciation is only an arbitrary accounting procedure, it is never a ca sh expense that has to be paid.

[Si m ple analogy: if you buy a PC for $2,000, and after one year it is worth only $1,500, in som e way, you have "lost" $500. And yet, you did not have to pay $500 to anybody, during this past year.]

Ta x considerations

It was stated previously that depreciation is introduced so tha t incom e state m ents better reflect the activity of a com pany during a give n period. However, only cash flows m a tter for com panies, and depreciation allowa nces are not cash expenses. From this perspective, one m i ght think that companies should not be concerned about depreciation and de preciation schedules. In reality they are concerned about them, because depreciation allowances are im portan t to calcu late inc o m e taxes (s ee tab l e 2.)

Taxes in table 2 are constant over the life of the investm e nt. This is because we chose straight line depreciation and a ssum e d constant operating revenues and expenses. Note that the total am ount of taxes received by the govern m e nt is: 2,550 * 4 = 10,200 (we neglect the tim e value of m o ney here.) In table 1, the to tal am ount of taxes was: 1,200 + 3,000 * 3 = 10,200.

Hence, depreciation does not change the total am ount of taxes paid. However, it is easy to see that the distribution of the tax cash flows over tim e changes. In the case considered, introducing depreciation shifted $ 1, 350 from ye ars 2, 3 and 4 to year 1. Because of the tim e value of m oney, com p anies always prefer to post pone expenditures as m uch as possi ble (provided of course that the am ount of the expenditure does not change.) Th is is true for taxes too, which explains why com panies prefer depreciation schedules with high depreciation allowances during the first years. It also explains why companies prefer to expe ns e their expend itur es ra ther than to c apitaliz e them (when they legally can.)

Suggeste d E x ercise:

As an exercise, the inco m e statem ent and cash fl ow calculations of Mr. Sm ith' s business can be redone, assum i ng that the car is sold at the e nd of year 4 for $2,000 (salvage value = $ 2,000). Keeping straight line deprecia tion, one finds net incom e s of $ 2,300 per year, and net cash flows of $1,300 for year 1, $7,300 for years 2 and 3, and $9,300 for year 4.

C) CONCL U SION

The sim ple case discussed above illustrated the following ideas:

1. Depreciation is an accounting pr ocedure, not a cash expense.

2. Depreciation is supposed to reflect in the incom e statem ent the loss of value of capital assets with tim e.

3. Depreciation schedules only really m a tter fo r tax calcu latio n s. Po ssible depreciation schedules for a given class of i nvestm e nt are determ ined by law.

4. In a given year, higher deprecia tion allowances m ean lower taxes. Sin ce com p anies prefer to postpone taxes, they prefer depreciation schedul es with high depreciati on allowances during the early years of the project.

5. Com p anies are r equir ed by law to ca pita lize th eir capital investm e nts. They can (and do) expense any other expenditure.

6. Net cash flo w s describe the actu al flows of m oney associated with the investm e nt during a given period, whereas net incom e s describe the "theoretical" financial result of the investm e nt during this period, by taking depreciation into account.