Depreciation, the CCA & Inflation

Chapter 7 &12

Outline

• Depreciation defined• Types of Depreciation• Before and After-tax MARR• UCC and the 1/2 yr rule• The Capital Cost Tax Factor• Components of a complete Tax Calculation• Approximate After Tax Rate-of-Return

Calculations

Why Depreciation

• Production equipment deteriorates with time.

• The firm needs to keep track of this depreciation in order to:– make managerial decisions

– have an understanding of the net worth of the enterprise at any given time

– calculate tax savings that result from depreciation.

Significance of the word Depreciation

• Implies a loss of value as a function of time– Use-related physical loss

• wear and tear

– Time-related physical loss• corrosion

– Functional loss• function becomes outdated

Caused by the elements

Depreciation

EconomicDepreciation

Physical

Functional

AccountingDepreciation

BookDepreciation

TaxDepreciation

Caused byUsage

Style Capacity

Classifications of Depreciation

Also called asset depreciation

Depreciable Property

• Must be used for business or held for the production of income

• Must have a definite useful life, longer than one year

• Must be something that is subject to wear, decay, gets used up, becomes obsolete, or loses value from natural causes

The Value of an Asset

• Depreciation models estimate the loss in value as a function of time. The value that remains can have several names– Market Value - amount it can be sold for on the open

market– Book Value - depreciated value for accounting

purposes (cost basis – accumulated depreciation)– Scrap Value- for items with no useful life remaining – Salvage Value - actual value at end of useful life or an

estimate of this value based on a depreciation model

Methods: Book and Tax Depreciation

• Two legitimate methods for different purposes:– For financial reports (book depreciation)

– For the purpose of calculating taxes (Capital Cost Allowance CCA)

• Revenue Canada generally allows assets to depreciate faster than would be reflected in the financial reports.

• The books are balanced, however, when the firm disposes of the asset.

Book Depreciation Methods

• Straight-Line Method

• Declining Balance Method

Example (to demonstrate the two methods):A machine used to produce ball bearings costs $21 000and has a salvage value of $1 000 at the end of it’s5 yr. Service life.

Straight Line MethodThe book value (Bn) is a linear function of time:

depreciation = Initial cost - Salvage Value

Service Life

=21 000 - 1 000

5= $4 000/ yr

= P - S

N

0 1 2 3 4 5

21 000

1 000

Bn = n(P – S)N

Straight-Line Depreciation Equations

= P - S

NDn

Dn= Depreciation charge during year nP = Cost of the asset including installation expenseS = Salvage Value at end of useful lifeN = Useful lifeBn = Book value in year n

Bn = n(P – S)N

Quick Check

• Consider the following automobile data:

– Cost Basis for the asset, P = $10 000– Useful life, N = 5 years– Estimated Salvage Value S = $2 000

• Compute the annual depreciation allowances and the resulting book values using the straight-line depreciation method.

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

0 1 2 3 4 5 6

Straight-Line Depreciation

Annual Depreciation

Book ValueP=B0D1

D2

D3

D4

D5

B1

B2

B3

B4

B5

Year

Tot

al d

epre

ciat

ion

at

end

of li

fe

Declining Balance Method

• Used for book depreciation, but also the basis for CCA, i.e., Obligatory for most tax purposes in Canada

• The value of the asset declines at a fixed percentage rate per yr.; d %

• This rate is fixed by the government and varies depending on the type of equipment

• The depreciation rate is called the Capital Cost Allowance (CCA)

• The remaining balance is called the Undepreciated Capital Cost (UCC)

Example - Declining BalanceSuppose that the government CCA rate for the ball bearing machinehas been set at 20%

Year

123

etc

Depreciation

.20($21 000)

.20($16 800)

.20($13 440)etc

CCA

$4 200$3 360$2 688

etc

Bn

$16 800$13 440$10 752

etc

CCA = Capital Cost Allowance = Annual depreciation expense

for tax purposes

Declining Balance Equations

For any year ,n, we can calculate the depreciation charge Dn as:

Dn = dP(1-d)n-1, n > 1

We can also calculate the total declining balance depreciation (TDB) at the end of n years as:

TDBn = P[1-(1-d)n]

The book value, Bn, at the end of n years will be the cost of the assetP minus the total depreciation at the end of n years:

Bn = P(1-d)n See pp 429-430

The Capital Cost Allowance (CCA) System

• Capital expenditures (assets purchased to enable the firm to make profit) depreciate over time

• Firms are allowed to deduct this as an expense on an annual basis, before calculating net profit and taxes.

• It is in the company’s best financial interest to “write-off” an investment as rapidly as possible

• The Canadian tax system defines the amount of depreciation allowed in any given year as the Capital Cost Allowance (CCA)

Example - Full Depreciation in 1 yr.Year 1 2 3 4 5Income 300 000 300 000 300 000 300 000 300 000Expenses ex. dep. 100 000 100 000 100 000 100 000 100 000Depreciation Expense 200 000 0 0 0 0Net Income 0 200 000 200 000 200 000 200 000Taxes 0 100 000 100 000 100 000 100 000Profit 0 100 000 100 000 100 000 100 000A ccumulated Profit 0 100 000 210 000 331 000 464 100Cash 200 000 100 000 100 000 100 000 100 000Accumulated Cash 200 000 320 000 452 000 597 200 756 920

•Firm just purchased $200 000 worth of equipment•Income is $300 000 per year•Expenses (excluding depreciation) are $10 0000 per yr•The Tax rate is 50%•MARR = 10%•Salvage value after 5 yrs. is $0

F5

Concept test

• If the previous example is changed to use straight line depreciation over the 5 year life of the asset, the FE of the accumulated cash flow at the end of year 5 will be

A. the sameB. greaterC. less

Example - Straight Line Depreciation

Year 1 2 3 4 5Income 300 000 300 000 300 000 300 000 300 000Expenses ex. dep. 100 000 100 000 100 000 100 000 100 000Depreciation Expense 40 000 40 000 40 000 40 000 40 000Net Income 160 000 160 000 160 000 160 000 160 000Taxes 80 000 80 000 80 000 80 000 80 000Profit 80 000 80 000 80 000 80 000 80 000A ccumulated Profit 80 000 168 000 264 800 371 280 488 408Cash 120 000 120 000 120 000 120 000 120 000Accumulated Cash 120 000 252 000 397 200 556 920 732 612

•Depreciation = $200 000/5 = $40 000 per yr.•Reduces net income to $160 000•Therefore $80 000 paid in taxes•$732612 vs $756920 from previous example•SL depreciation reduces accum cash at end of yr 5 by $24308

F5

The CCA System in Canada

• Companies wish to depreciate as quickly as possible to save on taxes

• The government would prefer to receive more taxes

• The government gets to make the rules• The CCA system specifies the amount and timing

of depreciation expenses• Tangible assets are required by law to use the

declining balance method in Canada

CCA - categories for the declining balance method

Category CCA Rate Description

3 5% buildings made of brick or steel6 10% other buildings 7 15% ships8 20% machinery and equipment not included

in other categories10 30% Cars, trucks, etc.24 and 29 50% Pollution control equipment for water

and other assets dedicated to environment protection

Effect of Different CCA RatesR

emai

ning

val

ue s

ubje

ct to

taxe

s

Number of years

5%

20%30%

Undepreciated Capital Cost (UCC)

• The basis for calculating the CCA is the UCC of all assets in the same class

• UCC is the undepreciated portion of the original capital cost of acquisition

• The UCC is the remaining book value subject to depreciation for tax purposes

• The UCC may or may not equal the market or salvage value of the asset

The 1/2 yr Rule

• Prior to 13 Nov 1981 companies were allowed to depreciate based on the full acquisition cost of any assets purchased during the current year

• Since that date, only 1/2 of the acquisition cost has been allowed for depreciation during the first year

• Provides an incentive to purchase major assets towards the end of the fiscal year

Calculating UCC balances for any given year

UCC opening + additions - disposals - CCA = UCC ending

Half-Year Rule Summary

Component Treatment

Purchase Add only 1/2 of the acquisition cost to thebase UCC amount for its CCA class in the year of purchase. After the CCA calculationadd the other 1/2 to the remaining UCC (note that the second half is not considered a purchase in the following year).

Disposition Subtract the full amount of a disposition ofan asset from the base CCA amount for itsCCA class.

Purchases and Subtract total dispositions from total purchasesdispositions in the for a CCA class. If the remainder is +’vesame yr. Treat as a purchase, if -’ve treat as a disposition

Example

The UCC for a firm’s automobile fleet at the end of 1996 was $10,000.There was one truck in service at this time. At the beginning of 1997they purchased two trucks for a total of $50,000. At the beginning ofof 1999, they purchased another truck for $20,000. At the beginning of 2000, the truck owned in 1996 was sold for $3000. The CCA rate for automobiles is 30%. What was the firm’s UCC for this class at the end of 2000?

Solution - Quick Check

Year19961997199819992000

Adjustment0

50000

Base UCC0

CCA@30%0

Remaining UCC1000

Solution

Year Adjustment Base UCC CCA@30% Remaining UCC1996 100001997 50000 35000 10500 495001998 0 49500 14850 346501999 20000 44650 13395 412552000 -3000 38255 11477 26779

The UCC at the end of 2000 was $26 779

Quick Check

If the actual salvage value is less than the Bn at the time of sale of the asset the effect on taxes will be:

A. Positive (a savings)

B. Negative (we must pay more tax)

C. Negligible

Recommended problems

• Level 1– 7.1, 7.5, 7.7, 7.13, 7.14, 7.15, 7.17, 7.18

• Level 2– 7.24 a and b, 7.27

Inflation

Chapter 12

Inflation - Outline

• Introduction

• Measuring the Inflation Rate

• Real vs. Actual Dollars

• The effect on– MARR– IRR

• Project Evaluation Methods with Inflation

Introduction• On average, prices have gone up every year in Canada

(except 1940)• Inflation

– The average increase, over time, in average prices of goods and services

– A decrease in the purchasing power of money over time

• Deflation– The average decrease, over time, in average prices of goods and

services– An increase in the purchasing power of money over time

• Price changes will impact the economic viability of projects

Measuring the Inflation Rate

• Definition– The Inflation Rate is the rate of increase in average

prices of goods and services over a specified time period (usually 1 year).

• In any period, some prices may rise while othe prices may fall

• Stats Canada tracks the movement of average prices for various “baskets” of goods

The Consumer Price Index (CPI)

• One set of prices tracked by stats Canada consisting of the primary goods and services purchased by Canadians.

• Using 1992 as a base year (CPI set at 100) , the CPI for any other year indicates the number of dollars needed that year to buy a fixed basket of goods that cost $100 in 1992.

Canadian CPI 1996 - 2000(1992 = 100)

Canada 1996 1997 1998 1999 2000ALL 105.9 107.6 108.6 110.5 113.5Food 105.9 107.6 109.3 110.7 112.2Shelter 103.1 103.3 103.7 105.1 108.8Household 105.3 106.6 108.2 109 110Clothing/Footwear 101.4 102.7 103.9 105.3 105.5Transpt 117.8 121.5 120.5 124.5 130.7Health 104.1 105.9 108.1 110.2 112Recr/Education 112.1 114.9 117.5 119.6 122.5Alcohol/Tobacco 86.6 89.3 92.6 94.5 97.6

www.statcan.ca

Canadian Price Index(1992=100)

102104106108110112114116

1996 1997 1998 1999 2000

The Inflation Rate

• Can be estimated directly from the CPI by expressing the percentage change in CPI from year to year.

• Can be expressed as the percentage change in CPI for any period of years.

Inflation 1996-2000

1997 1998 1999 2000ALL 1.61 0.93 1.75 2.71Food 1.61 1.58 1.28 1.36Shelter 0.19 0.39 1.35 3.52Household 1.23 1.50 0.74 0.92Clothing/Footwear 1.28 1.17 1.35 0.19Transpt 3.14 -0.82 3.32 4.98Health 1.73 2.08 1.94 1.63Recr/Education 2.50 2.26 1.79 2.42Alcohol/Tobacco 3.12 3.70 2.05 3.28

www.statcan.ca

Inflation Rates

0.00

0.50

1.00

1.50

2.00

2.50

3.00

1997 1998 1999 2000

Economic Evaluation with Inflation

• If prices change over time, the purchasing power of the dollars earned on an investment also change.

• Real (constant) dollars – monetary value is constant relative to a base year (e.g.,

in 1995 dollars).

• Actual (current) dollars – monetary value is measured at the time of the cash

flow.

Converting between Real and Actual Dollars

Let,AN = actual dollars in year NR0,N = real dollars equivalent to AN relative to year 0I0,N = the value of the CPI at year N relative to year 0

R0,N =AN

I0,N/100

Converting between Real and Actual Dollars with f

Let,AN = actual dollars in year NR0,N = real dollars equivalent to AN relative to year 0f = the inflation rate per year, assumed to be constant

from year 0 to year N

R0,N =AN

(1 + f) N

R0,N = AN (P/F,f,N)

Actual/Real Conversion Ex. 1If your income increased from $40 000 in 1990 to $43 000 in 1993were you better off in terms of purchasing power?

Since 1992 is the base yr for the CPI, let’s convert the actual dollarsto real (constant) 1992 dollars (CPI92 = 93, CPI93 = 101.8).

R92,90 =40 000

0.933= $42 872

R92,93 =42 000

1.018= $41 257

R0,N =AN

I0,N/100

Actual/Real Conversion Ex. 2The cost of replacing a storage tank in 15 yrs is expected to be$2 000 000. If inflation is assumed to be 5% per year, what isthe cost of the tank in today’s (real) dollars?

R0,N =AN

(1 + f) N

R15 = 2 000 000(1 .05) 15

= $962 040

The Actual/Real Interest Rate•If we expect inflation, the number of actual dollars returned froman investment does not tell us the purchasing power (value) of thefuture cash flow.•The actual interest rate i is the stated or observed interest rate basedon actual dollars.•The real interest rate i´ is the interest rate that would yield the samenumber of real dollars in the absence of inflation as the actualinterest rate yields in the presence of inflation

i´=(1+i)

(1 + f) - 1

Calculating actual interest rates

If an investor wants a real rate of return i´ over the next year andthe inflation rate is expected to be f, he can calculate the requiredactual interest rate from:

i = (1+ i´)(1+f ) - 1

Quick Check

• The actual MARR is the minimum acceptable rate of return when calculations are made in actual dollars. In the presence of inflation, the real MARR will be:

A. Greater than

B. Less than

the actual MARR?

The Actual MARR

i = (1+ i´)(1+f ) - 1

i = i´+f + i´f

MARRA = MARRR + f + MARRR x f

Thr Real MARR

MARRR =(1+MARRA )

(1 + f) - 1

i´=(1+i)

(1 + f) - 1

Canadian Averages 1961-1996Prime Interest Rates & Inflation

Period1961-19711972-19811982-19911992-1996

i´ (%)Average

1.820.084.843.89

f (%)Average

2.758.475.291.43

i (%)Average

11.28.6

10.45.4

i = (1+ i´)(1+f ) - 1

Example

Your bank is offering to pay 12% on a 1-yr GIC. The inflationrate is expected to be 5%. What is the real rate of interest? Ifyou purchase a $5000 GIC, what is the real dollar value at theend of 1 yr?

i´=(1+i)

(1 + f) - 1

i´=(1.12)

(1 .05) - 1 = 0.067 or 6.7%

A $5000 GIC will return $5600 at 12%, but the real value intoday’s dollars is 5600/1.05 = $5333. Same as 6.7% interest with no inflation!

The Effect of Inflation on IRR

IRRR =(1+IRRA ) (1 + f )

- 1

The actual IRR will be the real IRR plus an upward adjustmentwhich reflects the effect of inflation.

Project Evaluation with Inflation• Typically start with an actual MARR and base

analysis on actual dollars– actual MARR consists of 2 parts

• real rate of return• adjustment upward for inflation

• To use actual MARR projected cash flows must be actual (include effects of inflation)

• Otherwise, use real dollars and a real MARR• Never mix real and actual interest rates or dollars

in the same analysis!

Example

• Consider a one-year project which requires a $1000 investment today and yields $1200 in one year. The Actual MARR is 25%. Is this project acceptable?

Solution - $1200 Actual Dollars?

• If the future cash flow is measured in actual dollars then the actual IRR is 200/1000 = 20%, therefore not acceptable (<MARR)

-1000 + 1200/(1+i*) = 0

i* = IRRA = 20%

Solution - 1200 Real Dollars

• If the $1200 is taken to be the real value of the cash flow in one year, and inflation is expected to be 5% over the year, then actual internal rate of return is found by solving..

-1000 +1200(1+0.05)

(1 + i*) = 0

i* = IRRA= 26%, hence, acceptable (> MARR)

Recommended Problems

• Level 1– 12.1 to 12.6, 12.10 to 12.14, 12.17

• Level 2– 12.18, 12.20, 12.21, 12.22