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time –Use-related physical loss wear and tear –Time-related physical loss corrosion –Functional loss function becomes outdated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 Economic Depreciation Physical Functional Accounting Depreciation Book Depreciation Tax Depreciation Caused by Usage StyleCapacity 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 $ and has a salvage value of $1 000 at the end of it’s 5 yr. Service life.

Straight Line Method The book value (B n ) is a linear function of time: depreciation = Initial cost - Salvage Value Service Life = = $4 000/ yr = P - S N B n = n(P – S) N

Straight-Line Depreciation Equations = P - S N DnDn D n = Depreciation charge during year n P = Cost of the asset including installation expense S = Salvage Value at end of useful life N = Useful life B n = Book value in year n B n = n(P – S) N

Quick Check Consider the following automobile data: –Cost Basis for the asset, P = $ –Useful life, N = 5 years –Estimated Salvage ValueS = $2 000 Compute the annual depreciation allowances and the resulting book values using the straight-line depreciation method.

Straight-Line Depreciation Annual Depreciation Book Value P=B 0 D1D1 D2D2 D3D3 D4D4 D5D5 B1B1 B2B2 B3B3 B4B4 B5B5 Year Total depreciation at end of life

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 Balance Suppose that the government CCA rate for the ball bearing machine has been set at 20% Year etc Depreciation.20($21 000).20($16 800).20($13 440) etc CCA $4 200 $3 360 $2 688 etc B n $ $ $ etc CCA = Capital Cost Allowance = Annual depreciation expense for tax purposes

Declining Balance Equations For any year,n, we can calculate the depreciation charge D n as: D n = dP(1-d) n-1, n > 1 We can also calculate the total declining balance depreciation (TDB) at the end of n years as: TDB n = P[1-(1-d) n ] The book value, B n, at the end of n years will be the cost of the asset P minus the total depreciation at the end of n years: B n = P(1-d) n See pp

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. Firm just purchased $ worth of equipment Income is $ per year Expenses (excluding depreciation) are $ per yr The Tax rate is 50% MARR = 10% Salvage value after 5 yrs. is $0 F5F5

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 same B. greater C. less

Example - Straight Line Depreciation Depreciation = $ /5 = $ per yr. Reduces net income to $ Therefore $ paid in taxes $ vs $ from previous example SL depreciation reduces accum cash at end of yr 5 by $24308 F5F5

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 CategoryCCA RateDescription 35% buildings made of brick or steel 610% other buildings 715% ships 820% machinery and equipment not included in other categories 1030% Cars, trucks, etc. 24 and 29 50% Pollution control equipment for water and other assets dedicated to environment protection

Effect of Different CCA Rates Remaining value subject to taxes 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 PurchaseAdd only 1/2 of the acquisition cost to the base UCC amount for its CCA class in the year of purchase. After the CCA calculation add the other 1/2 to the remaining UCC (note that the second half is not considered a purchase in the following year). DispositionSubtract the full amount of a disposition of an asset from the base CCA amount for its CCA class. Purchases and Subtract total dispositions from total purchases dispositions in thefor a CCA class. If the remainder is +’ve same 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 1997 they purchased two trucks for a total of $50,000. At the beginning of of 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 Year Adjustment Base UCC 0 0 Remaining UCC 1000

Solution The UCC at the end of 2000 was $26 779

Quick Check If the actual salvage value is less than the B n 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 (1992 = 100)

Canadian Price Index (1992=100)

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

Inflation Rates

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, A N = actual dollars in year N R 0,N = real dollars equivalent to A N relative to year 0 I 0,N = the value of the CPI at year N relative to year 0 R 0,N = ANAN I 0,N /100

Converting between Real and Actual Dollars with f Let, A N = actual dollars in year N R 0,N = real dollars equivalent to A N relative to year 0 f= the inflation rate per year, assumed to be constant from year 0 to year N R 0,N = ANAN (1 + f) N R 0,N = A N (P/F,f,N)

Actual/Real Conversion Ex. 1 If your income increased from $ in 1990 to $ in 1993 were you better off in terms of purchasing power? Since 1992 is the base yr for the CPI, let’s convert the actual dollars to real (constant) 1992 dollars (CPI 92 = 93, CPI 93 = 101.8). R 92,90 = = $42 872R 92,93 = = $ R 0,N = ANAN I 0,N /100

Actual/Real Conversion Ex. 2 The cost of replacing a storage tank in 15 yrs is expected to be $ If inflation is assumed to be 5% per year, what is the cost of the tank in today’s (real) dollars? R 0,N = ANAN (1 + f) N R 15 = (1.05) 15 = $

The Actual/Real Interest Rate If we expect inflation, the number of actual dollars returned from an investment does not tell us the purchasing power (value) of the future cash flow. The actual interest rate i is the stated or observed interest rate based on actual dollars. The real interest rate i ´ is the interest rate that would yield the same number of real dollars in the absence of inflation as the actual interest rate yields in the presence of inflation i´=i´= (1+i) (1 + f) - 1

Calculating actual interest rates If an investor wants a real rate of return i ´ over the next year and the inflation rate is expected to be f, he can calculate the required actual 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 MARR A = MARR R + f + MARR R x f

Thr Real MARR MARR R = (1+MARR A ) (1 + f) - 1 i´=i´= (1+i) (1 + f) - 1

Canadian Averages Prime Interest Rates & Inflation Period i´ (%) Average f (%) Average i (%) Average i = (1+ i´)(1+f ) - 1

Example Your bank is offering to pay 12% on a 1-yr GIC. The inflation rate is expected to be 5%. What is the real rate of interest? If you purchase a $5000 GIC, what is the real dollar value at the end of 1 yr? i´=i´= (1+i) (1 + f) - 1 i´=i´= (1.12) (1.05) - 1 = or 6.7% A $5000 GIC will return $5600 at 12%, but the real value in today’s dollars is 5600/1.05 = $5333. Same as 6.7% interest with no inflation!

The Effect of Inflation on IRR IRR R = (1+IRR A ) (1 + f ) - 1 The actual IRR will be the real IRR plus an upward adjustment which 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) /(1+i*) = 0 i* = IRR A = 20%

Solution 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 (1+0.05) (1 + i*) = 0 i* = IRR A = 26%, hence, acceptable (> MARR)

Recommended Problems Level 1 –12.1 to 12.6, to 12.14, Level 2 –12.18, 12.20, 12.21, 12.22