IE463 Chapter 5. Depreciation. Depreciable Property. Basic Terminology STRAIGHT-LINE (SL) METHOD DEPRECIATION AND INCOME TAXES
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1 Depreciation IE463 Chapter 5 DEPRECIATION AND INCOME TAXES Depreciation is the decrease in the value of physical properties with passage of time Because, depreciation is a non-cash cost that affects income taxes we must consider depreciation properly, when making After-Tax Engineering Economy studies CHAPTER 5 Depreciable Property It is a property for depreciation is allowed under governmental income tax laws and regulations In general, property is depreciable if it meets the following basic requirements: It must be used in business or held to produce income. It must have a determinable useful life, and the life must be longer than one year. It must be something that wears out, decays, gets used up, becomes obsolete, or loses value from natural causes. CHAPTER 5 3 Basic Terminology Depreciation = an annual non-cash charge against income. It represents an estimate of the dollar cost of fixed assets used in the production of a good or service. Cost Basis (B) = actual cash cost plus book value of trade-in (if any) plus costs of making asset serviceable (e.g., installation). Book Value ( ) = value of asset as shown on the accounting records. Represents amount of money still invested in the property. = book value at EOY k SV N = estimated salvage value in year N (used in depreciation calculations where applicable) MV N = market (resale) value at EOY N from the disposal of an asset CHAPTER 5 4 STRAIGHT-LINE (SL) METHOD DECLINING BALANCE (DB) METHOD A constant amount is depreciated each year over the asset's life. N = depreciable life of the asset in years. d k = annual depreciation deduction in year k d k = (B - SV N ) / N for k = 1,,..., N d k * = cumulative depreciation through year k. d k * = k x d k = B - d k * Annual depreciation is a constant percentage of the asset's value at the BOY R = /N 00% declining balance R = 1.5/N 150% declining balance d 1 = B x R d k = B(1-R) k-1 (R) = -1 (R) d k * = B[1 - (1 - R) k ] = B(1 - R) k BV N = B(1 - R) N CHAPTER 5 5 CHAPTER 5 6 1
2 SL and DB Example The La Salle Bus Company has decided to purchase a new bus for $85,000, with a trade-in of their old bus. The old bus has a trade-in value of $10,000. The new bus will be kept for 10 years before being sold. Its estimated salvage value at that time is expected to be $5,000. Compute the following quantities using (a) the straight-line method, (b) the 00% declining balance method depreciation deduction in the first year and the fourth year cumulative depreciation through year four book value at the end of the fourth year CHAPTER 5 7 Cost basis: B = $10,000 + $85,000 = $95,000 trade-in value cash-cost Deduction amounts are fixed for SL: 95,000-5,000 d k $9,000for k 1 to10 10 Deduction ratios are fixed for DB: R 0., thus,(dk 0. BVk- 1) 10 SV 10 CHAPTER 5 8 N 00% DB Straight Line Method (k = 1 to 4) Straight Line Method (k = 5 to 10) , ,000 86,000 = 95,000 9,000 9,000 77,000 = 86,000 9, ,000 68,000 = 77,000 9, ,000 59,000 = 68,000 9,000 d 4 = d 1 BV 4 = 95,000 36,000 d 4 * = 4 x 9000 = 36,000 CHAPTER ,000 50,000 = 59,000 9, ,000 41,000 = 50,000 9, ,000 3,000 = 41,000 9, ,000 3,000 = 3,000 9, ,000 14,000 = 3,000 9, ,000 5,000 = 14,000 9,000 SV 10 = B N x d k CHAPTER % Declining Balance Method (k = 1 to 4) , ,000 76,000 15,00 60, ,160 48, ,78 38,91 d 4 * = 19, ,78 = 56,088 d 1 = BV 0 x R = B x 0. = 95,000 x 0. = 19,000 BV 1 = BV 0 d 1 = B d 1 = 95,000 19,000 BV 4 = B d 4 * d 4 = 48,640 x 0. CHAPTER % Declining Balance Method (k = 5 to 10) 5 7,78 31, ,6 4, ,981 19,93 8 3,985 15, ,188 1,750 10,550 10,00 BV 10 = B d 10 * = BV 9 d 10 CHAPTER 5 1
3 SL vs. DB Consideration of Income Taxes in EE Income tax represents a significant cash outflow that we cannot ignore Notation: R k = gross revenues in year k E k = operating expenses in year k plus interest paid on borrowed capital d k = depreciation allowance for year k t = effective income tax rate used for computing income taxes T k = income tax liability for year k CHAPTER 5 13 CHAPTER 5 14 General Tax Procedure BTCF = Before tax cash flow = R E NIBT = Net income before tax = R E d T = tax liability = t ( NIBT ) = t (R E d) NIAT = Net income after tax = NIBT T = (R E d) t (R E d) = (1 t)(r E d) ATCF = After tax cash flow = NIAT + d ATCF = BTCF t (R E d) General Tax Procedure - Example You invested $113,08 on an asset with the depreciable life of 10 years. You can earn $30,000 per year from this investment for 10 years. Asset has a negligible or zero MV at the end of its useful life. Published income tax rate is 40% on annual taxable income (NIBT). Use after-tax MARR of 15% per year, and straight line depreciation method. a) NIBT? b) NIAT? c) ATCF? d) Is it profitable investment after taxes? CHAPTER 5 15 CHAPTER 5 16 Solution to (a), (b) and (c) Solution to part (d) d = 113,08 / 10 = $11,303 (depreciation amount) (+) Net income 30,000 (-) Deprecation 11,303 (a) NIBT $18,697 (R E d) (-) Income Tax (0.4) 7,479 (b) NIAT $11,18 (1 t)(r E d) (+) Depreciation 11,303 (c) ATCF $,51 (1 t)(r E d)+d AW (15%) = ATCF 113,08 (A/P, 15%, 10) =,51,51 = $0 CHAPTER 5 17 CHAPTER
4 Typical Before-Tax Cash Flow Diagram: After-Tax Cash Flow Analysis Typical After-Tax Cash Flow Diagram: CHAPTER 5 19 CHAPTER 5 0 After-tax MARR To perform an after-tax evaluation of a project's after-tax cash flows, we must use an after-tax MARR. Before - tax MARR MARR BT MARR 1- t AT After - tax MARR 1- effective income tax rate, t Example: Suppose the before-tax MARR = 0% and t = 40%. What is the approximate after-tax MARR? MARR AT 0.(1-0.4) 0.1 ATCF Analysis Example Investment $10,000 Net Annual Receipts $4,000/yr Study Period 4 years Market Value at EOY 4 $5,000 After-tax MARR 15% Effective income tax rate 40% Depreciable recovery period 5 years Is this a worthwhile investment after taxes? Use Straight Line Method for depreciation. CHAPTER 5 1 CHAPTER 5 Step 1: Find depreciation amounts for the study period of 4 years: d k 10, $,000for k 1 to CHAPTER 5 3 Step : Determine the ATCF with tax rate of 40%: EOY, k BTCF k d k TI k (t = 0.4) ATCF k 0-10,000-10, a b MV 4 BV 4 = T k CHAPTER 5 4 4
5 Step 3: Use the ATCF to evaluate this MARR = 15%: After-tax cash flow diagram: PW(15%) = 10, ,00 (P/A, 15%, 3) + 7,000 (P/F, 15%, 4) = + $1,309 Non-depreciable asset - Example Construction cost of the facility $600,000 Purchasing cost of land $550,000 Annual gross income $30,000 Operating expenses per year $30,000 Facility will be depreciated for 5 years, using 00% DB MARR AT 1% Tax rate 40% Is the investment worthwhile after taxes for the study period of 5 years? Note: Land will be kept after the five-year operation! Facility has a market value of CHAPTER 5 5 CHAPTER % DB R = /5 = 0.4 ATCF analysis with t = , , , ,000 16, ,400 19, ,840 77, ,104 46,656 cost basis for only depreciable asset 600,000 x ,000 40,000 BV 5 MV 5 = 0 CHAPTER 5 7 EOY a BTCF -1,150,000 d Tax ATCF -1,150,000 40,000-40,000 16,000 16, ,000 56,000 -, ,600 86, ,600-45, ,560 51, ,160-59,64 140,736 31, ,896-67,558 13,44 5b 550,000-46,656 18,66 568,66 MV 5 BV 5 = 0 46,656 CHAPTER 5 550, ,66 8 TI ATCF analysis with MARR AT = 1% EOY a 5b ATCF -1,150,000 16, , , ,736 13,44 568,66 PW(1%) = - 1,150, ,000(P/F, 1%, 1) + 177,600(P/F,1%, ) + 154,560(P/F, 1%, 3) + 140,736(P/F, 1%, 4) + (13, ,66)(P/F, 1%, 5) = - $18,83 < 0 reject! CHAPTER 5 9 Lease versus Purchase - Example Determine the more economic means of acquiring a copier in your business if you may either: a) purchase the copier for $5,000 with a probable resale value of $1,000 at the end of 5 years or b) rent the copier for an annual fee of $900 per year for 5 years with an initial deposit of $500 refundable upon returning the copier in good condition. If you own the copier, you will depreciate it by using the 150% DB method (class life of 5 years). All rental fees are deductible for income tax purposes. As the owner or lessee, you will pay all expenses associated with the operation of the copier. A deposit does not affect taxes when paid out or received back. Compare these alternatives by using the equivalent uniform annual cost method. The after-tax MARR is 10% per year, and the effective income tax rate is 40%. CHAPTER
6 Option A Purchase Copier EOY BTCF R=0.3 d TI t= -0.4 Tax ATCF a b Option A Purchase Copier EOY ATCF a 144 5b 936 AW(10%) = [ (P/F,10%,1) +40(P/F,10%,) +94(P/F,10%,3) +06(P/F,10%,4) +( )(P/F,10%,5)](A/P,10%,5) = (A/P,10%,5) = CHAPTER 5 31 CHAPTER 5 3 Option B Rent (lease) Copier EOY BTCF d TI t = -0.4 Tax ATCF a b Option B Rent (lease) Copier EOY ATCF a b 500 AW (10%) = -500(A/P,10%,5) + 500(A/F,10%,5) 540 = Option B (lease) is the least cost alternative for having the coppier CHAPTER 5 33 CHAPTER 5 34 Before tax leasing cost? Over what range of before-tax leasing costs would you choose the purchase option based on an after-tax analysis? AW_lease =AW_purchase AW_lease = (A/P,10%,5) (A/F,10%,5) + (1 t) L say L = before tax leasing cost 0.6 L = (A/P,10%,5) 500 (A/F,10%,5) L = 169 (if before tax leasing cost is greater than 169, purchasing option will be preferred) CHAPTER
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