IE463 Chapter 5 DEPRECIATION AND INCOME TAXES

Transcription

1 IE6 Chapter 5 DEPRECIATION AND INCOME TAXES Depreciation 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 6

2 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 6 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 (BV k ) = value of asset as shown on the accounting records. Represents amount of money still invested in the property. BV k = 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 6

3 STRAIGHT-LINE (SL) 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 =,,..., N d k * = cumulative depreciation through year k. d k * = k x d k BV k = B - d k * CHAPTER 6 5 DECLINING BALANCE (DB) METHOD Annual depreciation is a constant percentage of the asset's value at the BOY R = /N 00% declining balance R =.5/N 50% declining balance d = B x R d k = B(-R) k- (R) = BV k- (R) d k * = B[ - ( - R) k ] BV k = B( - R) k BV N = B( - R) N CHAPTER 6 6

4 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 $0,000. The new bus will be kept for 0 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 6 7 Cost basis: B = $0,000 + $85,000 = $95,000 trade-in value cash-cost Deduction amounts are fixed for SL: 95,000-5,000 d k = = $ for k = to 0 0 Deduction ratios are fixed for DB: R = = 0., thus, (d k = 0. BVk- ) 0 SV 0 N 00% DB CHAPTER 6 8

5 Straight Line Method (k = to ) EOY, k 0 d k 0 BV k 95,000 86,000 77,000 68,000 5 = 95,000 = 86,000 = 77,000 = 68,000 d = d BV = 95,000 6,000 d * = x 9000 = 6,000 CHAPTER 6 9 Straight Line Method (k = 5 to 0) EOY, k d k BV k 50,000,000,000,000,000 5,000 = 5 = 50,000 =,000 =,000 =,000 =,000 SV 0 = B N x d k CHAPTER 6 0 5

6 00% Declining Balance Method (k = to ) d = BV 0 x R = B x 0. EOY, k d k BV k = 95,000 x 0. = ,000 5,00,60 9,78 76,000 60,800 8,60 8,9 d * = ,78 = 56,088 BV = BV 0 d = B d = 95,000 BV = B d * d = 8,60 x 0. CHAPTER 6 00% Declining Balance Method (k = 5 to 0) EOY, k d k 7,78 6,6,98,985,88,550 BV k,0,90 9,9 5,98,750 0,00 BV 0 = B d 0 * = BV 9 d 0 CHAPTER 6 6

7 SL vs. DB CHAPTER 6 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 6 7

8 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) R < (E + d) tax credit (savings) NIAT = Net income after tax = NIBT + T R > (E + d) tax liability NIAT = Net income after tax = NIBT T = (R E d) t (R E d) = ( t)(r E d) ATCF = After tax cash flow = NIAT + d ATCF = BTCF t (R E d) CHAPTER 6 5 General Tax Procedure - Example You invested $,08 on an asset with the depreciable life of 0 years. You can earn $0,000 per year from this investment for 0 years. Asset has a negligible or zero MV at the end of its useful life. Published income tax rate is 0% on annual taxable income (NIBT). Use after-tax MARR of 5% per year, and straight line depreciation method. a) NIBT? b) NIAT? c) ATCF? d) Is it profitable investment after taxes? CHAPTER 6 6 8

9 Solution to (a), (b) and (c) d =,08 / 0 = $,0 (depreciation amount) (+) Net income 0,000 (-) Deprecation,0 (a) NIBT $8,697 (R E d) (-) Income Tax (0.) 7,79 (b) NIAT $,8 ( t)(r E d) (+) Depreciation,0 (c) ATCF $,5 ( t)(r E d)+d CHAPTER 6 7 Solution to part (d) AW (5%) = ATCF,08 (A/P, 5%, 0) =,5,5 = $0 CHAPTER 6 8 9

10 Typical Before-Tax Cash Flow Diagram: Typical After-Tax Cash Flow Diagram: CHAPTER 6 9 After-Tax Cash Flow Analysis A EOY BTCF B d k C =A B TI or NIBT D = t x C T k E = A + D ATCF 0 I I R E d R E d - t(r E d) R E t(r E d) N R E d R E d - t(r E d) R E t(r E d) N MV MV BV - t(mv BV) MV t(mv BV) MARR(Before-tax) MARR(After-tax) CHAPTER 6 0 0

11 After-tax MARR To perform an after-tax evaluation of a project's after-tax cash flows, we must use an after-tax MARR. After - tax MARR Before - tax MARR = - effectiveincome tax rate, t Example: Suppose the before-tax MARR = 0% and t = 0%. What is the approximate after-tax MARR? MARRAT MARRBT = MARRAT = 0. (- 0.) = 0. - t CHAPTER 6 ATCF Analysis Example Investment $0,000 Net Annual Receipts $,000/yr Study Period years Market Value at EOY $5,000 After-tax MARR 5% Effective income tax rate 0% Depreciable recovery period 5 years Is this a worthwhile investment after taxes? Use Straight Line Method for depreciation. CHAPTER 6

12 Step : Find depreciation amounts for the study period of years: 0,000-0 d k = = $,000 for k = to 5 5 EOY, k 0 d k BV k CHAPTER 6 Step : Determine the ATCF with tax rate of 0%: EOY, k BTCF k 0-0,000 d k a b 5000 MV BV = TI k T k (t = 0.) ATCF k - 0, CHAPTER 6

13 Step : Use the ATCF to evaluate this MARR = 5%: After-tax cash flow diagram: PW(5%) = 0,000 +,00 (P/A, 5%, ) + 7,000 (P/F, 5%, ) = + $,09 CHAPTER 6 5 Solve the same example with 00% DB CHAPTER 6 6

14 Affordable Investment - Example An asset purchased at the price of (I), and it is depreciated for 0 years, with straight line method. Estimated market EOY 0 is zero, how much can you afford to purchase this asset when it produces annual $0,000 net income for 0 years. Effective income tax is 0% and MARR AT = 5%. CHAPTER 6 7 Solve for I? d = (I 0) / 0 ATCF = (0000 d) AW(5%) = I(A/P,5%,0) ( 0.) + 0. (I/0) AW(5%) = 0 I = 0000( 0.) / ((A/P,5%,0) 0.0) I = $, CHAPTER 6 8

15 Non-depreciable asset - Example Construction cost of the facility $600,000 Purchasing cost of land $550,000 Annual gross income $0,000 Operating expenses per year $0,000 Facility will be depreciated for 5 years, using 00% DB MARR AT % Tax rate 0% 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 % DB R = /5 = 0. EOY, k 0 5 d k --- 0,000,000 86,00 5,80,0 BV k 600,000 60,000 6,000 9,600 77,760 6,656 cost basis for only depreciable asset 600,000 x ,000 0,000 BV 5 MV 5 = 0 CHAPTER 6 0 5

16 ATCF analysis with t = - 0. EOY BTCF d TI Tax ATCF 0 -,50,000 -,50,000 00,000 0,000-0,000 6,000 6,000 00,000,000 56,000 -,00 77,600 00,000 86,00,600-5,0 5,560 00,000 5,80 8,60-59,6 0,76 5a 00,000,0 68,896-67,558, 5b 550,000-6,656 8,66 568,66 MV 5 BV 5 = 0 6, , ,66 CHAPTER 6 ATCF analysis with MARR AT = % EOY 0 5a 5b ATCF -,50,000 6,000 77,600 5,560 0,76, 568,66 PW(%) = -,50, ,000(P/F, %, ) + 77,600(P/F,%, ) + 5,560(P/F, %, ) + 0,76(P/F, %, ) + (, + 568,66)(P/F, %, 5) = - $8,8 < 0 reject! CHAPTER 6 6

17 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 $,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 50% 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 0% per year, and the effective income tax rate is 0%. CHAPTER 6 Option A Purchase Copier EOY BTCF R=0. d TI t= -0. Tax ATCF a b CHAPTER 6 7

18 Option A Purchase Copier EOY 0 5a 5b ATCF AW(0%) = [ (P/F,0%,) +0(P/F,0%,) +9(P/F,0%,) +06(P/F,0%,) +(+96)(P/F,0%,5)](A/P,0%,5) = - 075(A/P,0%,5) = CHAPTER 6 5 Option B Rent (lease) Copier EOY BTCF d TI t = -0. Tax ATCF a 60 5b CHAPTER 6 6 8

19 Option B Rent (lease) Copier EOY 0 5a 5b ATCF AW (0%) = -500(A/P,0%,5) + 500(P/F,0%,5) 50 = Option B (lease) is the least cost alternative for having the coppier CHAPTER 6 7 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,0%,5) (A/F,0%,5) + L t x L say L = before tax leasing cost 0.6 L = (A/P,0%,5) 500 (A/F,0%,5) L = 69 (if before tax leasing cost is greater than 69, purchasing option will be preferred) CHAPTER 6 8 9