STRAIGHT-LINE (SL) METHOD
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1 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 = 1, 2,..., N d k * = cumulative depreciation through year k. d k * = k x d k BV k = B - d k * CHAPTER 5 1
2 DECLINING BALANCE (DB) METHOD Annual depreciation is a constant percentage of the asset's value at the BOY R = 2/N 200% declining balance R = 1.5/N 150% declining balance d 1 = B x R d k = B(1-R) k-1 (R) = BV k-1 (R) d k * = B[1 - (1 - R) k ] BV k = B(1 - R) k BV N = B(1 - R) N CHAPTER 5 2
3 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 200% 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 3
4 Cost basis: B = $10,000 + $85,000 = $95,000 trade-in value cash-cost SV 10 Deduction amounts are fixed for SL: d k 95,000-5, $9,000 for k 1to10 N Deduction ratios are fixed for DB: 2 R 0.2, thus,(dk 0.2 BVk- 1) % DB CHAPTER 5 4
5 Straight Line Method (k = 1 to 4) EOY, k d k BV k , ,000 86,000 = 95,000 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 5 5
6 Straight Line Method (k = 5 to 10) EOY, k d k BV k 5 9,000 50,000 = 59,000 9, ,000 41,000 = 50,000 9, ,000 32,000 = 41,000 9, ,000 23,000 = 32,000 9, ,000 14,000 = 23,000 9, ,000 5,000 = 14,000 9,000 SV 10 = B N x d k CHAPTER 5 6
7 200% Declining Balance Method (k = 1 to 4) EOY, k d k BV k , ,000 76, ,200 60, ,160 48, ,728 38,912 d 1 = BV 0 x R = B x 0.2 = 95,000 x 0.2 = 19,000 BV 1 = BV 0 d 1 = B d 1 = 95,000 19,000 BV 4 = B d 4 * d 4 * = 19, ,728 = 56,088 d 4 = 48,640 x 0.2 CHAPTER 5 7
8 200% Declining Balance Method (k = 5 to 10) EOY, k d k BV k 5 7,782 31, ,226 24, ,981 19, ,985 15, ,188 12, ,550 10,200 BV 10 = B d 10 * = BV 9 d 10 CHAPTER 5 8
9 SL vs. DB CHAPTER 5 9
10 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 10
11 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) CHAPTER 5 11
12 General Tax Procedure - Example You invested $113,028 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 12
13 Solution to (a), (b) and (c) d = 113,028 / 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 $11,218 (1 t)(r E d) (+) Depreciation 11,303 (c) ATCF $22,521 (1 t)(r E d)+d CHAPTER 5 13
14 Solution to part (d) AW (15%) = ATCF 113,028 (A/P, 15%, 10) = 22,521 22,521 = $0 CHAPTER 5 14
15 Typical Before-Tax Cash Flow Diagram: Typical After-Tax Cash Flow Diagram: CHAPTER 5 15
16 After-Tax Cash Flow Analysis CHAPTER 5 16
17 After-tax MARR To perform an after-tax evaluation of a project's after-tax cash flows, we must use an after-tax MARR. Aftertax MARR 1- effective income tax rate, tax MARR Before - t Example: Suppose the before-tax MARR = 20% and t = 40%. What is the approximate after-tax MARR? MARR BT MARR 1- t AT MARR AT 0.2 (1-0.4) 0.12 CHAPTER 5 17
18 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 18
19 Step 1: Find depreciation amounts for the study period of 4 years: d k 10, $2,000 for k 1to5 EOY, k d k BV k CHAPTER 5 19
20 Step 2: 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 20
21 Step 3: Use the ATCF to evaluate this MARR = 15%: After-tax cash flow diagram: PW(15%) = 10, ,200 (P/A, 15%, 3) + 7,000 (P/F, 15%, 4) = + $1,309 CHAPTER 5 21
22 Affordable Investment - Example An asset purchased at the price of (I), and it is depreciated for 10 years, with straight line method. Estimated market EOY 10 is zero, how much can you afford to purchase this asset when it produces annual $30,000 net income for 10 years. Effective income tax is 40% and MARR AT = 15%. CHAPTER 5 22
23 Solve for I? d = (I 0) / 10 ATCF = (30000 d) AW(15%) = I(A/P,15%,10) (1 0.4) (I/10) AW(15%) = 0 I = 30000(1 0.4) / ((A/P,15%,10) 0.04) I = $113, CHAPTER 5 23
24 Non-depreciable asset - Example Construction cost of the facility $600,000 Purchasing cost of land $550,000 Annual gross income $230,000 Operating expenses per year $30,000 Facility will be depreciated for 5 years, using 200% DB MARR AT 12% 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 24
25 200% DB R = 2/5 = 0.4 EOY, k d k BV k , , , , , , , ,840 77, ,104 46,656 cost basis for only depreciable asset 600,000 x , ,000 BV 5 MV 5 = 0 CHAPTER 5 25
26 ATCF analysis with t = EOY 0 BTCF -1,150,000 d TI Tax ATCF -1,150, , ,000-40,000 16, , a 200, , , , ,000 56,000-22, ,600 86, ,600-45, ,560 51, ,160-59, ,736 31, ,896-67, ,442 5b 550,000-46,656 18, ,662 MV 5 BV 5 = 0 46, , ,662 CHAPTER 5 26
27 ATCF analysis with MARR AT = 12% EOY a 5b ATCF -1,150, , , , , , ,662 PW(12%) = - 1,150, ,000(P/F, 12%, 1) + 177,600(P/F,12%, 2) + 154,560(P/F, 12%, 3) + 140,736(P/F, 12%, 4) + (132, ,662)(P/F, 12%, 5) = - $218,283 < 0 reject! CHAPTER 5 27
28 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 5 28
29 Option A Purchase Copier EOY BTCF R=0.3 d TI t= -0.4 Tax ATCF a b CHAPTER 5 29
30 Option A Purchase Copier EOY ATCF a 144 5b 936 AW(10%) = [ (P/F,10%,1) +420(P/F,10%,2) +294(P/F,10%,3) +206(P/F,10%,4) +( )(P/F,10%,5)](A/P,10%,5) = (A/P,10%,5) = CHAPTER 5 30
31 Option B Rent (lease) Copier EOY BTCF d TI t = -0.4 Tax ATCF a b CHAPTER 5 31
32 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 32
33 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 = 1269 (if before tax leasing cost is greater than 1269, purchasing option will be preferred) CHAPTER 5 33
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