ISE 2014 Sections

Transcription

1 ISE 2014 Sections Notation: INCOME TAX REPRESENTS A SIGNIFICANT CASH OUTFLOW THAT WE CANNOT IGNORE! Rk = gross revenues in year k Ek = operating expenses in year k plus interest paid on borrowed capital dk = depreciation allowance for year k t = effective income tax rate used for computing income taxes Tk = income tax liability for year k 1

2 Comparison of before and after tax cash flow diagrams Typical before-tax CFD: Typical after-tax CFD: 2

3 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 = Equation (6-16) 1 effective income tax rate, t Example: Suppose the before-tax MARR = 20% and t = 40%. What is the approximate after-tax MARR? Solving Equation. (6-16) for the after-tax MARR, MARR BT = MARR 1 t AT 0.20 = MARR AT MARR AT = 3

4 If we are interested in the effect of both federal and state income taxes, the following equation is used to determine t. t = state rate + federal rate (1 state rate) (6-19) This equation holds true for the common case in which taxable income is computed the same way for both taxes, except that state taxes are deductible from taxable income for federal tax purposes but federal taxes are not deductible from taxable income for state tax purposes. Example Suppose the federal tax rate is 34% and that the state tax rate is 6%. What is the effective income tax rate? Federal Rate = 34% State Rate = 6% t = (1 0.06) = or 38% 4

5 After-Tax Cash Flow Analysis (Fig 6-5) EOY (A) BTCF (B) d k (C)=(A)-(B) TI or NIBT (D)=-t(C) T k (E)=(A)+(D) ATCF 0 -I I : N R 1 -E 1 R 2 -E 2 R 3 -E 3 : R N -E N N MV N --- MV N - BV N -t(mv N -BV N ) MV-t(MV N -BV N ) 5

6 When an asset is disposed of for more(less) than its book value, the resulting gain(loss) is taxed. (Refer to last row in Figure 6-5) Depreciation recapture and capital gains (losses) are taxed as ordinary income. In the past, the capital gains tax rate was different from that of ordinary income. Capital Gain (Loss) = MV BV If an asset is sold for less than its current book value (MV < BV), it is termed a capital loss, and taxes on the loss represent a tax credit. 6

7 Chapter 6 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% MACRS recovery period 5 years Question: Is this a worthwhile investment after taxes? Side Question: What is the approximate before-tax MARR? MATT MARRAT 0.15 = = Equation t BT = 7

8 Chapter 6 Example Continued EOY k BTCF k d k TI k Income Tax (t = 0.4) ATCF 0 -$10, $10, ,000 $2,000 $2, , ,000 3, ,000 1,920 2, a 4, ,424-1, b 5, ,696-1,078.4 PW(15%) = - $10,000 + $3,200(P/F,15%,1) + $3,680(P/F,15%,2) + $3,168(P/F,15%,3) + ($2, $3,921.6) (P/F,15%,4) = $ 8

9 Chapter 6 Example Continued What are the values of the following? ATCF 3 = NIAT 3 = Show how the following values were calculated: d 4 = Capital Related Gain in Year 4 = 9

10 Another Chapter 6 Example An asset having an investment cost of $500,000 is expected to produce a net annual cash flow of $300,000 each year for 4 years. No salvage value is expected. This asset qualifies for a 3-year MACRS recovery period. The after-tax MARR is 30% and the effective income tax rate is 40%. 1. Is this investment profitable on an after-tax basis? 2. Is this investment profitable on a before-tax basis? Use Equation (7-16) to approximate the before-tax MARR. 10

11 Ch. 6 Example 2 Continued Depreciation Amounts: After-tax Cash Flows: Year MACRS Rate dk $166, , , ,050 d k Taxable Income Year BTCF k = Tax Liability ATCF k = R k - E k TI k =(R k -E k - d k ) T K =-0.4(TI k ) BTCF k +T k 0 -$500, $500, ,000 $133,350-53, , ,000-31, , , , , ,

12 Ch 6. Example 2 After-tax CFD PW(30%) = - $500,000 + $246,660(P/F,30,1) + $268,900(P/F,30,2) + $209,620(P/F,30,3) + $194,820(P/F,30,4) = $ PW(MARRAT ) < or > 0 12

13 Chapter 6 Example 2 Continued Before-Tax Evaluation MATT MARR 1 t = = AT BT = = 0.5 or 50% AW(50%) = - $500,000(A/P,50,4) + $300,000 = AW(MARRBT ) < or > 0 13

14 Section 6.11 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 MACRS 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%. 14

15 Option A Purchase Copier Investment = $5,000 MV 5 = $1,000 MACRS recovery period = 5 years EOY BTCF d TI Tax ATCF 0 -$5, $5, $1,000 -$1,000 $ ,600-1, , d 5 = (0.1152)($5,000)(0.5) = $ BV 5 = $ ($1,000 + $1,600 + $960 + $576 + $288) = $ Capital Related Gain at EOY 5 =? PW(10%) = - $5,000 + $400(P/F,10,1) + $640(P/F,10,2) + $384(P/F,10,3) + $230.4(P/F,10,4) + ($ $830.4)(P/F,10,5) = - $ AW(10%) = - $ (A/P,10,5) = - $ 15

16 Option B Rent (lease) Copier Rent = $900 / year Deposit = $500 (returned at EOY 5) EOY BTCF d TI Tax ATCF 0 -$ $ $900 $ AW(10%) = - $500(A/P,10,5) - $540 + $500(A/F,10,5) = - $ Based on the annual equivalent of the after-tax cash flows, the copier is the minimum cost alternative. Note: In general, After-tax cost of lease = Leasing Cost (1 - t) = $900 (1-0.4) = $540 16

17 Lease vs. Purchase Example Continued Over what range of before-tax leasing costs would you choose the purchase option based on an after-tax analysis? Let X = before-tax annual leasing cost of computer After-tax cost of lease = X (1-0.4) = 0.6X AW(10%) purchase = - $811 AW(10%) lease = - $500(A/P,10,5) - 0.6X + $500(A/F,10,5) AW purchase = AW lease - $811 = - $50-0.6X X = $ 17

18 Section 6.11 After-tax Breakeven Analysis Example Given the following: Investment cost $100,000 Study period 5 years Market value at EOY 5 $ 20,000 MACRS recovery period 7 years Effective income tax rate 40% After-tax MARR 15% What must be the value of the annual BTCF (R - E) for this project to be profitable when income taxes are considered and an after-tax return of 15% is desired on the investment? 18

19 After-tax Breakeven Analysis Example Continued EOY BTCF d TI Tax ATCF 0 -$100, $100,000 1 X $14,290 X-14, X+5, X+5,716 2 X 24,490 X-24, X+9, X+9,796 3 X 17,490 X-17, X+6, X+6,996 4 X 12,490 X-12, X+4, X+4,496 5 X 4,465 X-4, X+1, X+1, , ,775 2,710 22,710 Notes: R - E = X TI k = X - d k 19

20 After-tax Breakeven Analysis Example Continued d 5 = $100,000(0.0893)(0.5) = $ BV 5 = $100,000 - ($14,290 + $24,490 + $17,490 + $12,490 + $4,465) = $ TI 5 = MV 5 - BV 5 = $20,000 - $26,775 = - $ PW(15%) = 0 = - $100, X(P/A,15,5) + $5,716(P/F,15,1) +$9,976(P/F,15,2) + $6,696(P/F,15,3) +$4,496(P/F,15,4) + ($1,786 + $22,710)(P/F,15,5) 68,273 = 0.6X (3.3522) X = $ 20

21 Problem 6-35 Problem Statement Given: Investment cost = $50,000 Savings (R-E) = $14,000 per year for N years No MV at any time (specially designed machine) Straight Line Depreciation for 5 years Effective Income Tax Rate = 40% After-tax MARR = 10% Find: The minimum number of years your firm could operate the equipment to earn 10% after taxes on this investment. 21

22 Problem 7-35 Solution EOY BTCF d TI Tax ATCF 0 -$50, $50, ,000 $10,000 $4,000 -$1,600 12, ,000 10,000 4,000-1,600 12, ,000 10,000 4,000-1,600 12, ,000 10,000 4,000-1,600 12, ,000 10,000 4,000-1,600 12, , ,000-5,600 8,400 14, ,000-5,600 8,400 14, ,000-5,600 8,400 N 14, ,000-5,600 8,400 Let X = N-5 years (assumes N 5) and Solve for X: PW(10%) = 0 = -$50,000+$12,400(P/A,10%,5) +{$8,400(P/A,10%,X)(P/F,10%,5)} Solving for (P/A,10%,X) = From Tables, X ; therefore, N = 22