ESTIMATING CFs. C t (1 % k) t & C 0. NPV j. Need ATCFs to implement NPV (IRR or PI) O Accounting Profits ATCF (NIAT)

Transcription

1 ESTIMATING CFs O NPV j n i 1 C t (1 % k) t & C 0 Need ATCFs to implement NPV (IRR or PI) O Accounting Profits ATCF (NIAT) O ATCF = cash inflow - cash outflow Important to estimate CF after taxes. Discount rates will be on after-tax return basis. Record CFs only when they occur, not when work is done or liability is incurred.

2 Expansion Project independent investment decision Replacement Project mutually exclusive choice O Important to account for all incremental CFs Year Old New N-0 k = 10% 0 0 (7,000) (7,000) 1 5,000 10,000 5, ,000 11,000 6, ,000 10,000 6,000 Could calculate NPVs of old and new and compare NPV 0 = 5,000(PV 10,1 ) + 5,000(PV 10,2 ) + 4,000(PV 10,3 ) = $11, NPV N = 10,000(PV 10,1 ) + 11,000(PV 10,2 ) + 10,000(PV 10,3 ) - 7,000 = $18, Choose new because you are NPV N - NPV 0 = 18, , = $7, better off

3 Alternatively, we could work with incremental CFs the new investment provides. NPV N-0 = 5,000(PV 10,1 ) + 6,000(PV 10,2 ) + 6,000(PV 10,3 ) - 7,000 = $7, O NPV N-0 = NPV N - NPV 0 Advantages of incremental CF method: Q Q Less calculations CFs common to bottle investments can be ignored Suppose you need a pickup to operate your farm and are considering replacing your old pickup. Old New Cash Inflow 720, ,000 Cash Out Purchase Fuel/yr Dep/yr Repair/yr 0 3, ,000 15,000 2,000 3,

4 WHAT ARE INCREMENTAL CASH FLOWS? # Include all additional incremental cash flows # Include incidental effects # Sunk costs I can't abandon this project because I've invested too much in it already. There is no sense continuing with this investment because I will never get back the money I've already invested. # Overhead costs

5 # Opportunity cost of resources Include opportunity cost even if no cash is exchanged. Suppose you build a cattle lot land you already own. If you don't build the feedlot you could sell the land for $20,000. Wrong: Before After CF own land take project own land 0 Correct: Before After CF own land take project own land 0 don't take sell land 20,000 # Net Working Capital (NWC) - CA - CL Incremental CF = (20,000) from taking project Used to adjust accrual net income to ATCF? NWC =? CA -? CL Important CA: Cash, AR, Inv Important CL: A/P, Accruals? NWC > (<) ) implier cash (outflow) inflow Assume accural

6 HOW TO DEAL WITH INFLATION # Inflation general rise in the price of goods and services # Interest rates quoted in nominal terms that include the effects of inflation # Real rates remove inflation effects # Nominal interest rates and rates of return are used to calculate our discount rates (k) # Since k includes inflation effects we need to include inflation in our estimates of future cash flows to be consistent # Possible to work in real CFs and real discount rates # May not be able to inflate CFs using a single inflation rate sales prices labor costs input costs depreciation expenses All may have different inflation rates

7 O Initial Investment THREE STAGES OF CASH FLOWS (RTA APPROACH) Q Q Q Buy new asset Sell old asset Taxes on sale O Operating CFs? ATCF i =? R i (1 - t) -? E i (1 - t) +? Dep i t -? NWC i O Terminal Value Q Q Q Q Sell new asset Taxes on sale Lost sale of old asset Tax on sale of old asset

8 O Sell new asset in terminal period Y inflow O Taxes on sale Y capital gain creates tax liability O Lost sale of old asset (MV - BV)t = tax liability Y outflow Y capital loss generate tax savings (BU - MV)t = tax savingsy inflow Important to account for the opportunity cost of the old asset if it is replaced and sold in the initial phases of the new project. i = 0 Y cash inflow gained by selling the old asset i = n Y cash inflow lost by selling old asset at i = 0

9 Example: Suppose you are considering the purchase of a new car to replace your old car. New Old MV 0 10,000 6,000 (MV today) MV 3 5,000 2,000 (MV in 3 yrs) What is the incremental cost of a new car? (k = 10%) I: 10,000-6,000 = $4,000 TV: 5,000-2,000 = $3,000 8 lost sale of old asset PV = 3000(PVIF 10,3 ) - 4,000 = -$1,746.06

10 Lost sale of old asset decreases T.V. (as long as it is a positive value) O Taxes on lost sale tax liability 6 8 TV tax savings 6 8 TV (reduces value of lost sale) (increase value of lost sale) e.g. MV T = 20,000 BV T = 15,000 t = 40% MV T - BV = 20,000-15,000 = 5,000 tax liability = 5000(.4) = 2000 Effect on TV CF Lost Sale 9 TV : (20,000) Tax Liab 8 TV : 2,000 Net Impact (18,000)

11 LAWN CARE COMPANY Suppose you are considering starting a lawn care and snow removal service to help pay your way through college. You plan to operate the business for the next 4 years. You will need to buy snowblowers, lawnmowers, and other equipment that will cost a total of $40,000. The equipment falls into the MACRS 3-year class (25, 37.5, 25, 12.50) and has expected market value after 4 years of $10,000. You plan to charge $40 per service for both lawn care and snow removal. Your expense (labor, fuel, maintenance) will average $18 per service. You have done some market research and project the number of services each of the next 4 years to be Year Number Services ,000 Starting at the end of the first year, you estimate you will need to hold $1,000 in inventory, which will be fully recovered at the end of year 4. Your marginal tax rate and capital gains tax rates are 20%, and you can earn 12% after taxes on funds that you invest elsewhere. Should you start the business?

12 P Initial Investment Buy new equipment $40,000 Initial equity investment $40,000 The total investment to start the business is $40,000. P Operating Cash Flows Year? R? E? Dep? NWC 1 $20,000 $9,000 $10,000 $1, ,000 13,500 15, ,000 16,200 10, ,000 18,000 5,000 -$1,000 Now we can calculate the ATCFs as follows, ATCF 1 = $20,000(1-.2) - $9,000(1-.2)+$10,000(.2) - $1,000 = $9,800 ATCF 2 = $30,000(1-.2) - $13,500(1-.2)+$15,000(.2) - $0 = $16,200 ATCF 3 = $36,000(1-.2) - $16,200(1-.2)+$10,000(.2) - $0 = $17,840 ATCF 4 = $40,000(1-.2) - $18,000(1-.2)+$ 5,000(.2) + $1,000 = $19,600

13 P Terminal Value Sell equipment $10,000 Taxes on sale (2,000) Terminal Cash Flow $ 8,000 Capital gain = $10,000 - $0 = $10,000 Taxibility = $10,000(.2) = $2,000 P Net Present Value NPV = $9,800(PVIF 12,1 ) + $16,200(PVIF 12,2 ) + $17,840(PVIF 12,3 ) +($19,600 + $8,000)(PVIF 12,4 ) - $40,000 = $11,903

14 DOUGHNUT EXAMPLE Suppose you bought a doughnut machine 3 years ago for $90,000. You are depreciating the machine over 5 years using the MACRS method. You expect the market value of the machine 5 years from today to be $10,000. The machine generates $30,000 in cash revenues and produces $15,000 in cash expenses each year. If you sold the machine today you could get $30,000 from a local competitor. A salesman for a "new and improved" doughnut machine has just stopped by and tried to sell you a new machine which will increase your cash revenues to $45,000 each year and decrease your cash expenses to only $10,000 each year. The new machine costs $90,000 and will require $10,000 for delivery and installation costs. The machine will fall into the MACRS five depreciation class (15, 25.5, 17.85, 16.66, 16.66, 8.33). You would sell the machine after 5 years for $40,000. In addition, because of the increase in sales the new machine would require you to buy $5,000 of additional inventory and also increase accounts payable by $2,000. The change in net working capital is estimated to occur at the end of the first year and will be fully recovered at the end of the last year of the project s life. If your cost of capital is 10%, your marginal tax rate is 40%, and the capital gain tax rate is 20%, should you purchase the new machine? Assume capital losses can be used to offset ordinary income.

15 DOUGHNUT EXAMPLE MV -3 = $90,000 Old MV 0 = 30,000 MV 0 = $100,000 MACRS 5 yrs (15, 25.5, 17.85, 16.66, 16.66, 8.33) New MACRS(5 year) (15, 17.85, 16.66, 16.66, 8.33) MV 5 =$10,000 MV 5 = $40,000 CR 1-5 = $30,000 CR 1-5 = 45,000 CE 1-5 = 15,000 CE 1-5 = 10,000 t = 40% t g = 20% 8 INV 1 = $5,000 9 INV 5 = $5,000 k = 10% 8 A/P 1 = $2,000 9 A/P 5 = $2,000 t = 40% t g = 20% k = 10%

16 # Initial Investment Buy New $100,000 Sell Old (30,000) Tax Savings (2,994) Initial Investment $67,006 BV = $90,000 - (.5835)(90,000) = $37,485 Capital Loss = $37,485 - $30,000 = $7,485 Tax Savings = $7,485(.4) = $2,994

17 # Operating CFs Year Dep. New Dep. Old? Dep 1 $15,000 $14,994 $ ,500 14,974 10, ,850 7,497 10, , , , ,660 Year? R? E? Dep? NWC 1 $15,000 $-5,000 $ 6 $ 3, ,000-5,000 10, ,000-5,000 10, ,000-5,000 16, ,000-5,000 16,660-3,000? ATCF i =? R i (1 - t) -? E(1-t) +? Dep i (t) -? NWC i ATCF 1 = $15,000(1 -.4)-($-5,000)(1-.4)+6(.4)-3,000 =$ 9, ATCF 2 = $15,000 (1-.4)-($-5,000)(1-.4)+$10,506(.4)-0 =$16, ATCF 3 = $15,000 (1-.4)-($-5,000)(1-.4)+$10,353(.4)-0 =$16, ATCF 4 = $15,000 (1-.4)-($-5,000)(1-.4)+$16,660(.4)-0 =$18,664 ATCF 5 = $15,000 (1-.4)-($-5,000)(1-.4)+$16,660(.4)-0 =$21,664

18 # Terminal Value Sell New Machine $40,000 Tax on Sale (6,334) Lost Sale (10,000) Lost Tax Liability 2,000 Terminal Value $25,666 Tax Implication of New Machine BV = $100,000 - $91,670 = $8,330 Capital gain = $40,000 - $8,330 = 31,670 x.2 Tax liability $6,334 Tax Implications of Old Machine Lost capital gain = $10,000 - $0 = $10,000 Lost tax liability = $10,000(.20) = $2,000 NPV = $9,002.40(PVIF 10 )+$16,204.20(PVIF 10,2 )+$16,141.20(PVIF 10,2 ) +$18,664(PVIF 10,4 )+($21,664+$25,666)(PVIF 10,5 )- $67,006 = $8,831.51

19 ADVANCED DOUGHNUT MACHINE EXAMPLE Suppose you bought a new doughnut machine 3 years ago for $90,000. You are depreciating the machine over 8 years using straight line depreciation toward a salvage value of $10,000. You actually expect the value of the machine to be $20,000 in 5 years. During the last year the machine produced $40,000 in revenues and generated $25,000 in expenses (cost of goods sold and operating expenses). If you sold the machine today you could get $40,000 from a local competitor. A salesman for a "new and improved" doughnut machine has just stopped by and tried to sell you a new machine. The machine can produce a wider variety of doughnuts that will allow you to expand revenues by 30% over those produced by the old machine. In addition, the new machine is more efficient than the old machine and so projected expenses will only be 20% higher than those produced by the old machine. The new machine will cost $90,000 and will require $10,000 for delivery and installation costs. The machine will fall into the MACRS 5 year depreciation class (20, 32, 19.2, 11.52, 5.76). You would sell the machine after 5 years for $40,000. Assume that any proceeds from selling the machines after 5 years of operating will be received during year 6. In the past you have required current assets (Cash, A/R, Inventory) to be maintained at a level of approximately 10% of sales. Likewise current liabilities (accounts payable and accruals) have been at a level of approximately 8% of expenses. You expect these proportions to remain the same if the new machine is purchased.

20 You are anticipating that revenues and expenses will both show a real growth rate of 10% per year regardless of whether the new machine is purchased. In addition, the expected rate of inflation during the next five years is 4% per year. If your cost of capital (what you can earn somewhere else for the same level of risk) is 15% and your marginal tax rate is 40% on ordinary income and 20% on capital gains or losses should you purchase the new machine?

21 O Summarize Information Old Asset New Asset MV -3 = pp = $90,000 S.L. Dep (8 yrs) MACRS(20, 32, 19.2, 11.52, 5.70) SV 5 = 10,000 MV 5 = 20,000 MV 6 = $40,000 R 0 = $40,000 E 0 = $25,000 R 0 = $40,000(1 +.30) = $52,000 E 0 = $25,000(1 +.20) = $30,000 MV 0 = $40,000 MV 0 = $100,000 CA i =. 10 R i CL i =.08E i CA i =.10R i CL i =.08E i R j = (1 +.10)(1 +.04) R i-1 E i = (1 +.10)(1 +.04) E i-1 R j = (1 +.10)(1 +.04) R i-1 E i = (1 +.10)(1 +.04) E i-1 k = 15% t = 40% t g = 20%

22 DEP old = 90,000 & 10,000 8 = 10,000/yr O Depreciation Year Old Asset New Asset? Dep 1 $10,000 $20,000 10, ,000 32,000 22, ,000 19,000 9, ,000 11,520 1, ,000 11,520 1, ,760 5,760 Initial Investment Buy new machine = $100,000 Sell old machine = (40,000) Tax on sale = (4,000) savings C 0 $56,000 MV 0 = 40,000 BV 0 = 90,000 - (3x10,000) = 60,000

23 Loss = BV - MV = 60,000-40,000 = 20,000 Tax Savings = 20,000 (.2) = 4,000

24 O Operating CFs? R 1 = 52,000 (1.10) (1.04) - 40,000 (1.10) (1.04) = $13,728? R 2 = 52,000 (1.10) 2 (1.04) 2-40,000 (1 +.10) 2 (1.04) 2 = $15,705!? E 1 = 30,000 (1.10) (1.04) - 25,000 (1.10) (1.04) = $5,720? E 2 = 30,000 (1.10) 2 (1.04) 2-25,000(1.10) 2 (1.04) 2 =$6,544!? Dep 1 = $20,000 - $10,000 = $10,000? Dep 2 = $37,000-10,000 = $22,000! NWC - one time changes Year NWC N - NWC 0 NWC N NWC !

25 (1.10) (1.04) 9 NWC N 1 52,000(1.144)(.10)&30,000(1.44)(.08) 3203 NWC ,000(1.144)(.10)&25,000(1.44)(.08) 2288

26 Year? R? E? Dep? NWC 1 $13,728 $5,720 $10,000 $ ,705 6,544 22, ,966 7,486 9, ,553 8,564 1, ,513 9,797 1, ,567? ATCF =? R(1 - t) -? E(1 - t) +? Dep(t) -? NWC Year ATCF 1 $13,728(1 -.4) - $5,720(1 -.4) + $10,000(.4) - $915 = $ 7, ,705(1 -.4) - 6,544(1 -.4) + 22,000(.4) = 14, ,966(1 -.4) - 7,486(1 -.4) + 9,200(.4) = 9, ,553(1 -.4) - 8,564(1 -.4) + 1,520(.4) = 7, ,513(1 -.4) - 9,797(1 -.4) + 1,520(.4) = 8, ,567 = 1,567

27 Terminal Value (yr. 6) Sell new machine $40,000 Tax on sale (6,848) Lost sale of old (20,000) Tax on sale of old 2,000 TV 15,152 MV N 40,000 MV 0 20,000 BV N 5,760 BV 0 10,000 Gain 34,240 Gain 10,000 (.2) (.2) Tax Liab 6858 Tax Liab 2000 Analysis NPV 7890 (1.15) % (1.15) 2 % 9817 (1.15) 3 % 7629 (1.15) 4 % % % & 56,000 5 (1.15) (1.15) 6 = 37,817-56,000 = -$16,087