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# Problems in Financial Management Fin 526

WSU

GPA 3.79

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This 29 page Class Notes was uploaded by Zechariah Gerlach on Thursday September 17, 2015. The Class Notes belongs to Fin 526 at Washington State University taught by Staff in Fall. Since its upload, it has received 82 views. For similar materials see /class/205954/fin-526-washington-state-university in Finance at Washington State University.

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Date Created: 09/17/15

CHAPTER 18 Does Debt Policy Matter Answers to Practice Questions 9 a The two rms have equal value let V represent the total value of the rm Rosencrantz could buy one percent of Company B s equity and borrow an amount equal to 001 X DA D3 0002v This investment requires a net cash outlay of 0007V and provides a net cash return of 001 X Pro ts 0003 X rf x V where rf is the riskfree rate of interest on debt Thus the two investments are identical Guildenstern could buy two percent of Company A s equity and lend an amount equal to 002 X DA D3 0004V This investment requires a net cash outlay of 0018V and provides a net cash return of 002 X Pro ts 0002 X rf x V Thus the two investments are identical The expected dollar return to Rosencrantz original investment in A is 001 X C 0003 X rf gtlt VA where C is the expected pro t cash ow generated by the rm s assets Since the rms are the same except for capital structure C must also be the expected cash ow for Firm B The dollar return to Rosencrantz alternative strategy is 001 X C 0003 X rf gtlt VB Also the cost ofthe original strategy is 0007VA while the cost ofthe alternative strategy is 0007VB If VA is less than VB then the original strategy of investing in Company A would provide a larger dollar return at the same time that it would cost less than the alternative Thus no rational investor would invest in Company B if the value of Company A were less than that of Company B 181 When a rm issues debt it shifts its cash flow into two streams MM s Proposition l states that this does not affect rm value ifthe investor can reconstitute a firm s cash ow stream by creating personal leverage or by undoing the effect ofthe rm s leverage by investing in both debt and equity It is similar with Carruther s cows lfthe cream and skim milk go into the same pail the cows have no special value lfan investor holds both the debt and equity the rm does not add value by splitting the cash flows into the two streams In the same vein the cows have no special value if a dairy can costlessly split up whole milk into cream and skim milk Firm borrowing does not add value if investors can borrow on their own account Carruther s cows will have extra value if consumers want cream and skim milk and if the dairy cannot split up whole milk or if it is costly to do so a The market price ofthe stock is not affected by the announcement b Since the market price of the shares is 10 the company can buy back 160 million10 16 million shares c After the change in capital structure the market value of the firm is unchanged Equity Debt 9 million x 10 160 million 250 million d After the change in structure the debt ratio is DebtDebt Equity 160 million250 million 064 e No one gains or loses See the answer to the next question a The market value of the firm s equity increases by 30 million the amount of the decrease in the market value of the rm s existing debt Therefore the price ofthe stock increases to 150 million 30 million15 million shares 12 b Since the market price of the shares is 12 the company can buy back 60 million12 5 million shares c After the change in capital structure the market value of the firm is unchanged Equity Debt 10 million x 12 130 million 250 million 182 d After the change in structure the debt ratio is DebtDebt Equity 130 million250 million 052 e The investors in the existing debt lose 30 million while the shareholders gain this 30 million The value of each share increases by 30 million15 million shares 2 The company cost of capital is rA 08 x 012 02x 006 0108 108 Under Proposition I this is unaffected by capital structure changes With the bonds remaining at the 6 defaultrisk free rate we have DebtEquity Ratio E m 000 0108 0108 010 0113 0108 050 0132 0108 100 0156 0108 200 0204 0108 300 0252 0108 See figure on next page This is not a valid objection MM s Proposition ll explicitly allows for the rates of return for both debt and equity to increase as the proportion of debt in the capital structure increases The rate for debt increases because the debtholders are taking on more of the risk of the rm the rate for common stock increases because ofincreasing financial leverage See Figure 182 and the accompanying discussion 183 Rates of Return 250 rE 200 150 108 FA 060 rD 1 2 3 Debt Equity 184 a Under Proposition l the firm s cost of capital rA is not affected by the choice of capital structure The reason the quoted statement seems to be true is that it does not account for the changing proportions of the rm nanced by debt and equity As the debtequity ratio increases it is true that both the cost of equity and the cost of debt increase but a smaller proportion ofthe rm is nanced by equity The overall effect is to leave the rm s cost of capital unchanged b Moderate borrowing does not significantly affect the probability of nancial distress but it does increase the variability and market risk borne by stockholders This additional risk must be offset by a higher average return to stockholders a lfthe opportunity were the rm s only asset this would be a good deal Stockholders would put up no money and therefore would have nothing to lose However rational lenders will not advance 100 of the asset s value for an 8 promised return unless other assets are put up as collateral Sometimes rms find it convenient to borrow all the cash required for a particular investment Such investments do not support all of the additional debt lenders are protected by the rm s other assets too In any case if rm value is independent of leverage then any asset s contribution to rm value must be independent of how it is nanced Note also that the statement ignores the effect on the stockholders of an increase in financial leverage b This is not an important reason for conservative debt levels So long as MM s Proposition l holds the company s overall cost of capital is unchanged despite increasing interest rates paid as the firm borrows more However the increasing interest rates may signal an increasing probability of financial distress and that can be important Examples of such securities are given in the text and include unbundled stock units preferred equity redemption cumulative stock and oatingrate notes Note that in order to succeed such securities must both meet regulatory requirements and appeal to an unsatisfied clientele 185 a As leverage is increased the cost of equity capital rises This is the same as saying that as leverage is increased the ratio of the income after interest which is the cash ow stockholders are entitled to to the value of equity increases Thus as leverage increases the ratio of the market value of the equity to income after interest decreases b i Assume MM are correct The market value ofthe rm is determined by the income of the firm not how it is divided among the firm s security holders Also the rm s income before interest is independent of the firm s financing Thus both the value of the rm and the value ofthe rm s income before interest remain constant as leverage is increased Hence the ratio is a constant ii Assume the traditionalists are correct The firm s income before interest is independent of leverage As leverage increases the rm s cost of capital rst decreases and then increases as a result the market value ofthe firm rst increases and then decreases Thus the ratio of the market value ofthe rm to rm income before interest rst increases and then decreases as leverage increases We begin with rE and the capital asset pricing model rE rf 3E rm rf 010 15 018 010 022 220 Similarly for debt I39D H Ho I39m Ff 012 010 39 018 010 39 025 Also we know that l r 7x r1rixrWO5gtltO1205gtlt022017170 A KDE D t D E E To solve for Lu use the following D X E BA 30 m X 3E05gtlt02505gtlt15O875 186 20 21 We know from Proposition I that the value of the rm will not change Also because the expected operating income is unaffected by changes in leverage the rm s overall cost of capital will not change In other words rA remains equal to 17 and 1A remains equal to 0875 However risk and hence the expected return for equity and for debt will change We know that rD is 11 so that for debt I39D rf 50 I39mFf 011 010 19 018 010 D0125 Forequity D E r7xr xr A DE D DE E 017 03 X 011 07 X rE rE 0196 196 Also I39E H E I39m Ff 0196 010 0E 018 010 0E 120 Note In the following solution we have assumed that 200 million oflongterm bonds have been issued a E 55 X 10 million 550 million V D E 200 million 550 million 750 million D 200million V 750million 0267 E 550million V 750million 0733 D E Aftertax WACC rD1 TCVrE V 007 X 1 035 X 0267012gtlt 0733 01001 1001 187 b The aftertax WACC would increase to the extent of the loss of the tax deductibility ofthe interest on debt Therefore the aftertax WACC would equal the opportunity cost of capital computed from the WACC formula without the taxdeductibility of interest WACC rD rE 5 007 X O267012 gtlt 0733 01067 1067 We make use of the basic relationship r r17TEr XE A D c V E V Since overall beta 8A is not affected by capital structure or taxes then rA rf 3A rm rf 006 15 x 008 018 The following table shows the value of rE for various values of DE and the corresponding values of DV derived from the above formula The graph is on the next page DE DV rA rD rE 000 000000 018 00600 01800 005 004762 018 00600 01871 010 009091 018 00600 01941 015 013043 018 00600 02012 020 016667 018 00600 02082 025 020000 018 00600 02153 030 023077 018 00610 02221 035 025926 018 00620 02289 040 028571 018 00630 02356 045 031034 018 00640 02423 050 033333 018 00650 02489 055 035484 018 00660 02554 060 037500 018 00670 02619 065 039394 018 00680 02683 070 041176 018 00690 02746 075 042857 018 00690 02814 080 044444 018 00700 02876 085 045946 018 00725 02929 090 047368 018 00750 02981 095 048718 018 00775 03031 1 00 050000 018 00800 03080 188 Retu rn 035000 030000 025000 020000 015000 010000 005000 000000 000 020 DE 060 080 189 Challenge Questions 23 24 25 Assume the election is near so that we can safely ignore the time value of money Because one and only one of three events will occur the guaranteed payoff from holding all three tickets is 10 Thus the three tickets taken together could never sell for less than 10 This is true whether they are bundled into one composite security or unbundled into three separate securities However unbundled they may sell for more than 10 This will occur ifthe separate tickets ll a need for some currently unsatisfied clientele lfthis is indeed the case then Proposition l fails The sum of the parts is worth more than the whole Some shoppers may want only the chicken drumstick They could buy a whole chicken cut it up and sell offthe other parts in the supermarket parking lot This is costly It is far more ef cient for the store to cut up the chicken and sell the pieces separately But this also has some cost hence the observation that supermarkets charge more for chickens after they have been cut The same considerations affect financial products but a The proportionate costs to companies of repackaging the cash ow stream are generally small b Investors can also repackage cash ows cheaply for themselves In fact specialist nancial institutions can often do so more cheaply than the companies can do it themselves Firms that are able to identify an unsatis ed clientele and then design a nancial service or instrument that satis es the demands of this clientele can in violation of MM s capitalstructure irrelevance theory enhance rm value However if this is done successfully by one nancial innovator others will follow eventually restoring the validity of the MM irrelevance theory lfthe financial innovation can be patented the creator ofthe innovation can restrict the use of the innovation by other financial managers and thereby continue to use the innovation to create value Consequently MM s capital structure irrelevance theory would potentially be violated during the life of the patent 1810 CHAPTER 7 Making Investment Decisions with The Net Present Value Rule Answers to Practice Questions 10 See the table below We begin with the cash flows given in the text Table 76 line 8 and utilize the following relationship from Chapter 4 Real cash flow nominal cash ow1 inflation ratet Here the nominal rate is 20 the expected inflation rate is 10 and the real rate is given by the following 1 rnominal 1 rreal x 1 in ation rate 120 1 rreal x 110 rreal 00909 909 As can be seen in the table the NPV is unchanged to within a rounding error YearO Year1 Year2 Year3 Year4 Year5 Year6 Year7 Net Cash Flows Nomina126OO 1484 2947 6323 10534 9985 5757 3269 Net Cash Flows Real 12600 1349 2436 4751 7195 6200 3250 1678 NPV of Real Cash Flows at 909 3804 11 No this is not the correct procedure The opportunity cost ofthe land is its value in its best use so Mr North should consider the 45000 value of the land as an outlay in his NPV analysis of the funeral home 12 Investment in net working capital arises as a forecasting issue only because accrual accounting recognizes sales when made not when cash is received and costs when incurred not when cash payment is made If cash ow forecasts recognize the exact timing ofthe cash ows then there is no need to also include investment in net working capital 71 Ifthe 50000 is expensed at the end of year 1 the value of the tax shield is 035gtlt50000 105 Ifthe 50000 expenditure is capitalized and then depreciated using a veyear MACRS depreciation schedule the value of the tax shield is 020 L 032 0192L01152L01152L00576 105 391052 391053 39 1054 39 1055 39 1056 16667 035 gtlt50000 gtlt 15306 Ifthe cost can be expensed then the tax shield is larger so that the aftertax cost is smaller 5 26000 a NPVA 100000 Z 108t 3810 NPVB nvestment PVaftertax cash ow PVdepreciation tax shield 5 NPVB 100000Z 263900 32 03935 t1 020 032 108 1082 0192 01152 1083 1084 01152 1085 035gtlt100000gtlt 00576 1086 NPVB 4127 Another perhaps more intuitive way to do the Company B analysis is to rst calculate the cash ows at each point in time and then compute the present value of these cash flows tO t1 t2 t3 t4 t5 t6 100000 Investment Cash Inflow 26000 26000 26000 26000 26000 Depreciation 20000 32000 19200 11520 11520 5760 Taxablelncome 6000 6000 6800 14480 14480 5760 Tax 2100 2100 2380 5068 2016 Cash Flow 100000 23900 28100 23620 20932 20932 2016 NPV at 8 4127 9quot o 0 00 b IRRA 943 IRRB 639 00639 00943 Effective tax rate 1 0322 322 72 73 7 4 75 Assume the following a The rm will manufacture widgets for at least 10 years b There will be no inflation or technological change 0 The 15 cost of capital is appropriate for all cash flows and is a real aftertax rate of return All operating cash flows occur at the end of the year 0 Note Since purchasing the lids can be considered a oneyear project the two projects have a common chain life of 10 years Compute NPV for each project as follows 1o NPVpurchase Z W 1304880 t1 1o NPVmake 150000 30000 Z t1 035X150 JOOXO14219 024429 017439 012419 115 115 115 115 008953 008963 008973 004415 3001000 1 118 328 115 115 115 115 115 Thus the widget manufacturer should make the lids a Capital Expenditure 1 lfthe spare warehouse space will be used now or in the future then the project should be credited with these bene ts 2 Charge opportunity cost ofthe land and building 3 The salvage value at the end ofthe project should be included Research and Development 1 Research and development is a sunk cost Working Capital 1 VWI additional inventories be required as volume increases 2 Recovery of inventories at the end of the project should be included 3 Is additional working capital required due to changes in receivables payables etc Revenue 1 Revenue forecasts assume prices and quantities will be unaffected by competition a common and critical mistake Operating Costs 1 Are percentage labor costs unaffected by increase in volume in the early years 2 Wages generally increase faster than inflation Does Reliable expect continuing productivity gains to offset this 76 Overhead 1 Is overhead truly incremental Depreciation 1 Depreciation is not a cash ow but the ACRS deprecation does affect tax payments 2 ACRS depreciation is xed in nominal terms The real value ofthe depreciation tax shield is reduced by inflation Interest 1 It is bad practice to deduct interest charges or other payments to security holders Value the project as if it is all equity nanced Tax 1 See comments on ACRS depreciation and interest 2 If Reliable has pro ts on its remaining business the tax loss should not be carried fonNard Net Cash Flow 1 See comments on ACRS depreciation and interest 2 Discount rate should re ect project characteristics in general it is not equivalent to the company s borrowing rate 1 Potential use of warehouse 2 Opportunity cost of building 3 Other working capital items 4 More realistic forecasts of revenues and costs 5 Company s ability to use tax shields 6 Opportunity cost of capital The table on the next page shows a sample NPV analysis for the project The analysis is based on the following assumptions 1 In ation 10 per year 2 Capital Expenditure 8 million for machinery 5 million for market value of factory 24 million for warehouse extension we assume that it is eventually needed or that electric motor project and surplus capacity cannot be used in the interim We assume salvage value of 3 million in real terms less tax at 35 3 Working Capital We assume inventory in year t is 91 of expected revenues in year t 1 We also assume that receivables less payables in year t is equal to 5 of revenues in year t 4 Depreciation Tax Shield Based on 35 tax rate and 5year ACRS class This is a simplifying and probably inaccurate assumption ie not all the investment would fall in the 5year class Also the factory is currently owned by the company and may already be partially depreciated We assume the company can use tax shields as they arise 77 Revenues Sales of2000 motors in 2007 4000 motors in 2008 and 10000 motors thereafter The unit price is assumed to decline from 4000 real to 2850 when competition enters in 2009 The latter is the figure at which new entrants investment in the project would have NPV 0 6 Operating Costs We assume direct labor costs decline progressively from 2500 per unit in 2007 to 2250 in 2008 and to 2000 in real terms in 2009 and after 7 Other Costs We assume true incremental costs are 10 of revenue 8 Tax 35 of revenue less costs 9 Opportunity Cost of Capital Assumed 20 Capital Expenditure Changes in Working Capital Inventories Receivables Payables Depreciation Tax Shield Revenues Operating Costs Other costs Tax Net Cash Flow Capital Expenditure Changes in Working Capital Inventories Receivables Payables Depreciation Tax Shield Revenues Operating Costs Other costs Tax Net Cash Flow NPV at 20 5991 M m M M M M 15400 801 961 1 690 345 380 418 440 528 929 190 209 1078 1725 1035 621 621 8800 19360 37934 41727 45900 5500 10890 26620 29282 32210 880 1936 3793 4173 4590 847 2287 2632 2895 3185 16201 1250 3754 4650 5428 5909 M M M M m M 5058 459 505 556 612 6727 229 252 278 306 336 3696 310 50489 55538 61092 67202 73922 35431 38974 42872 47159 51875 5049 5554 6109 6720 7392 3503 3854 4239 4663 5129 6128 6399 7038 7742 20975 3696 78 18 The table below shows the real cash flows The NPV is computed using the real rate which is computed as follows 1 rnominal 1 rreal X 1 in ation rate 109 1 rreal X 103 rreal 00583 583 t 0 Investment 350000 Savings Insurance Fuel Net Cash Flow NPV at 583 272542 19 Sales Manufacturing Costs Depreciation R t en Earnings Before Taxes axes Cash Flow Operations Working Capital 3500 Increase in WC 3500 Initial Investment 12000 Sale of Plant Tax on Sale Net Cash Flow 15500 NPVat 12 858 20 t1 1 t2 10530 10530 t2 t3 t3 4 t4 5 t5 t6 10530 10530 10530 10530 350000 84330 84330 84330 84330 84330 84330 t6 t 42000 44100 46305 48620 51051 53604 37800 39690 41675 43758 45946 48244 50656 1200 1000 2000 700 2500 4200 700 1800 1040 2170 760 2611 4410 210 2401 1200 1082 2348 822 2726 4631 221 2505 2618 2735 2858 t7 t 8 150000 85800 85800 85800 85800 85800 85800 85800 85800 12000 12000 12000 12000 12000 12000 12000 12000 10530 10530 84330 234330 2988 Note Section 72 provides several different calculations of pretax pro t and taxes based on different assumptions the solution below is based on Table 76 in the text See the table below With full usage ofthe tax losses the NPV of the tax payments is 4779 V th tax losses carried fonNard the NPV ofthe tax payments is 5741 Thus with tax losses carried forward the project s NPV decreases by 962 so that the value to the company of using the deductions immediately is 962 53188 1200 1316 3394 1188 3406 00 5628 4000 560 12474 t0 t1 t2 t3 t4 t5 t6 t7 Pretax Pro t 4000 4514 748 9807 1694011579 5539 1949 Full usage oftax losses immediately Table 76 1400 1580 262 3432 5929 4053 1939 682 NPV at 20 4779 Tax loss carryfonNard 0 0 0 714 5929 4053 1939 682 NPV at 20 5741 21 In order to solve this problem we calculate the equivalent annual cost for each of the two alternatives All cash ows are in thousands Alternative 1 Sell the new machine lfwe sell the new machine we receive the cash ow from the sale pay taxes on the gain and pay the costs associated with keeping the old machine The present value ofthis alternative is 30 PV50 03550 0 40 7 7 7 7 7 1 1 112 1122 1123 1124 1125 5 o355 0 9380 1125 1125 The equivalent annual cost for the veyear period is computed as follows PV1 EAC1 gtlt annuity factor 5 time periods 12 9380 EAC1 gtlt 3605 EAC1 2602 or an equivalent annual cost of 26020 Alternative 2 Sell the old machine If we sell the old machine we receive the cash ow from the sale pay taxes on the gain and pay the costs associated with keeping the new machine The present value of this alternative is 20 20 20 20 20 PV 25 03525 0 7 2 1 112 1122 1123 1124 1125 1125 1126 1127 1128 1129 11210 5 0355 0 12751 11210 11210 710 22 The equivalent annual cost for the tenyear period is computed as follows PV2 EAC2 gtlt annuity factor 10 time periods 12 12751 EAC2 gtlt 5650 EAC2 2257 or an equivalent annual cost of 22570 Thus the least expensive alternative is to sell the old machine because this alternative has the lowest equivalent annual cost One key assumption underlying this result is that whenever the machines have to be replaced the replacement will be a machine that is as efficient to operate as the new machine being replaced The current copiers have net cost cash ows as follows Before Tax Net Cash M Cash Flow AfterTax Cash Flow Fl 1 2000 2000 x 65 35 x 0893 x 20000 6749 2 2000 2000 x 65 35 x 0892 x 20000 6756 3 8000 8000 x 65 35 x 0893 x 20000 45749 4 8000 8000 x 65 35 x 0445 x 20000 48885 5 8000 8000 x 65 52000 6 8000 8000 x 65 52000 These cash ows have a present value discounted at 7 of 15857 Using the annuity factor for 6 time periods at 7 4767 we find an equivalent annual cost of 3326 Therefore the copiers should be replaced only when the equivalent annual cost of the replacements is less than 3326 When purchased the new copiers will have net cost cash ows as follows Before Tax Net Cash M Cash Flow AfterTax Cash Flow Fl 0 25000 25000 250000 1 1000 1000 x 65 35 x 1429 x 25000 6004 2 1000 1000 x 65 35 x 2449 x 25000 14929 3 1000 1000 x 65 35 x 1749 x 25000 8804 4 1000 1000 x 65 35 x 1249 x 25000 4429 5 1000 1000 x 65 35 x 0893 x 25000 1314 6 1000 1000 x 65 35 x 0892 x 25000 1305 7 1000 1000 x 65 35 x 0893 x 25000 1314 8 1000 1000 x 65 35 x 0445 x 25000 2606 These cash ows have a present value discounted at 7 of 21967 The decision to replace must also take into account the resale value of the machine as well as the associated tax on the resulting gain or loss 711 Consider three cases a The book depreciated value of the existing copiers is now 6248 lfthe existing copiers are replaced now then the present value ofthe cash ows is 21967 8000 035 x 8000 6248 14580 Using the annuity factor for 8 time periods at 7 5971 we nd that the equivalent annual cost is 2442 Two years from now the book depreciated value ofthe existing copiers will be 2678 lfthe existing copiers are replaced two years from now then the present value ofthe cash flows is 67491 071 67561072 219671072 3500 035 x 3500 26781072 17602 Using the annuity factor for 10 time periods at 7 7024 we nd that the equivalent annual cost is 2506 Six years from now both the book value and the resale value ofthe existing copiers will be zero lfthe existing copiers are replaced six years from now then the present value of the cash ows is 15857 219671076 30495 Using the annuity factor for 14 time periods at 7 8745 we nd that the equivalent annual cost is 3487 The copiers should be replaced immediately The equivalent annual cost of the depreciation tax shield is computed by dividing the present value ofthe tax shield by the annuity factor for 25 years at 7 Equivalent annual cost 11457 million11654 983 million The equivalent annual cost of the capital investment is 343 million 983 million 2447 million 712 24 25 The extra cost per gallon after tax is 2447 million900 million gallons 00272 per gallon The pretaX charge 00272065 00418 per gallon 10000 10000 10000 7 106 1062 1063 PVA 66730 Note that this is a cost 8000 8000 8000 8000 106 1062 1063 1064 PVB 77721 Note that this is a cost Equivalent annual cost EAC is found by PVA 40000 PVB 50000 PVA EACA gtlt annuity factor 6 3 time periods 66730 EACA gtlt 2673 EACA 24964 per year rental PVB EACB gtlt annuity factor 6 4 time periods 77721 EACB gtlt 3465 EACB 22430 per year rental Annual rental is 24964 for Machine A and 22430 for Machine B Borstal should buy Machine B The payments would increase by 8 per year For example for Machine A rent for the rst year would be 24964 rent for the second year would be 24964 X 108 26961 etc Because the cost ofa new machine now decreases by 10 per year the rent on such a machine also decreases by 10 per year Therefore 9000 81007290 106 1062 1063 PVA 61820 Note that this is a cost 7200 6480 5832 5249 7 2 3 4 106 106 106 106 PVB 71614 Note that this is a cost PVA 40000 PVB 50000 713 26 Equivalent annual cost EAC is found as follows PVA EACA gtlt annuity factor 6 3 time periods 61820 EACA gtlt 2673 EACA 23128 a reduction of 735 PVB EACB gtlt annuity factor 6 4 time periods 71614 EACB gtlt 3465 EACB 20668 a reduction of 786 V th a 6year life the equivalent annual cost at 8 of a new jet is 1 1000004623 237941 lfthe jet is replaced at the end of year 3 rather than year 4 the company will incur an incremental cost of 237941 in year 4 The present value of this cost is 2379411084 174894 3 80000 The present value ofthe saVIngs Is 2 W t1 The president should allow wider use of the present jet because the present value of the savings is greater than the present value ofthe cost 206168 714 Challenge Questions 27 28 Year0 Year1 Year2 Year3 Year4 Year5 Year6 Year7 PreTax Flows 14000 3064 3209 9755 1646314038 7696 3951 IRR 335 PostTax Flows 12600 1630 2381 6205 1068510136 6110 3444 IRR 268 Effective Tax Rate 200 Ifthe depreciation rate is accelerated this has no effect on the pretax IRR but it increases the aftertax IRR Therefore the numerator decreases and the effective tax rate decreases Ifthe inflation rate increases we would expect pretax cash ows to increase at the in ation rate while aftertax cash ows increase at a slower rate Aftertax cash ows increase at a slower rate than the in ation rate because depreciation expense does not increase with in ation Therefore the numerator of TE becomes proportionately larger than the denominator and the effective tax rate increases L l1 TC l1 TC C 9 l1 TC TE C Hc C l 1 1 Tc Tc 1 TC Hence if the upfront investment is deductible for tax purposes then the effective tax rate is equal to the statutory tax rate V th a real rate of 6 and an in ation rate of 5 the nominal rate r is determined as follows 1 r 1 006 X 1 005 r 0113 113 For a threeyear annuity at 113 the annuity factor is 24310 For a twoyear annuity the annuity factor is 17057 For a threeyear annuity with a present value of 2837 the nominal annuity is 283724310 1167 For a twoyear annuity with a present value of 21 00 the nominal annuity is 21 001 7057 1231 These nominal annuities are not realistic estimates of equivalent annual costs because the appropriate rental cost ie the equivalent annual cost must take into account the effects of in ation 715 29 V th a real rate of 6 and an in ation rate of 25 the nominal rate r is determined as follows 1 r 1 006 x 1 025 r 0325 325 For a threeyear annuity at 325 the annuity factor is 17542 For a twoyear annuity the annuity factor is 13243 For a threeyear annuity with a present value of 2837 the nominal annuity is 283717542 1617 For a twoyear annuity with a present value of 21 00 the nominal annuity is 21 001 3243 1586 V th an in ation rate of 5 Machine A has the lower nominal annual cost 1167 compared to 1231 V th inflation at 25 Machine B has the lower nominal annual cost 1586 compared to 1617 Thus it is clear that in ation has a signi cant impact on the calculation of equivalent annual cost and hence the warning in the text to do these calculations in real terms The rankings change because at the higher inflation rate the machine with the longer life here Machine A is affected more The spreadsheet on the next two pages indicates that the NPV forthe MidAmerican wind farm investment is 87271675 By eliminating the tax in the spreadsheet we nd that the NPV is still negative 7692376 NPV becomes positive with a tax subsidy of approximately 35 Using the same spreadsheet we can show that a capacity factor of 30 reduces NPV to 138249182 716 ESTIMATED NPV OF MIDAMERICAN ENERGY39S WINDFARM PROJECT IN THE ABSENCE OF ANY TAX BREAKS PROJECT DATA Capacity megawatts 3605 Load factor 35 Year 1 electricity price mWh 5500 Year 1 maintenance amp other costs 18900000 Inflation 300 Total capital cost 386000000 MACRSyears 20 Cost of capital 120 Year 0 1 2 3 4 5 6 Capital cost 386000000 Revenues 60791115 62614848 64493294 66428093 68420936 70473564 Maintenanceampothercosts 18900000 19467000 20051010 20652540 21272117 21910280 MACRSdepreciation 14475000 27869200 25784800 23854800 22040600 20380800 Pretaxprofit 27416115 15278648 18657484 21920752 25108219 28182484 Tax 9595640 5347527 6530119 7672263 8787877 9863869 Cashflow 386000000 32295475 37800321 37912165 38103289 38360942 38699414 PV 386000000 28835245 30134185 26985130 24215329 21767029 19606328 NPV 87271675 MACRS depreciation 375 722 668 618 571 528 717 Year Capital cost Revenues Maintenance amp other costs MACRS depreciation Pretax profit Tax Cash flow PV NPV MACRS depreciation Year Capital cost Revenues Maintenance amp other costs MACRS depreciation Pretax profit Tax Cash flow PV NPV MACRS depreciation 7 72587770 22567588 18875400 31144782 10900674 39119508 17695679 489 15 91952016 28587946 17215600 46148470 16151965 47212106 8625475 446 718 8 74765404 23244616 17447200 34073588 11925756 39595032 15991769 452 16 94710576 29445584 17215600 48049392 16817287 48447705 7902870 446 9 77008366 23941955 17215600 35850811 12547784 40518627 14611423 446 17 97551894 30328952 17215600 50007342 17502570 49720372 7241491 446 10 79318617 24660213 17215600 37442803 13104981 41553422 13379090 446 18 100478450 31238820 17215600 52024030 18208411 51031220 6636079 4 46 11 81698175 25400020 17215600 39082556 13678894 42619261 12252019 446 19 103492804 32175985 17215600 54101219 18935427 52381392 6081835 446 12 84149120 26162020 17215600 40771500 14270025 43717075 11221084 446 20 106597588 33141264 17215600 56240724 19684253 53772070 5574377 446 13 86673594 26946881 17215600 42511113 14878890 44847824 10277964 446 21 0 0 8607800 8607800 3012730 3012730 278857 223 14 89273802 27755287 17215600 44302915 15506020 46012495 9415068 446

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