Solutions to Chapter Using Discounted Cash-Flow Analysis to Make Investment Decisions A General Note: Many of the questions, for which solutions are provided below, require only that the NPV or IRR or some other evaluation criterion be calculated These questions have not asked that you make a decision based on such criteria In Chapter 7, we discussed the decision rules when we use these criteria For instance, a positive NPV project should be accepted whereas a project with a negative NPV should be rejected These decision rules should generally be kept in mind while working on the solutions below Net income = ($74  42  10)  35  ($74  42  10) = $22  $7.7 = $14.3 million  Revenues  cash expenses  taxes paid = $74  $42  $7.7 = $24.3 million  Net Profit + Deprec = $14.3 + $10 = $24.3 million  (Revenues  cash expenses)  (1  T) + T  Deprec = $32  65 + 35  $10 = $24.3 million a NWC = Acct Receivable + Inventory  Acct Payable = $1,500 + $1,000  $2,000 = $2,500 b Cash flow = $36,000  $24,000 + $2,500 = $14,500 Net income = ($7   1)  40  ($7   1) = $2  $0.8 = $1.2 million  Revenues  cash expenses  taxes paid = $3  $0.8 = $2.2 million  Net Profit + Deprec = $1.2 + $1.0 = $2.2 million  (Revenues  cash expenses)  (1  T) + T  Deprec = $3  60 + 40  $1 = $2.2 million While depreciation is a non-cash expense, it still has an impact on net cash flow because of its impact on taxes Every dollar of depreciation reduces taxable income by one dollar, and thus reduces taxes owed by $1 times the firm’s marginal tax rate In Canada, such tax savings can be generated by capital cost allowance (CCA) which, for most assets, is computed using the written-down value method CCA is computed for asset classes rather than for individual assets Also, in the 8­1 Copyright © 2009 McGraw-Hill Ryerson Limited first year of the asset’s life, the half-year rule becomes applicable The various unique features of the declining balance CCA system make it quite different from straight-line depreciation Compared with straight-line depreciation, declining balance CCA will move the tax benefits in time, and thus provide a different present value of the tax shield, thereby altering the value of the project Gross revenues from new chip = 12 million  $25 = $300 million Cost of new chip = 12 million  $8 = $96 million Lost sales of old chip = million  $20 = $140 million Saved costs of old chip = million  $6 = $42 million Increase in cash flow = (300 – 96) – (140 – 42) = $106 million Revenue Rental costs Variable costs Depreciation Pretax profit Taxes (35%) Net income $160,000 35,000 45,000 10,000 70,000 24,500 $45,500 a Net Profit + Depreciation = $45,500 + $10,000 = $55,500 b Revenue – rental costs – variable costs – taxes = $160,000 – $35,000 – $45,000 – $24,500 = $55,500 c (Revenue – rental costs – variable costs)  (1–.35) + 35  (Depreciation) = ($160,000 – $35,000 – $45,000)  65 + 35  $10,000 = $52,000 + $3,500 = $55,500 Change in working capital = Accounts receivable – Accounts payable = ($4500 – $1200) – ($200 – $600) = $3,700 Cash flow = $16,000 – $9,000 – $3,700 = $3,300 8­2 Copyright © 2009 McGraw-Hill Ryerson Limited Incremental cash flows are: b The cash that could have been realized by selling the art d The reduction in taxes paid 10 Capital investment: $1,000,000        CCA calculation: Year UCC CCA (5%) $1,000,000 975,000 926,250 879,937 835,940 794,143 $25,000 48,750 46,313 43,997 41,797 39,707 End of Year UCC $975,000 926,250 879,937 835,940 794,143 754,436 Operating cash flows of the project for the next six years (figures in thousands of dollars) Year: Capital Investment Revenues Operating Expenses: Direct production costs Fixed maintenance costs Pre-tax Profits Tax @35% Operating Cash Flow (excluding CCA Tax Shield) CCA Tax Shield (CCA x 35%) Total Cash Flow 11 a -1,000 120 120 120 120 120 120 40 40 40 40 40 40 15 15 15 15 15 65 22.75 65 22.75 65 22.75 65 22.75 65 22.75 15 65 22.75 -1,000 42.25 42.25 42.25 42.25 42.25 42.25 8.75 17.063 16.209 15.399 14.629 13.898 51.000 59.313 58.459 57.649 56.879 56.148 CCA calculation for the first years: Year UCC CCA (30%) $40,000 34,000 23,800 $6,000 10,200 7,140 8­3 Copyright © 2009 McGraw-Hill Ryerson Limited End of year UCC $34,000 23,800 16,660 b If the company has other assets in class 46 and the equipment is sold after years, the adjusted cost of disposal is the sale price of $20,000 This amount is then deducted from the UCC of asset class 46 If overall UCC remains positive, we not have to worry about CCA recapture If, however, overall UCC becomes negative, we consider CCA recapture The firm’s after-tax proceeds from the sale are $20,000 – PV of CCA tax shield lost - (0.35 x amount of CCA recapture, if applicable) c If no other assets exist in Class 46 and the equipment is sold after years, the adjusted cost of disposal is the sale price of $20,000 Subtracting this amount from the UCC of asset class 46 ($16,660 - $20,000 = -$3,340), we arrive at a negative balance, and thus recaptured depreciation This amount is now added back to taxable income and the UCC of the asset class becomes zero At the time of sale, the present value of tax shields lost as a result of the sale is calculated as: 16,660 0.30 0.35  1  0.5r  =    r  , where r is the cost of capital r  0.30  The firm’s after-tax proceeds from the sale are thus $20,000 – (0.35 x 3,340) – PV of tax shields lost = $18,831 – PV of CCA tax shields lost 12 a If the office space would have remained unused in the absence of the proposed project, then the incremental cash outflow from allocating the space to the project is effectively zero The incremental cost of the space used should be based on the cash flow given up by allocating the space to this project rather than some other use b One reasonable approach would be to assess a cost to the space equal to the rental income that the firm could earn if it allowed another firm to use the space This is the opportunity cost of the space 13 Cash flow = Net income + depreciation – increase in NWC 1.2 = 1.2 + – NWC NWC = $0.5 million 14 Cash flow = profit – increase in inventory = $10,000 – $1,000 = $9,000 8­4 Copyright © 2009 McGraw-Hill Ryerson Limited 15 NWC2007 = $32 + $25 – $12 = $45 million NWC2008 = $35 + $30 – $25 = $40 million Net working capital has decreased by $5 million 16 Depreciation per year = $40/5 = $8 million Book value of old equipment = $40 – (3  $8) = $16 million Sales price = $18 million After-tax cash flow = $18 – 35  ($18 – $16) = $17.3 million 17 CCA calculation for the new capital investment (figures in thousands of dollars): Year UCC CCA (25%) $10,000 8,750 6,562 4,922 3,691 $1,250 2,188 1,641 1,231 923 End of year UCC $8,750 6,562 4,922 3,691 2,768 Since the project ends after years, and the equipment is sold, the adjusted cost of disposal is $4 million, which is deducted from the UCC asset class, that is 2.768 – = -1.232 million This results in a negative balance and recaptured depreciation The after-tax cash flow from the sale = $4 million – (.35 x $1.232) – PV of CCA tax shield lost This equals $3.569 million – PV of tax shields lost 18 a The UCC increases by $6,000 to the extent of the purchase of the new washer but decreases by $2,000 to the extent of sale of the old washer The net effect is an UCC increase of $4,000 CCA calculations are as follows: Year UCC CCA (30%) $ 4,000 3,400 2,380 1,666 1,166 816 $ 600 1,020 714 500 350 245 8­5 Copyright © 2009 McGraw-Hill Ryerson Limited End of year UCC $ 3,400 2,380 1,666 1,166 816 571 All dollar values should be interpreted as incremental results from making the purchase First, we calculate operating cash flows excluding CCA tax shields Year: Earnings from Savings (before CCA) Tax (40%) Cash Flow from Operations (excluding CCA) 1–6 1,500 600 $900 Now we consider the effect of the CCA tax shield on Bottoms Up’s cash flows Year: Capital Investment After-tax Cash Flow from Operations (excl CCA) Cash Flow from Sale of Old Equipment Total Cash Flow (excl CCA) CCA Tax Shield (CCA x 4) Total Project Cash Flow b -6,000 900 900 900 900 900 900 2000 0 0 0 -4,000 900 900 900 900 900 240 408 286 200 140 -4,000 1,140 1,308 1,186 1,100 1,040 900 98 998 The project NPV is calculated in two phases First, we compute the total present value of cash flows excluding the CCA tax shield: PV = -4,000 + 900 x annuity factor(15%, years) = -$594.4 Second, we calculate the present value of the CCA tax shield: PV of CCA tax shield = CdTc 1  0.5r  SdTc   , where S =   r  d   r  d  r 1  r  t 4000 0.3 0.4 1   0.5 0.15     0.15  0.3  0.15 = = $997.10 NPV = Total PV excluding CCA tax shields + PV of CCA tax shield = -$594.40 + $997.10 = $402.7 c Using straight-line depreciation, net cash flow at time remains -$4,000, but the net cash flow at times through becomes $1,300, which is calculated as follows: 8­6 Copyright © 2009 McGraw-Hill Ryerson Limited Earnings before depreciation Depreciation (6000/6 years) Taxable income Taxes (0.40) Net Income + Depreciation Operating Cash Flow $1,500 1,000 500 200 300 1,000 $1,300 NPV = -4,000 + 1,300 x annuity factor (15%, years) = $919.83 IRR = 23.21% 19 If the firm uses straight-line depreciation, the present value of the cost of buying, net of the annual depreciation tax shield (which equals 40  1000 = 400), is: 6000 – 400  annuity factor(15%, years) = 4486.21 The equivalent annual cost, EAC, is therefore determined by: EAC  6-year annuity factor = 4486.21 EAC  3.7845 = 4486.21 EAC = $1185.42 Note: this is the equivalent annual cost of the new washer, and does not include any of the washer’s benefits 20 a.  The year-wise CCA for the new grill, over its expected life, is as follows: Year UCC CCA (30%) $20,000 17,000 11,900 $3,000 5,100 3,570 End of year UCC $17,000 11,900 8,330 Operating cash flow contribution, excluding tax shields, for year through = Saving in energy expenses x (1 - 35) = $10,000 x (1 - 35) = $6,500 Now, we must consider the effect of the CCA tax shield on the project’s yearly cash flows Year: Contribution from saving in energy expenses CCA Tax Shield (CCA x 35) Total Operating Cash Flow 8­7 Copyright © 2009 McGraw-Hill Ryerson Limited 6,500 6,500 6,500 1,050 1,785 7,550 8,285 1,250 7,750 b Total Cash Flow (0-3) = Operating CF + CF associated with investments At time 0, the CF from the investment is -$20,000 At the end of year 3, the grill is sold for $5,000 Therefore, total cash flows are: Time c Cash Flows ($) -20,000 7,550 8,285 12,750 [=7,750 + 5,000] First, we compute present value of cash flows excluding the CCA tax shield: PV = -20,000 + 6,500 x annuity factor(12%, years) + 5,000 x discount factor (12%, years) = -$829.3 We next calculate the present value of the CCA tax shield: PV of CCA tax shield: CdTc 1  0.5r  SdTc     r  d   r  d  r 1  r  t = 20000 0.3 0.35 1   0.5 0.12   5000 0.3 0.35     12   12  12 1  0.12  = = $3,842.41 NPV = Total PV excluding CCA tax shields + PV of CCA tax shield = -$829.3 + $3, 842.41 = -$3,013.11 21 a Initial investment = $50,000 + $8,000 for working capital (20% of 40,000) = $58,000 b CCA for the first years of the plant and equipment’s life is as follows: Year UCC CCA (25%) $50,000 43,750 32,812 24,609 18,457 $6,250 10,938 8,203 6,152 4,614 8­8 Copyright © 2009 McGraw-Hill Ryerson Limited End of year UCC $43,750 32,812 24,609 18,457 13,843 Year: Sales Expenses = Profit before tax -tax @ 40% = Operating Cash Flow (excl CCA tax shield) (In thousands of dollars) 40 30 20 10 16 12 24 18 12 9.6 7.2 4.8 2.4 14.4 10.8 7.2 3.6 For calculating project cash flows for each year, we will need to calculate the tax savings generated from the CCA tax shield We this by multiplying each year’s CCA by the firm’s tax rate (40% in this case) (in thousands of dollars) Year: Decrease in working capital from previous year 2.0 2.0 2.0 2.0 Operating Cash Flow (excluding CCA tax shield) 14.4 10.8 7.2 3.6 16.4 12.8 9.2 5.6 2.5 4.4 3.3 2.5 18.9 17.2 12.5 8.1 Capital investment -50.00 Initial investment in working capital - 8.00 Total Cash Flow (excluding CCA tax shield) - 58.00 CCA tax shield (CCA x 0.40) Total c - 58.00 The project NPV is calculated in two phases First, we calculate the present value from cash flows excluding the CCA tax shield: Year: Total Cash Flow (excluding CCA tax shield) x Discount Factor (10%) PV of total cash flow (excl CCA tax shield)* Total PV (excl CCA tax shield) (58) 16.40 12.80 9.20 5.60 1.000 0.909 0.826 0.751 0.683 (58) 14.91 10.57 6.91 3.83 (21.78) 8­9 Copyright © 2009 McGraw-Hill Ryerson Limited * Notice, you could also calculate this as follows, keeping in mind that there could be some difference of result due to rounding errors 16.4 12.8 9.2 5.6  58     1.1 (1.1) (1.1) (1.1) We next calculate the present value of the CCA tax shield: PV of CCA tax shield = CdTc 1  0.5r  SdTc   , where S =   r  d   r  d  r 1  r  t 50000 0.25 0.4 1   0.5 0.10     0.10  0.25  0.10 = = $13,636 NPV (in thousands of dollars) = Total PV excluding CCA tax shields + PV of CCA tax shield = -$21.78 + $13.64 = -$8.14 22 a The present value of costs from buying is $25,000 – $5000/(1.10)5 = $21,895 The cost of leasing (assuming that lease payments come at the end of each year) is $5,000  annuity factor(10%, years) = $18,954 Leasing is less expensive b 23 The maximum lease payment, L, would be chosen so that L  annuity factor(10%, years) = $21,895 L = $5,776 The initial investment is $100,000 for the copier + $10,000 in working capital, for a total outlay of $110,000 Depreciation expense each year = ($100,000  $20,000)/5 = $16,000 8­10 Copyright © 2009 McGraw-Hill Ryerson Limited EAC for Quick and Dirty: $7.63m = Annuity (3.605) Annuity = 7.63 $2.12 m 3.605 EAC for Do-It-Right: $9.16m = Annuity (4.968) Annuity = 9.16 $1.84m 4.968 Since the operating costs are the same, the project with the lower EAC is cheaper This is Do-It-Right * Investment – PV of CCA tax shield ** Annuity discounted at 12%; number of years = project life 26 Net working capital Investment in NWC Investment in Plant & eq Cash flow from investment activity (A) $220 220 200 –$420 Revenue Cost Pretax profit (excluding CCA) – Taxes (35%) Operating cash flow (excluding CCA tax shield) (B) Total CF –$420 (excluding CCA tax shield) (A+B) All figures in thousands of dollars $300 $140 $ 50 80 –$ 80 –160 +$160 – 90 +$ 90 All figures in thousands of dollars $880 550 330.00 115.50 $214.50 $1200 750 450.00 157.50 $292.50 $560 350 210.00 73.50 $136.50 $134.50 $452.50 $226.50 8­13 Copyright © 2009 McGraw-Hill Ryerson Limited $0 –50 +$ 50 $200 125 75.00 26.25 $ 48.75 $98.75 Present Value of CCA Tax Shield (PVTS):  200 0.25 0.35 1  (0.5 0.20)   0.20  0.25   20  17.5  1.1  $35.65 0.45 1.2  NPV (in thousands of dollars): = PVTS + PV TOTAL CF (excluding CCA tax shield) = 35.65  420  134.5 452.5 226.5 98.75    1.2 (1.2) (1.2) (1.2) = 35.65 – 420 + 112.08 + 314.24 + 131.08 + 47.62 = $ 220.67 27 All figures are on an incremental basis Labour savings $125,000 –Cost to run lathe 35,000 Net Savings (excluding CCA) 90,000 –Taxes (35%) 31,500 After tax savings (excluding CCA) $58,500 PV of CCA tax shield (PVTS): = =  1,000,000 0.25 0.35 1  (0.5 0.10)  100,000 0.25 0.35    10    0.10  0.25 0.25  0.10 (1  0.10)    0.10   87,500 1.05   8,750    0.3855   0.35 1.10   0.35  = 238,636.36 – 9,637.50 = $ 228,998.86 NPV = – 1,000,000 + 228,998.86 + 58,500  annuity factor (10%, 10 years) + 100,000/(1.10)10 = -$372,987.71 8­14 Copyright © 2009 McGraw-Hill Ryerson Limited 28 You can access information on CCA asset classes and rates on commonly used assets by going to the following link on Revenue Canada’s website: http://www.cra-arc.gc.ca/tax/business/topics/solepartner/reporting/capital/classes-e.html As of May 29, 2008 this site had a table with 17 listed asset classes The minimum eligible CCA rate is percent and the maximum eligible rate is 100 percent Fifteen of the 17 asset classes have declining balance CCA rates These include asset Class 13 (leasehold interest) and asset Class 14 (patents, franchises, concessions or licenses for a limited period) Notice that these classes include assets for which the cost to a business may not be a onetime initial outlay but rather a fixed recurring periodic cost over their economic life (such as, on leasehold interests) The CCA on such items is also computed as a fixed charge on a straight line basis 29 Rogers Communication and Microsoft Inc ($ million) 2007 Net capital expenditure Net Cap Expd to sales Sales & net cap-expd to total assets 2006 2005 Rogers Microsoft Rogers Microsoft Rogers 3,404.788 33.2 % 88.0 % 2,143.000 4.2 % 84.3% 1,486.170 19.6 % 74.9 % 848.000 1.9 % 64.8% 1,829.708 28.5 % 69.5 % Microsof t (114.000) (.3) % 56.0 % Note: Calculations were done as follows:  Capital expenditure = change in gross Physical Plant &Equipment (PP&E) from year to year For example, capital expenditure for 2007 = PP&E for 2007 minus PP&E for 2006  Net capital expenditure (net Cap.Expd.) = capital expenditure – after tax sales of fixed assets Differences in ratios between the two companies may be explained as follows: Given the nature of the businesses of the two companies, the extent of capital intensity for Rogers Communication is much more than Microsoft Rogers invests more in tangible physical assets to generate a certain dollar amount of sales than does Microsoft On the other hand Microsoft invests a lot on intangibles such as Research and Development and skilled human resources Also, during the period under consideration, Microsoft has a commanding market presence with a large and growing sales revenue and is much more cash rich company than Rogers Communications From the website, we also note that working capital investments for Microsoft have been increasing, reflecting growth and prosperity Relevant information on working capital for Rogers Communication was not available 8­15 Copyright © 2009 McGraw-Hill Ryerson Limited 30 If the savings are permanent, it is worth $250,000 to the firm It can take $250,000 out of the project now without ever having to replace it So the most the firm should be willing to pay is $250,000 31. Project Evaluation  Assumptions Plant and Equipment Start up cost before tax Start up cost after tax # of years Sales revenue year Growth in sales: 1-4 Year Depreciation Operating Exp Tax rate Cost of capital Sales Operating cost Operating cash flow before tax Taxes Operating cash flow (after tax) Depreciation tax shield Salvage value Total Cash Flow 100,000.00 25,000.00 16,500.00 60,000.00 5% -5% 20,000.00 10,000.00 34% 12% 60,000.00 63,000.00 - 10,000.00 - 10,500.00 50,000.00 52,500.00 - 17,000.00 - 17,850.00 33,000.00 34,650.00 6,800.00 6,800.00 39,800.00 41,450.00 66,150.00 - 11,025.00 55,125.00 - 18,742.50 36,382.50 6,800.00 69,457.50 - 11,576.25 57,881.25 - 19,679.63 38,201.63 6,800.00 65,984.63 - 10,997.44 54,987.19 - 18,695.64 36,291.54 6,800.00 43,182.50 45,001.63 43,091.55 (a) i) Note: Cash flow at year includes initial investment after tax [100,000+ (25,000 *(1-.34)] Year Cash flow - 116,500.00 39,800.00 41,450.00 43,182.50 45,001.63 43,091.55  Payback Period =   Cumulative cash flow - 116,500.00 -76,700.00 -35,250.00 7,932.50 52,934.13 96,025.68  35,250.00    43,182.50  = 2.82 years Discount Payback Year Cash flow - 116,500.00 39,800.00 41,450.00 43,182.50 Discount Factor (12%) 1.000 0.893 0.797 0.712 8­16 Copyright © 2009 McGraw-Hill Ryerson Limited PV of cash flow 12 % - 116,500.00 35,541.40 33,035.65 30,745.94 Cumulative cash flow - 116,500.00 - 80,958.60 - 47,922.95 -17,177.01 45,001.63 43,091.55  NPV = $35,876.93  IRR = 23.57 % b) 28,621.03 24,432.91 11,444.02 35,876.93  17,177.01   Discounted Payback period =    28,621.03  = 3.6 years   0.636 0.567  35,876.93   0.31 Profitability Index =   116,500  Using NPV and IRR decision rule the project should accepted It has a positive NPV of $35,876.93 and an IRR of 23.57 % which is higher that the cost of capital rate (c) i) CdTc 1  0.5r  SdTc   , where S =   r  d   r  d  r 1  r  t 100,000 0.25 0.34 1  (0.5 0.12)     0.12  0.12  0.25 8,500 1.06   $21,742.28 0.37 1.12  PV tax shield with zero salvage value = NPV including CCA tax shield = $35,876.93 + $21,742.48 = $57,619.21 (ii) Sales Operating cost Operating cash flow before tax Taxes Operating cash flow (after tax) Depreciation tax shield Salvage value Total Cash Flow Year Cash flow - 116,500.00 39,800.00 41,450.00 43,182.50 60,000.00 - 10,000.00 50,000.00 63,000.00 - 10,500.00 52,500.00 69,457.50 - 11,576.25 57,881.25 65,984.63 - 10,997.44 54,987.19 - 17,850.00 66,150.00 - 11,025.00 55,125.00 18,742.50 - 17,000.00 - 19,679.63 - 18,695.64 33,000.00 6,800.00 34,650.00 6,800.00 36,382.50 6,800.00 38,201.63 6,800.00 39,800.00 41,450.00 43,182.50 45,001.63 36,291.55 6,800.00 10,000.00 53,091.55 Discount Factor (12%) 1.000 0.893 0.797 0.712 8­17 Copyright © 2009 McGraw-Hill Ryerson Limited PV of cash flow 12 % - 116,500.00 35,541.40 33,035.65 30,745.94 Cumulative cash flow - 116,500.00 - 80,958.60 -47,922.95 -17,177.01 NPV 45,001.63 53,091.55 0.636 0.567 28,621.03 30,102.91 41,546.93 PV of CCA tax shield with salvage value = = 11,444.02 41,546.93 CdTc 1  0.5r  SdTc     r  d   r  d  r 1  r  t  100,000 0.25 0.34 1  (0.5 0.12)  10,000 0.25 0.34       0.12  0.25 0.25  0.12 (1  0.12)    0.12   = $20,438.73 NPV including CCA tax shield = $41,546.93 + $20,438.73 = $61,985.66 32 All cash flows are in millions of dollars Sales price of machinery in year is shown on an after-tax basis in year as a positive cash flow on the capital investment line Cash flow calculations are as follows: YEAR: Sales (traps) Revenue Working capital Change in Wk Cap 0.00 0.00 0.20 0.20 0.50 2.00 0.24 0.04 0.60 2.40 0.40 0.16 1.00 4.00 0.40 0.00 1.00 4.00 0.24 –0.16 0.60 2.40 0.00 –0.24 Revenue Expense Depreciation Pretax profit Tax After-tax profit CF from operations 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.0000 0.7500 1.2000 0.0500 0.0175 0.0325 1.2325 2.400 0.900 1.200 0.300 0.105 0.195 1.3950 4.000 1.500 1.200 1.300 0.455 0.845 2.0450 4.000 1.500 1.200 1.300 0.455 0.845 2.0450 2.400 0.900 1.200 0.300 0.105 0.195 1.3950 –6.00 –0.20 0.00 –6.20 –6.20 0.0000 –0.0400 1.2325 1.1925 1.0647 0.0000 –0.1600 1.3950 1.2350 0.9845 0.0000 0.0000 2.0450 2.0450 1.4556 0.0000 0.1600 2.0450 2.2050 1.4013 0.3250 0.2400 1.3950 1.9600 1.1122 Cash flow CF: capital investments CF from wk cap CF from operations Total PV @ 12% Net present value 33 –0.1817 If working capital requirements were only one-half of those in the previous problem, then the working capital cash flow forecasts would change as follows: Year 8­18 Copyright © 2009 McGraw-Hill Ryerson Limited Original forecast –.20 Revised forecast –.10 Change in cash flow +.10 –.04 –.02 +.02 –.16 –.08 +.08 0.0 0.0 0.0 16 08 –.08 24 12 –.12 The PV of the change in the cash flow stream at a discount rate of 12% is $.0627 million 34 a Annual depreciation is (115  15)/5 = $20 million Book value at the time of sale is $115  (2  $20) = $75 million Sales price = $80 million, so net-of-tax proceeds from the sale are: $80  (.35  $5) = $78.25 million Therefore, the net cash outlay at time is $150  $78.25 = $71.75 million b The project saves $10 million in expenses, and increases sales by $25 million The new machine would entail depreciation of $50 million per year Therefore, including the depreciation tax shield, operating cash flow increases by $35  (1  35) + 35  $50 = $40.25 million per year c NPV = 71.75 + 40.25  annuity factor(12%, years) = $24.92 million To find IRR, set the PV of the annuity to $71.75 and solve for the discount rate to find that IRR = 31.33% d All figures in $ millions After-tax annual operating cash flows: $35 × (1 – 0.35) = $ 22.75 million PV of after-tax operating cash flows: $35 × (1 – 0.35) × annuity factor (12%, 3) = $54.64 Net cash outlay at time 0: $150 – $80 = $70 million PV of net salvage value of new modem pool: ($30  $15)  $10.68 (1.12) PV of CCA tax shield: 8­19 Copyright © 2009 McGraw-Hill Ryerson Limited   70 0.3 0.35 1  (0.5 0.12)  15 0.3 0.35    0.12  0.3   0.12  0.12  0.3  (1.12)  7.35 1.06  1.575       0.42 1.12  0.42 1.404928  16.56  2.67 $13.89 NPV  70  54.64  10.68  13.89 $9.21 million 35 Project evaluation Note: The 1-year feasibility study is a sunk cost and should not be considered Price/volume increase factor = (1+ inflation)*(1+ unit sales increase) = (1.015)*(1.04)= 1.0556 For example to find sale revenue in year 2, we multiply year revenue by the price/volume factor T1 T2 T3 T4 T5 T6 Sales Revenue Less: Variable cost Fixed cost 255,000 269,178 284,144 299,942 316,619 334,223 16,000 40,000 16,889.6 40,000 17,828.7 40,000 18,819.9 40,000 19,866.3 40,000 20,970.9 40,000 EBIT Less: Taxes35 % 199,000 69,650 212,288.4 74,300.9 226,315.3 79,210.4 241,122.1 84,392.7 256,758.7 89,865.5 273,252.1 95,638.2 Net Income 129,350 137,987.5 147,104.9 156,729.4 166,893.2 177,613.9 Net Working Capital T0 40,000 T1 44,000 T2 48,400 T3 53,240 T4 58,564 T5 64,420 T6 70,862 4,000 4,400 4,840 5,324 5,856 6,442 Change in NWC Investment: Land Building Equipment Net working Capital ∆ NWC Net Income (Excluding CCA tax shield ) Salvage Value: Building T0 150,000 350,000 250,000 40,000 (790,000) T1 T2 T3 T4 T5 T6 (4,000) (4,400) (4,840) (5,324) (5,856) (6,442) 129,350 137,987.5 147,104.9 156,729.4 166,893.2 177,613.9 300,000 8­20 Copyright © 2009 McGraw-Hill Ryerson Limited 125,000 Equipment Total Cash flow (excluding CCA tax shield) Discount Factor (12%) PV excluding CCA tax shield Total PV (excluding CCA tax shields) T0 T1 T2 T3 T4 T5 T6 (790,000) 125,350 133,587.5 142,264.9 151,405.4 161,037.2 596,171.9 1.000 8929 7972 7118 6355 5674 5066 (790,000) 111,925 106,495.9 101,264.1 96,218.13 91,372.5 302,020.7 19,296.33 PV of CCA tax shield: Building =  350,000 0.04 0.35 1  (0.5 0.12)   300,000 0.04 0.35       0.12  0.04 0.12  04 (1  0.12)    0.12   = = 4,900 1.06   4,200    0.50663   0.16 1.12   0.16  15,685.34 Manufacturing Equipment =  250,000 0.25 0.35 1  (0.5 0.12)  125,000 0.25 0.35       0.12  0.12  0.25 0.25  0.12 (1  0.12)   21,875 1.06  10,937.5    0.50663   0.37 1.12   0.37  = (59,121.62 x 94643) – 14,976.39 = 40,978.08 = NPV = 19,296.33 + 15,685.34 + 40,978.08 = $ 75,959.75 Since the project has a positive net present value we should go ahead with it 36.  Assumptions Plant and Equipment Building Number useful life (yrs) Sales revenue year Growth in sales: 1-3 Growth in sales: 4-6 160,000.00 40,000.00 60,000.00 10 % 8­21 Copyright © 2009 McGraw-Hill Ryerson Limited Growth in sales: 6-8 Depreciation P&E Building -5% 20,000.00 5,000.00 15,000.0 34% 12% Operating Exp Tax rate Cost of capital Sales Operating cost Operating cash flow before tax 60,000 -15,000 60,000 - 15,000 45,000 Taxes Operating cash flow (after tax) Dep tax shield: P&E Building Total Cash Flow 60,000 -15,000 66,000 -16,500 72,600 -18,150 79,860 -19,965 75,867 -18,967 72,074 -18,018 45,000 45,000 49,500 54,450 59,895 56,900 54,055 -15,300 - 15,300 -15,300 -16,830 -18,513 -20,364 -19,346 -18,379 29,700 6,800 1,700 38,200 29,700 6,800 1,700 38,200 29,700 6,800 1,700 38,200 32,670 6,800 1,700 41,170 35,937 6,800 1,700 44,437 39,531 6,800 1,700 48,031 37,554 6,800 1,700 46,054 35,676 6,800 1,700 44,176 (a) Years NPV Cash flow - 200,000.00 38,200.00 38,200.00 38,200.00 41,170.00 44,437.00 48,030.70 46,054.17 44,176.46 Discount Factor (12%) 1.00000 0.89286 0.79719 0.71178 0.63552 0.56743 0.50663 0.45235 0.40388 PV of CF (12 %) - 200,000.00 34,107.14 30,452.81 27,190.01 26,164.28 25,214.75 24,333.85 20,832.57 17,842.13 6,137.54 Cumulative cash flow - 200,000.00 - 165,892.86 - 135,440.05 - 108,250.04 - 82,085.76 - 56,871.01 - 32,537.16 - 11,704.59 6,137.54 Based on the positive NPV Virtual Printing should accept the finance manager’s recommendations (b) The technique used in part (a) is the net present value decision rule Accordingly, accept projects with positive NPV because the total present value of future cash flows is greater than the initial cost (c) i) Years Cash flow - 200,000.00 38,200.00 38,200.00 38,200.00 41,170.00 44,437.00 48,030.70 46,054.17 44,176.46 Cumulative cash flow - 200,000.00 - 161,800.00 - 123,600.00 - 85,400.00 - 44,230.00 207.00 48,237.70 94,291.87 138,468.33 8­22 Copyright © 2009 McGraw-Hill Ryerson Limited Payback period = + (44,203/44437) = 4.995 years (ii) Discounted payback =  11,704.59 7.66 years 17,842.13 Advantage for payback period – It is relatively easy to use Disadvantage for payback period – Does not take into consideration the time value of money This method also ignores cash flows beyond the payback period Advantage of discounted payback- this method considers time value of money, unlike payback period Also, if the projects meet the cutoff, it must have a positive NPV Disadvantage of discounted payback – It does not consider cash flows beyond the payback period and therefore, it may incorrectly reject positive NPV projects Also, it is not easier to use than NPV rule because both projected cash flow and discount rate must be determined (d) IRR = 12.84 (e) Years Cash flow 200,000.00 Discount Factor (12%) PV of cash flow (12% ) Cumulative cash flow 1.000 - 200,000.00 - 200,000.00 38,200.00 0.89286 34,107.14 - 165,892.86 38,200.00 0.79719 30,452.81 - 135,440.05 38,200.00 0.71178 27,190.01 - 108,250.04 41,170.00 0.63552 26,164.28 - 82,085.76 44,437.00 0.56743 25,214.75 - 56,871.01 0.50663 24,333.85 - 32,537.16 - 11,704.59 48,030.70 46,054.17 0.45235 20,832.57 54,176.46 0.40388 21,880.96 10,176.37 PV tax shield Building 10,176.37 CdTc 1  0.5r  SdTc   , where S =   r  d   r  d  r 1  r  t 10,000 0.04 0.34 1  (0.5 0.12)     0.12  0.12  0.04 = $804.46 = 8­23 Copyright © 2009 McGraw-Hill Ryerson Limited PV tax shield P&E with salvage value = = CdTc r d 1  0.5r  SdTc   r   d  r 1  r  t  160,000 0.25 0.34 1  (0.5 0.12)  10,000 0.25 0.34    8   0.12  0.25 0.25  0.12 (1  0.12)    0.12   = 34,787.64 – 927.72 = $33,859.92 PV tax shield building = $804.46 Total NPV with salvage value = 33,859.92 + 804.46+ 10,176.37 = $ 44,840.75 8­24 Copyright © 2009 McGraw-Hill Ryerson Limited Solution to Minicase for Chapter The spreadsheet on the next page shows the cash flows associated with the project Lines – 11 match the data given in Table 8.11 except for the substitution of CCA Line 8, capital investment, shows the initial investment of $1.5 million in refurbishing the plant and buying the new machinery When the project is shut down after years, the machinery and plant will be worthless But they will not be fully depreciated and will continue to generate CCA tax shields assuming that Sheetbend has other assets in the respective asset classes The present value of the CCA tax shields on the refurbished plant and new machinery are entered in lines 14 and 15, respectively The working capital requirement is 10 percent of sales, or $300,000 This means, the investment in working capital (line 9) initially is $300,000, but in Year 5, when the project is shut down, the investment in working capital is recouped If the project goes ahead, the land cannot be sold until the end of year If the land is sold for $600,000 (as Mr Tar assumes it can be), the taxable gain on the sale is x $590,000 = $295,000, since the land is carried on the books at $10,000 Therefore, the cash flow from the sale of the land, net of tax at 35%, is $496750 The net present value of the project, which accounts for the present value of the total cash flows (Line 13) and the present value for CCA tax shield of the refurbished plant (Line 14) and the new machinery (Line 15), at a 12% discount rate, is $683,480 (Line 16) If the land can be sold for $1.5 million immediately, the after-tax proceeds will be 1,500,000 – 35 x 5(1,500,000 – 10,000) = 1,239,250 So it appears that immediate sale is the better option However, Mr Tar may want to reconsider the estimate of the selling price of the land in years If it can be sold today for $1,500,000 and the inflation rate is 4%, then perhaps it makes more sense to assume it can be sold in years for 1,500,000  1.045 = $1,824,979 In that case, the forecasted after-tax proceeds of the sale of the land in years rises to $1,507,357, which is $1,010,607 higher than the original estimate of $496,750; the present value of the proceeds from the sale of the land increases by $1,010,607/1.125 = $573,445 Therefore, under this assumption, the present value of the project increases from the original estimate of $683,480 to a new value of $1,256,925 and in this case the project is more valuable than the proceeds from selling the land immediately The extent to which the project is now more valuable is $1,256,925 – $1,239,250 = $17,675 8­25 Copyright © 2009 McGraw-Hill Ryerson Limited Dollar figures in thousands, except price per yard Year Yards sold 100.00 100.00 100.00 100.00 100.00 Price per yard 30.00 30.00 30.00 30.00 30.00 Revenue 3000.00 3000.00 3000.00 3000.00 3000.00 Cost of goods sold 2100.00 2184.00 2271.36 2362.21 2456.70 Operating cash flow (excluding CCA) 900.00 816.00 728.64 637.79 543.30 Tax at 35% 315.00 285.60 255.02 223.23 190.16 Cash flow from operations after-tax (excluding 585.00 530.40 473.62 414.56 353.14 CCA) Capital investment –1500.00 Investment in working capital –300.00 300.00 10 Sale of land (after tax) 496.75 11 Total cash flow –1800.00 585.00 530.40 473.62 414.56 1149.89 12 PV of total cash flow (excluding CCA) –1800.00 522.32 422.83 337.11 263.45 652.45 13 Total present value of the cash flows 398.16 (excluding CCA) (A) 14 PV of CCA tax shield on refurbished plant (B) 48.71 15 PV of CCA tax shield of new machinery (C) 236.61 16 Net present value (A) + (B) + (C) 683.48 The calculations for the CCA tax shields are as follows: PV of the CCA tax shield on the refurbished plant: = CdTc 1  0.5r  SdTc   , where S =   r  d   r  d  r 1  r  t  500000 0.05 0.35 1  (0.5 0.12)    0.12  0.12  0.05  8750 1.06  $48,713.24 0.17 1.12  PV of the CCA tax shield of the new machinery: 1000000 0.30 0.35 1  (0.5 0.12)     0.12  0.12  0.30 105000 1.06   $236,607.14 0.42 1.12  8­26 Copyright © 2009 McGraw-Hill Ryerson Limited (We compare the NPV of the project to the value of an immediate sale of the land This treats the problem as two competing mutually exclusive investments: sell the land now versus pursue the project The investment with higher NPV is selected Alternatively, we could treat the after-tax cash flow that can be realized from the sale of the land as an opportunity cost at time if the project is pursued In that case, the NPV of the project would be reduced by the initial cash flow given up by not selling the land Under this approach, the decision rule is to pursue the project if NPV is positive, accounting for that opportunity cost This approach would result in the same decision as the one we have presented.) 8­27 Copyright © 2009 McGraw-Hill Ryerson Limited ... Do-It-Right * Investment – PV of CCA tax shield ** Annuity discounted at 12%; number of years = project life 26 Net working capital Investment in NWC Investment in Plant & eq Cash flow from investment. .. $61,985.66 32 All cash flows are in millions of dollars Sales price of machinery in year is shown on an after-tax basis in year as a positive cash flow on the capital investment line Cash flow calculations... because both projected cash flow and discount rate must be determined (d) IRR = 12.84 (e) Years Cash flow 200,000.00 Discount Factor (12%) PV of cash flow (12% ) Cumulative cash flow 1.000 - 200,000.00