【正文】 1 OCF 2 OCF 3 OCF The result is a threeyear annuity with an unknown cash flow equal to “OCF.” Fall 2021 COMM 203 56 Example: Setting the Bid Price (Cont’d) ? The PV annuity factor for 3 years at 15% is . Setting NPV = $0, NPV = $0 = – $49,085 + (OCF ? ), thus OCF = $49,085/ = $21,500 ? Using the bottomup approach to calculate OCF, OCF = Net ine + Depreciation $21,500 = Net ine + $50,000/3 = Net ine + $16,667 Net ine = $4,833 Fall 2021 COMM 203 57 Example: Setting the Bid Price (Cont’d) ? Next, since annual costs are $40,000 + $12,000 = $52,000 Net ine = (S C D) ? (1 T) $4,833 = (S ? .66) (52,000 ? .66) (16,667 ? .66) S = $50,153/.66 = $75, Hence, sales need to be at least $76,000 per year (or $19,000 per MUDD)! Fall 2021 COMM 203 58 Another Example: Setting the Bid Price Background: Suppose we also have the following information. 1. The bid calls for 20 MUDDs per year for 3 years. 2. Our costs are $35,000 per unit. 3. Capital spending required is $250,000。 and depreciation = $250,000/5 = $50,000 per year 4. We can sell the equipment in 3 years for half its original cost: $125,000. The asset pool is then closed. Fall 2021 COMM 203 59 Another Example: Setting the Bid Price (continued) 5. The aftertax salvage value equals the cash in from the sale of the equipment, less the cash out due to the increase in our tax liability associated with the sale of the equipment for more than its book value: Book value at end of 3 years = $250,000 50,000(3) = $100,000 Book gain from sale = $125,000 100,000 = $25,000 Net cash flow = $125,000 25,000(.39) = $115,250 6. The project requires investment in working capital of $60,000. 7. Required return = 16%。 tax rate = 39% Fall 2021 COMM 203 60 Another Example: Setting the Bid Price (continued) ? The cash flows ($000) are: 0 1 2 3O C F $ O C F $ O C F $ O C F C h g. i n NW C 6 0 60C a pi t a l S pe n di n g 2 5 0 1 1 5 . 2 5 3 1 0 $ O C F $ O C F$ O C F +1 7 5 . 2 5Find the OCF such that the NPV is zero at 16%: +$310,000 175,250/ = OCF ? (1 1/)/.16 $197, = OCF ? OCF = $88,Fall 2021 COMM 203 61 Example: Setting the Bid Price (concluded) If the required OCF is $88, what price must we bid? Sales $812, Costs 700, Depreciation 50, EBIT $ 62, Tax 24, Net ine $ 38, Sales = $62, + 50,000 + 700,000 = $812, per year, and the bid price should be $812,$40,618 per unit. Fall 2021 COMM 203 62 Investments of Unequal Lives ? Suppose the firm needs to choose between two machines, A and B. The two machines are designed differently, but have identical capacity and do exactly the same job. The costs of running two machines are as follows. We assume no taxes in this example. ? Machine B has a lower PV of cost, but replaced earlier M a c h i n e C 0 C 1 C 2 C 3 P V a t 10% A 15 4 4 4 2 4 .9 5 B 10 6 6 2 0 .4 1 Fall 2021 COMM 203 63 Equivalent Annual Cost (EAC) ? Look at the following two investments ? How to calculate the EAC for machine A? ? For machine B, C 0 C 1 C 2 C 3 P V a t 1 0 % M a c h i n e A 15 4 4 4 2 4 . 9 5 3 y e a r a n n u i t y 1 0 . 0 3 1 0 . 0 3 1 0 . 0 3 2 4 . 9 5 3 ????????CCACCCC 2 ?????CCACFall 2021 COMM 203 64 Example: Equivalent Annual Cost Analysis with Taxes ? Two types of batteries are being considered for use in electric golf carts at City Country Club. Burnout brand batteries cost $36, have a useful life of 3 years, will cost $100 per year to keep charged, and have a salvage value of $5. Longlasting brand batteries cost $60 each, have a life of 5 years, will cost $88 per year to keep charged, and have a salvage value of $5. The tax rate for the club is 34%. Fall 2021 COMM 203 65 Example: Equivalent Annual Cost Analysis with Taxes (continued) ? Cash flows for Burnout are: OCF = (Sales Costs)(1 T) + Depreciation(T) = (0 100)(.66) + 12(.34) = $66 + 4 = $62 Operating Capital Total Year cash flow spending = cash flow 0 $ 0 $ 36 $36 1 62 0 62 2 62 0 62 3 62 + Fall 2021 COMM 203 66 Example: Equivalent Annual Cost Analysis with Taxes (continued) ? OCFs for Longlasting are: OCF = (Sales Costs)(1 T) + Depreciation(T) = (0 88)(.66) + 12(.34) = $58 + 4 = $54 Capital Total Year OCF spending = cash flow 0 $ 0 $ 60 $60 1 54 0 54 2 54 0 54 3 54 0 54 4 54 0 54 5 54 + Fall 2021 COMM 203 67 Example: Equivalent Annual Cost Analysis with Taxes (continued) ? Using a 15% required return, calculate the cost per year for the two batteries. Calculate the PV of the cash flows: The present value of total cash flows for Burnout is $ The present value of total cash flows for Longlasting is $ Fall 2021 COMM 203 68 Example: Equivalent Annual Cost Analysis with Taxes (continued) What 3 year annuity has the same PV as Burnout? The PV annuity factor for 3 years at 15% is : $ = EAC ? EAC = $$ What 5 year annuity has the same PV as Longlasting? The PV annuity factor for 5 years at 15% is : $ = EAC ? EAC = $$