【正文】 T) + Depreciation x T ? The BottomUp Approach OCF = (S C D) + D (S C D) ? T = (S C D) ? (1 T) + D = Net ine + Depreciation ? The TopDown Approach OCF = (S C D) + D (S C D) ? T = (S C) (S C D) ? T = Sales Costs Taxes Fall 2021 COMM 203 31 Tax Shield Approach ? OCF = (1TC) S – (1TC) C +TC *Depreciation ? Implications of the above formula ? $1 increase in sales raises OCF after taxes by $(1TC) ? $1 increase in costs decreases OCF after taxes by $(1TC) ? $1 increase in depreciation (CCA) increases the OCF by $TC. Fall 2021 COMM 203 32 Present Value of Tax Shield on CCA ? Notations C = Capital cost of new assets purchased d = CCA rate for the asset class (speed of depreciation) k = discount rate TC = Corporate marginal tax rate S = Salvage value of the asset at the end of year n Fall 2021 COMM 203 33 Present Value of Tax Shield on CCA ? Tax shield on CCA without halfyear rule Y e a r B e g inn ing U CC CCA E nd ing U CC T a x S hie ld 1 C Cd C(1 d) Cd T C 2 C(1 d) C(1 d )d C(1 d)2 C(1 d )d T C 3 C(1 d)2 C(1 d)2d C(1 d)3 C(1 d)2dT C … … … … … ? ?dkC d T C?? s hi e ld ) P V ( t a xFall 2021 COMM 203 34 Present Value of Tax Shield on CCA ? With halfyear rule, the tax shield each year is Y e ar B e g i nn i ng UCC CCA E nd i ng UCC T ax S hi e l d o n C C A 1 0. 5C 0. 5C d 0. 5C ( 1 d) 0. 5C d T C 2 0. 5C ( 1 d) + 0. 5C 0. 5C ( 1 d ) d + 0. 5C d 0. 5C ( 1 d)2 + 0. 5C ( 1 d) 0. 5C ( 1 d ) d T C + 0. 5C d T C 3 0. 5C ( 1 d)2 + 0. 5C ( 1 d) 0. 5C ( 1 d)2d + 0. 5C ( 1 d ) d 0. 5C ( 1 d)3 + 0. 5C ( 1 d)2 0. 5C ( 1 d)2dT C + 0. 5C ( 1 d ) d T C … … … … … ????????????????kkdkC d TkdkC d TdkC d TPVCCC11C C A ) on s h i e l d ( T a xFall 2021 COMM 203 35 Present Value of Tax Shield on CCA ? After nyear asset life, the asset is sold for its salvage value S. ? Assume the asset pool is still open, the firm will lose the tax shield associated with S. ? The tax shield on the salvage value is a growing perpetuity ? The PV of tax shield on CCA after adjustment for salvage value is nCCkdkS d TkkdkC d TPV)1(11( T S C C A )??????????????? If the asset pool is terminated, see the treatment in Chapter 2, pp. 4748. Fall 2021 COMM 203 36 The Fairways Example Revisited: Using Tax Shield Approach ? Variable cost is a growing annuity, its aftertax PV can be simplified as Y e a r 1 2 3 4 5 6R e v e n u e s 60000 62250 64500 66750 69000 71250A f t e r t a xR e v e n u e 48000 49800 51600 53400 55200 57000P V ( R e v ) 41739 37656 33928 30532 27444 24643s u m ( P V R e v ) 195941095, )(30006????????? ??????????PVFall 2021 COMM 203 37 The Fairways Example Revisited: Using Tax Shield Approach ? Fixed costs are an annuity, its aftertax PV is 4 6 2,1 6 0)( )(5 3 0 0 0 6 ??????? ???PV? The PV of tax shield on CCA is 140,2)(1))()(1 8 0 0()())()(1 8 0 0 0()1(116?????????? ????????????????nCCkdkS d TkkdkC d TFall 2021 COMM 203 38 The Fairways Example Revisited: Using Tax Shield Approach ? PV(OCF) = PV(aftertax revenue) PV(aftertax cost)+PV(TSCCA) =195,941(10,095+160,462)+2,140 =27,524 ? This is different from the result ($27,478) of previous approach of project cash flows. ? The difference = 27,52427,478 = 46 ? Why? Fall 2021 COMM 203 39 The Fairways Example Revisited: Using Tax Shield Approach ? The UCC (book value) at the end of year 6 =$2572 ? The salvage value (market value)=$1,800 ? Under the 1st approach, The difference of $772 is not depreciated and is still in the asset pool. Its PV is 45)(1))((772)1(16???????? nCkdkS d T? This is the difference between the two approaches Fall 2021 COMM 203 40 Another Example of Capital Budgeting: Pestech Co. Pestech Company developed a new householduse laserguided cockroach search and destroy system. The pany’s budgeting officer projects the sales of the product for the next five years as follows: Y ea r 1 2 3 4 5 U n i t Sal es ( i n t h o u s a n d ) 63 75 86 60 36 Fall 2021 COMM 203 41 Another Example of Capital Budgeting: Pestech Co. The new system will be priced to sell at $100 each. The cockroach eradicator project will require $685,000 in working capital to start, and total working capital will rise to 35 percent of sales. The variable cost per unit is $60, and total fixed costs are $35,000 per year. The equipment necessary to begin production will cost a total of $6 million. This equipment is mostly industrial machinery and thus qualifies for CCA at a rate of 20%. In five years, this equipment will actually be worth about onethird of its cost. The relevant tax rate is 40% percent, and the required rate of return is 20%. Based on these preliminary estimates, what is the NPV of the project? Fall 2021 COMM 203 42 Pestech Co. Example Project Cash Flow Approach Ye a r 0 1 2 3 4 5 O p e r a t i n g C a s h F l o w s (1 ) S a l e s (u