Question

60 answer 2. Your firm is considering a project that would require purchasing $7.2 million worth of new equipment. Determine the present value of the depreciation tax shield associated with this equipment if the firm's tax rate is 31%, the appropriate cost of capital is 9%, and the equipment can be depreciated a. Straight-line over a 10-year period, with the first deduction starting in one year. b. Straight-line over a five-year period, with the first deduction starting in one year. c. Using MACRS depreciation with a five-year recovery period and starting immediately. d. Fully as an immediate deduction. A Answer Equipment cost = 7.2 Tax rate = 31% Cost of capital = 9% PV(DTS) 1 [MACRS] 20% 32% 19% 12% 12% 6% Option a $1.43 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 Option t $1.74 0.45 0.45 0.45 0.45 0.45 Optione $1.93 0.45 0.71 0.43 0.26 0.26 0.13 Option d $2.23 10 0.22 2.23

How to calculate Present Value Tax Shield

Answer 1

Option a
Year	Depreciation	Tax on depreciation	PV of tax shield
0
1	0.72	0.2232	0.204770642
2	0.72	0.2232	0.187862974
3	0.72	0.2232	0.172351353
4	0.72	0.2232	0.158120507
5	0.72	0.2232	0.145064685
6	0.72	0.2232	0.133086867
7	0.72	0.2232	0.122098043
8	0.72	0.2232	0.112016554
9	0.72	0.2232	0.10276748
10	0.72	0.2232	0.094282092
		TOTAL	1.432421199

Option b
Year	Depreciation	Tax on depreciation	PV of tax shield
0
1	1.44	0.4464	0.409541284
2	1.44	0.4464	0.375725949
3	1.44	0.4464	0.344702705
4	1.44	0.4464	0.316241014
5	1.44	0.4464	0.290129371
6
7
8
9
10
		TOTAL	1.736340324

Option c
Year	Depreciation	Tax on depreciation	PV of tax shield
0	1.44	0.4464	0.4464
1	2.304	0.71424	0.655266055
2	1.368	0.42408	0.356939652
3	0.864	0.26784	0.206821623
4	0.864	0.26784	0.189744609
5	0.432	0.13392	0.087038811
6
7
8
9
10
		TOTAL	1.49581075

d: Depreciation = 7.2

Tax = 31%*7.2 = 2.23

this is also the present value since tax dedcution is taken immediately.

WORKINGS

Book1- Excel AutoSave Off Sign in X O Tell me what you want to do Comments Review File Home Insert Draw Page Layout Formulas Data View Help Share GInsert Delete X == A A General Calibri 10 L Paste Conditional Format as Cell Sort & Find & A = E 3 - $% BIU Format Formatting Table Styles Filter Select Clipboard Alignment Number Styles Cells Editing Font fr A1 Option a E A B C D F H J K L M N A 1 Option a Option c Option b 2 Year Depreciation Tax on depreciation PV of tax shield 7.2 20 % 7.2 32 % 7.2 19 % Depreciation Tax on depreciation PV of tax shield Year Depreciation Tax on depreciation PV of tax shield Year M3/1.09 K3 3 0 L3*31% 0 0 H4/1.09 F4 4 1 7.2/10 -B4 31% C4/1.09 A4 7.2/5 7.2/5 7.2/5 7.2/5 7.2/5 G4*31% -L4*31 % M4/1.09^K4 1 1 5 2 7.2/10 B5*31% C5/1.09 A5 G5 *31% H5/1.09 F5 L5*31% =M5/1.09 K5 2 2 6 3 7.2/10 -B6*31% C6/1.09 A6 G6*31% H6/1.09 F6 7.2*12% L6*31 % =M6/1.09 K6 3 3 7 4 7.2/10 =B7*31% C7/1.09 A7 G7*31 % -H7/1.09 F7 7,2*12% L7*31% M7/1.09 K7 4 C8/1.09 A8 8 5 7.2/10 =B8*31% -G8 31 % H8/1.09 F8 =7.2*6% L8+31% M8/1.09 K8 5 9 6 7.2/10 B9*31% C9/1.09 A9 C10/1.09 A10 C11/1.09 A11 C12/1.09 A12 C13/1.09 A13 6 10 7 7.2/10 =B10*31% 7 11 8 7.2/10 B11*31% 12 9 7.2/10 B12*31% 13 10 7.2/10 B13*31% 10 10 14 SUM(D4:D13) =SUM(14:113) 15 TOTAL TOTAL SUM(N4:N13) TOTAL 16