A proposed cost-saving device has an installed cost of $730,000. The device will
ID: 2644841 • Letter: A
Question
A proposed cost-saving device has an installed cost of $730,000. The device will be used in a five-year project but is classified as three-year MACRS property for tax purposes. The required initial net working capital investment is $55,000, the marginal tax rate is 35 percent, and the project discount rate is 9 percent. The device has an estimated year 5 salvage value of $80,000. What level of pretax cost savings do we require for this project to be profitable? Refer to chart below.
Property Class Year Three-Year 33.33% 44.45 14.81 7.41 Seven-Year 14.29% 24.49 17.49 12.49 8.93 8.92 8.93 4.46 Five-Year 2 3 4 5 6 7 20.00% 32.00 19.20 11.52 11.52 5.76Explanation / Answer
Depreciation schedule for 4 years as per MACRS is as follows:
Calculation of cash flows:
Let x be the cash savings every year.
Net savings after depreciation =X -$243,309
Savings after tax =0.65(X-$243,309)
=0.65x - $158150.85
Discount factor @9% for first year = 1/1.09 =0.91743
cash flows for year 1 =0.65x - $158,150 +243,309 =0.65x + 85,159.
Disocunted cash inflows for year 1 = (0.65x+85,159) * 0.91743
=0.59633x +$78,127 -------------(1)
Year 2:
Net savings after depreciation =X -$324485
Savings after tax =0.65(X-$324,485)
=0.65x - $210,915
Discount factor @9% for second year = 1/(1.09 )2=0.84168
cash flows for year 2 =0.65x - $210915 +$324,485 =0.65x + $113,570
Disocunted cash inflows for year 1 = (0.65x+$113,570) * 0.84168
=0.547092x + $95589.60 -------------(2)
Year 3:
Net savings after depreciation =X -$108,113
Savings after tax =0.65(X-$108,113)
=0.65x - $70,273.45
Discount factor @9% for year 3 = 1/(1.09)3 =0.77218
cash flows for year 3 =0.65x - $70,273.45 +$108,113 =0.65x + $37,839.55
Disocunted cash inflows for year31 = (0.65x+$37,839.55) * 0.77218
=0.501917x + $29,218.94---(3)
Year 4:
Net savings after depreciation =X -$54,039
Savings after tax =0.65(X-$54,039)
=0.65x - $35,125.35
Discount factor @9% for year4 = 1/(1.09)4 =0.70843.
cash flows for year 4 =0.65x - $35,125.35 +$54039 =0.65x + $18,913.65
Disocunted cash inflows for year4 = (0.65x+$18,913.65) * 0.70843
=0.46047x + $12,888.93---(4)
Year 5:
Cash savings in year 5 =x.
Cash flows after tax = 0.65x
Salvage value =$80,000.
After tax profit =$80,000* 0.65 =$52,000 ( as the asset is totally depreciated any amount realized as salvage value is a profit)
Cash inflows in year 5 = 0.65x+52000
Discount factor for year 5 =0.64993
Discountd cash inflows for year 5 =0.42246x + $33,796.36 ----------(5)
Discounted cash inflows over 5 years = 1+2+3+4+5
Discounted cash inflows =
0.59631x + 78125 +0.547092x + $95589.60 +0.501917x + $29,218.94+0.46047x + $12,888.93+0.42246x + $33,796.36
= 2.52827x +$249,618.83
Cash outflows = Cost of the machine + Increase in net working capital
=$730,000+$55,000 =$785,000.
For the project to be profitable, Discounted cash inflows must be greater than the Discounted cash outflows
= 2.52827x +$249,618.83 - $785,000 =0
2.52827x=$535381.17
x = $211757.90 rounded to $211,758.
Therefore, the project is profitable if it is able to produce a pretax cash savings of $211,758. per year
Year Depreciation 1 $243,309.00 2 $324,485.00 3 $108,113.00 4 $54,093.00.