A proposed cost-saving device has an installed cost of $750,000. The device will
ID: 2723348 • Letter: A
Question
A proposed cost-saving device has an installed cost of $750,000. 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 $57,000, the marginal tax rate is 34 percent, and the project discount rate is 10 percent. The device has an estimated Year 5 salvage value of $82,000. What level of pretax cost savings do we require for this project to be profitable? MACRS schedule (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
A proposed cost-saving device has an installed cost of $750,000. 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 $57,000, the marginal tax rate is 34 percent, and the project discount rate is 10 percent. The device has an estimated Year 5 salvage value of $82,000. What level of pretax cost savings do we require for this project to be profitable? MACRS schedule (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Explanation / Answer
The depreciation each year is:
Year 1 = $750,000(.3333) = $249,975
Year 2 = $750,000(.4445) = $333,375
Year 3 = $750,000(.1481) = $111,075
Year 4 = $750,000(.0741) = $55,575
Using the tax shield approach, the OCF each year is:
OCF 1 = (S C)(1 .34) + .34($249,975)
OCF 2 = (S C)(1 .34) + .34($333,375)
OCF 3 = (S C)(1 .34) + .34($111,075)
OCF 4 = (S C)(1 .34) + .34($55,575)
OCF 5 = (S C)(1 .34)
After-tax salvage value = $82,000(1 .34) = $54,120
Let us assume Pre tax saving as Sales – cost i.e S-C
The equation for the NPV of the project is :
NPV = 0
0= $750,000 57,000 + (S C)(.66)(PVIFA 10%,5 ) + .34($249,975 / 1.10 + $333,375 / 1.10 2 + $111,075 / 1.10 3 + $55,575 / 1.10 4 ) + ($57,000 + 54,120) / 1.10 5
0= -$ 807,000 +(S C)(.66)(PVIFA 10%,5 )+ 0.34 ($227,250 + 275,516.53 + 83,452.29 + 37,958.47 + 38,931.77 )
0=-$807,000 +(S C)(.66)(PVIFA 10%,5 )+ 0.34 x 663,109.06
0=--$807,000+ (S C)(.66)(PVIFA 10%,5 )+ 225,457.08
0= (S C)(.66)(PVIFA 10%,5 )- $525,782.94
(S C)(.66)(PVIFA 10%,5 )= $525,782.94
Solving this equation for the sales minus costs, we get:
(S C)(.66)(PVIFA 10%,5 ) = $525,782.94
(S-C) x 0.66 x 3.7908=$525,782.94
(S-C) x 2.5019 =$525,782.94
(S C) = $525,782.94/2.5019
(S C) =$210,151.84
Pretax savings = $210,151.84