Question

A proposed cost-saving device has an installed cost of $735,000. 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 $145,000, the marginal tax rate is 23 percent, and the project discount rate is 11 percent. The device has an estimated Year 5 salvage value of $104,000. 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.)

Answer 1

Initial investment, C₀ = installed cost of $735,000 + initial net working capital investment is $145,000 = 735,000 + 145,000 =  880,000

Terminal year cash flows:

• Since the device would be fully depreciated under MACRS schedule, taxable basis will be zero.
• Post tax salvage value at the end of year 5 = pre tax salvage value x (1 - Tax rate) = 104,000 x (1 - 23%) =  80,080
• Release of working capital = 145,000
• Hence terminal year cash flow = 80,080 + 145,000 =  225,080

Discount rate = R = 11%

PV(TCF) = Present value of terminal year cash flow = Terminal year cash flow / (1 + R)⁵ = 225,080 / (1 + 11%)⁵ = 133,574

Depreciation tax shield under MACRS 3 year depreciation schedule:

Asset Cost	A	735,000
Year	N	1	2	3	4
Depreciation rate	d	33.33%	44.45%	14.81%	7.41%
Depreciation	D = d x A	244,976	326,708	108,854	54,464
Tax rate	T	23%
Depreciation tax shield	DTS = D x T	56,344	75,143	25,036	12,527
PV Factor @ 11%	(1+R)(-N)	0.9009	0.8116	0.7312	0.6587
PV of Depreciation tax shield	DTS x PV Factor	50,761	60,988	18,306	8,252
Total PV of Depreciation tax shield; PV (DTS)	Sum of all the items in above row	138,306

Let's now assume that pre tax annual cost saving is S. Hence post tax cost savings will be = S x (1 - 23%) = 0.77S

Hence, the present value of post tax cost savings will be = PV of annuity of 0.77S over five years = 0.77S x Sum of PV factors over five years = 0.77S x [1 - (1+R)^-N] / R = 0.77S x [1 - (1 + 11%)^-5] / 11% =  2.84584S

NPV equation will be:

NPV = -C₀ + PV (DTS) + PV(TCF) + PV of post tax annual cost savings over five years = -880,000 + 138,306 + 133,574 + 2.84584S

For this project to be profitable, NPV = 0

or, -880,000 + 138,306 + 133,574 + 2.84584S = 0

Hence, S = (880,000 - 138,306 - 133,574) / 2.84584 =  213,687.21

Level of pretax cost savings do we require for this project to be profitable = S = $ 213,687.21