Question

Talia’s Tutus is considering purchasing a new sewing machine. The old machine it has right now was bought 2 years ago for $30,000, with an assume life of 6 years and an assume salvage value of $5,000. The firm uses straight-line depreciation. The old machine can be sold today for $25,000. If the firm continues using the old machine, it will be salvaged at the end of its life. The new machine can be purchased today for $40,000. The new machine falls in the MACRS 3-year class. With the new sewing machine, the firm is expected to have an additional revenue of $15,000 every year. The variable cost is 40% of the revenue, and the fixed cost is $3,000 each year. If the opportunity cost of capital is 12%, corporate tax rate is 35%, and capital gain tax is 15%, what are the project’s NPV and IRR?

Answer 1

existing machine book value

Book value = (purchase price-Final book value)*remaining life/total life+final book value
= (30000-5000)*4/6+5000
= 21666.6666666667

Time line		0	1	2	3	4
Proceeds from sale of existing asset	=selling price* ( 1 -tax rate)	16250
Tax shield on existing asset book value	=Book value * tax rate	7583.3345
Cost of new machine		-40000
=Initial Investment outlay		-16166.6655
3 years MACR rate			33.33%	44.45%	14.81%	7.41%
Sales			15000	15000	15000	15000
Profits	Sales-variable cost		9000	9000	9000	9000
Fixed cost			-3000	-3000	-3000	-3000
-Depreciation	=Cost of machine*MACR%		-13332	-17780	-5924	-2964
=Pretax cash flows			-7332	-11780	76	3036
-taxes	=(Pretax cash flows)*(1-tax)		-4765.8	-7657	49.4	1973.4
+Depreciation			13332	17780	5924	2964
=after tax operating cash flow			8566.2	10123	5973.4	4937.4
+Tax shield on salvage book value	=Salvage value * tax rate					0
=Terminal year after tax cash flows						0
Total Cash flow for the period		-16166.6655	8566.2	10123	5973.4	4937.4
Discount factor=	(1+discount rate)^corresponding period	1	1.12	1.2544	1.404928	1.5735194
Discounted CF=	Cashflow/discount factor	-16166.6655	7648.393	8069.994	4251.7481	3137.807
NPV=	Sum of discounted CF=	6941.276072

Total Cash flow for the period		-16166.6655	8566.2	10123	5973.4	4937.4
Discount factor=	(1+discount rate)^corresponding period	1	1.334788	1.781658	2.3781346	3.1743045
Discounted CF=	Cashflow/discount factor	-16166.6655	6417.651	5681.787	2511.8006	1555.4274
NPV=	Sum of discounted CF=	1.19338E-05
IRR is discount rate at which NPV = 0 =	33.48%