Question

Our company is considering a new machine which cost $1,000,000. The old machine cost $500,000, and was being depreciated to a zero book value over a 10 year period. The old machine is 5 years old, and could be sold for $300,000. The new machine will be depreciated to zero over 10 years, and could be sold for $400,000 at the end of 10 years. The new machine would require $50,000 to install, and increase net working capital by $30,000. The new machine would increase revenue by $200,000 per year and reduce our expenses by $50,000 per year. Calculate the net present value and IRR, with a tax rate of 35%, and a cost of capital of 11%. (Straight line depreciation)

Answer 1

Book value on existing machine

Book value = (purchase price)*remaining life/total life
= (500000)*5/10
= 250000

Time line		0	1	2	3	4	5	6	7	8	9	10
Proceeds from sale of existing asset	=selling price* ( 1 -tax rate)	195000
Tax shield on existing asset book value	=Book value * tax rate	87500
Cost of new machine		-1050000
Initial working capital		-30000
=Initial Investment outlay		-797500
Savings	increase in revenues-reduction in expenses		250000	250000	250000	250000	250000	250000	250000	250000	250000	250000
-Depreciation	Cost of equipment/no. of years		-105000	-105000	-105000	-105000	-105000	-105000	-105000	-105000	-105000	-105000
=Pretax cash flows			145000	145000	145000	145000	145000	145000	145000	145000	145000	145000
-taxes	=(Pretax cash flows)*(1-tax)		94250	94250	94250	94250	94250	94250	94250	94250	94250	94250
+Depreciation			105000	105000	105000	105000	105000	105000	105000	105000	105000	105000
=after tax operating cash flow			199250	199250	199250	199250	199250	199250	199250	199250	199250	199250
reversal of working capital												30000
+Proceeds from sale of equipment after tax	=selling price* ( 1 -tax rate)											260000
+Tax shield on salvage book value	=Salvage value * tax rate											0
=Terminal year after tax cash flows												290000
Total Cash flow for the period		-797500	199250	199250	199250	199250	199250	199250	199250	199250	199250	489250
Discount factor=	(1+discount rate)^corresponding period	1	1.11	1.2321	1.367631	1.5180704	1.6850582	1.8704146	2.07616	2.30454	2.558037	2.839421
Discounted CF=	Cashflow/discount factor	-797500	179504.5	161715.77	145689.88	131252.15	118245.18	106527.19	95970.44	86459.9	77891.76	172306.3
NPV=	Sum of discounted CF=	478062.9771

Total Cash flow for the period		-797500	199250	199250	199250	199250	199250	199250	199250	199250	199250	489250
Discount factor=	(1+discount rate)^corresponding period	1	1.2285592	1.50935763	1.8543351	2.2781604	2.7988549	3.4385588	4.224473	5.19001	6.376241	7.833589
Discounted CF=	Cashflow/discount factor	-797500	162181.85	132009.801	107450.91	87460.916	71189.829	57945.788	47165.65	38391	31248.82	62455.41
NPV=	Sum of discounted CF=	2.10563E-05
IRR is discount rate at which NPV = 0 =	22.86%