Question

The Cabbage Patch Company currently uses a printing press that was purchased 5 years ago. The machine has a life of 15 years and was purchased for $7500. The current book value of the machine is $5000. A new machine costing $12,000 can be purchased with a life of 10 years and will expand sales from $10,000 to $11,000 a year. Also labor cost would be reduced from $7,000 to $5,000. The new machine will have a salvage value of $2,000 at the end of 10 years. The old machine has a market value of $1000. Taxes are at a 40% rate and the firm’s cost of capital is 10%. The company will sell the new equipment at the end of its life for $2,000. The old equipment has a zero salvage value.

1. Use straight line depreciation to calculate the depreciation.

2. Calculate the net present value of the new machine

Answer 1

Time line		0	1	2	3	4	5	6	7	8	9	10
Proceeds from sale of existing asset	=selling price* ( 1 -tax rate)	600
Tax shield on existing asset book value	=Book value * tax rate	2000
Cost of new machine		-12000
=Initial Investment outlay		-9400
gain in sales + savings in labor cost	=11000-10000+7000-5000=		3000	3000	3000	3000	3000	3000	3000	3000	3000	3000
-Depreciation	(Cost of equipment-salvage value)/no. of years		-1400	-1400	-1400	-1400	-1400	-1400	-1400	-1400	-1400	-1400	-2000	=Salvage Value
=Pretax cash flows			1600	1600	1600	1600	1600	1600	1600	1600	1600	1600
-taxes	=(Pretax cash flows)*(1-tax)		960	960	960	960	960	960	960	960	960	960
+Depreciation			1400	1400	1400	1400	1400	1400	1400	1400	1400	1400
=after tax operating cash flow			2360	2360	2360	2360	2360	2360	2360	2360	2360	2360
+Proceeds from sale of equipment after tax	=selling price* ( 1 -tax rate)											1200
+Tax shield on salvage book value	=Salvage value * tax rate											-800
=Terminal year after tax cash flows												400
Total Cash flow for the period		-9400	2360	2360	2360	2360	2360	2360	2360	2360	2360	2760
Discount factor=	(1+discount rate)^corresponding period	1	1.1	1.21	1.331	1.4641	1.61051	1.771561	1.948717	2.14359	2.357948	2.593742
Discounted CF=	Cashflow/discount factor	-9400	2145.4545	1950.41322	1773.1029	1611.9118	1465.374	1332.1585	1211.053	1100.96	1000.87	1064.099
NPV=	Sum of discounted CF=	5255.39569