Question

A firm is considering an investment in a new machine with a price of $18.06 million to replace its existing machine. The current machine has a book value of $6.06 million and a market value of $4.56 million. The new machine is expected to have a four-year life, and the old machine has four years left in which it can be used. If the firm replaces the old machine with the new machine, it expects to save $6.76 million in operating costs each year over the next four years. Both machines will have no salvage value in four years. If the firm purchases the new machine, it will also need an investment of $256,000 in net working capital. The required return on the investment is 11 percent, and the tax rate is 35 percent. Assume the company uses straight-line depreciation.

a) What is the NPV of the decision to purchase a new machine? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. Enter your answer in dollars, not millions of dollars, e.g., 1,234,567.) b) What is the IRR of the decision to purchase a new machine? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

a

Time line		0	1	2	3	4
Proceeds from sale of existing asset	=selling price* ( 1 -tax rate)	2964000
Tax shield on existing asset book value	=Book value * tax rate	2121000
Cost of new machine		-18060000
Initial working capital		-256000
=Initial Investment outlay		-13231000
Savings			6760000	6760000	6760000	6760000
-Depreciation	Cost of equipment/no. of years		-4515000	-4515000	-4515000	-4515000
=Pretax cash flows			2245000	2245000	2245000	2245000
-taxes	=(Pretax cash flows)*(1-tax)		1459250	1459250	1459250	1459250
+Depreciation			4515000	4515000	4515000	4515000
=after tax operating cash flow			5974250	5974250	5974250	5974250
reversal of working capital						256000
+Tax shield on salvage book value	=Salvage value * tax rate					0
=Terminal year after tax cash flows						256000
Total Cash flow for the period		-13231000	5974250	5974250	5974250	6230250
Discount factor=	(1+discount rate)^corresponding period	1	1.11	1.2321	1.367631	1.5180704
Discounted CF=	Cashflow/discount factor	-13231000	5382207	4848835	4368320.1	4104058.7
NPV=	Sum of discounted CF=	5472421.29

b

Total Cash flow for the period		-13231000	5974250	5974250	5974250	6230250
Discount factor=	(1+discount rate)^corresponding period	1	1.291023	1.666742	2.1518026	2.7780278
Discounted CF=	Cashflow/discount factor	-13231000	4627530	3584389	2776393.1	2242688.2
NPV=	Sum of discounted CF=	0
IRR is discount rate at which NPV = 0 =	29.10%