Question

The Baldwin Company is considering investing in a machine that produces bowling balls. The cost of the machine is $100,000 and production is expected to be 8,000 units per year during the five-year life of the machine. The expected resale value is $5,000 (in real terms).
Since the interest in bowling is declining, the management believes that the nominal price of bowling balls will increase at only 2% per year. The nominal price of bowling balls in the first year will be $20. On the other hand, plastic used to produce bowling balls is rapidly becoming more expensive. Because of this, production costs are expected to grow at 10% (nominally) per year. First-year nominal production costs will be $10 per unit.
The company's nominal cost of capital is 15%. The rate of inflation is 5%. Ignore taxes. Should the project be undertaken?

Please give me a answer with equations and step by step solutions so that I can understand.

Answer 1

		Nominal cost of capital=15%=0.15
		Nominal cost of capital to be applied on nominal cash flows:
		CALCULATION OF NOMINAL CASH FLOWS:
		Initial Cash Flow	($100,000)
		Quantity of production in units	8000
		Annual nominal cash flows:
			A	B=A*8000	C	D=C*8000	E=B-D
		Year	Price	Annual Sales	Production cost per unit	Annual production costs	Annual Cash inflow
		1	$20	$160,000	$10	$80,000	$80,000
		2	$               20.40	$163,200	$11.0	$88,000	$75,200
		3	$               20.81	$166,464	$12.1	$96,800	$69,664
		4	$               21.22	$169,793	$13.3	$106,480	$63,313
		5	$               21.65	$173,189	$14.6	$117,128	$56,061
			2%increase per year		10% increase per year
		Present Value (PV)of Cash flow=(Cash flow)/((1+i)^N)
		i=discount rate=cost of capital=0.15
		N=Year of cash flow
		Year wise cash flow and PV of cash flows are given below:
		N	A	B=A/(1.15^N)
		Year	Cash flow	PV of cash flow
		0	($100,000)	-100000
		1	$80,000	69565.21739
		2	$75,200	56862.00378
		3	$69,664	45805.21082
		4	$63,313	36199.57333
		5	$56,061	27872.29735
			TOTAL	136,304.3027
		Net Present Value (NPV)=	$    136,304.30
		Net Present Value is positive
		The nominal return of the project is higher than the cost of capital
		The Project Should be undertaken