Question

1. Melbourne Metal is considering becoming a supplier of transmission housings. It would require buying a new forge that would cost $125,000 (including all setup costs) and is expected to last five years. Let the asset life be the life of the project.

Melbourne Metal does a best guess (Base) study of their costs and revenues. They anticipate setting their price at p = $50 per unit and they estimate the annual demand is q = 2,500 – 10p. Variable costs (labour, materials, etc.) are estimated to be $15 per unit. Total fixed costs (excluding depreciation of the forge) is estimated to be $10,000 per year.

Melbourne Metal uses the double declining balance method for depreciation. The book balance at the start of year 1 is the $125,000. The depreciation in a year is a fixed percentage 0 < α < 1 of the beginning of year book balance where the book balance at the beginning of year n is the book balance at the end of year n – 1. The book balance at the end of year n, Bn = Bn-1 – depreciation that year. With the double declining balance method, the depreciation rate ? = 2 ? where N is the life of the project. The salvage value is assumed to the book balance at the end of the project.

The tax rate is 40%. The MARR is 15%.

a. Set up an Income Statement and calculate annual net income for each year of the project. (15)

b. Set up a Statement of Cash Flows to calculate the net cash flows for the project. (10)

c. Find the net present value NPV of the project. (3)

d. Re-calculate NPV assuming the unit price is $10 higher and then $10 lower. Recalculate NPV assuming the average variable cost AVC is $10 higher and then $10 lower. Is the NPV of the project more sensitive to the unit price or the average variable cost? Explain. Note: Don’t do the % deviation I did in class since these are dollar unit changes – just change the unit price or AVC directly. (10)

e. At what unit price will the project breakeven? (Don’t do this by hand – five years is too complicated. If you don’t have Excel, try various prices until you get NPV close enough to zero).

Answer 1

		INCOME STATEMENT
		N=number of Years	5
		Depreciation rate =2/5=	40%
	N	Year	1	2	3	4	5
	p	Selling Price per unit	$50	$50	$50	$50	$50
	q=2500-10p	Sales Quantity	2,000	2,000	2,000	2,000	2,000
	A=p*q	Sales Revenue	$100,000	$100,000	$100,000	$100,000	$100,000
	V=q*15	Variable Costs	$30,000	$30,000	$30,000	$30,000	$30,000
	C=A-V	Contribution	$70,000	$70,000	$70,000	$70,000	$70,000
	F	Fixed Cost (Excluding depreciation)	$10,000	$10,000	$10,000	$10,000	$10,000
	G=C-F	Earnings before Taxes and Depreciation	$60,000	$60,000	$60,000	$60,000	$60,000
		DEPRECIATION;
	B	Book value at beginning of year	$125,000	$75,000	$45,000	$27,000	$16,200
	ALPHA	Depreciation Rate	40%	40%	40%	40%	40%
	D=B*ALPHA	Annual Depreciation	$50,000	$30,000	$18,000	$10,800	$6,480
	E=B-D	Book value at end of year	$75,000	$45,000	$27,000	$16,200	$9,720
	H=G-D	Earnings before Taxes (after Depreciation)	$10,000	$30,000	$42,000	$49,200	$53,520
	T=H*40%	Tax Expenses	$4,000	$12,000	$16,800	$19,680	$21,408
	I=H-T	Net Income for the year	$6,000	$18,000	$25,200	$29,520	$32,112
		STATEMENT OF CASH FLOWS
	N	Year	0	1	2	3	4	5
	ICF	Initial Cash Flow	($125,000)
	NI	Net Income		$6,000	$18,000	$25,200	$29,520	$32,112
	D	Depreciation (Non Cash expense)		$50,000	$30,000	$18,000	$10,800	$6,480
	S	Salvage Value(Book value at end of year5)						$9,720
	NCF=ICF+NI+D+S	Net Cash Flow	($125,000)	$56,000	$48,000	$43,200	$40,320	$48,312	SUM
	PV=NCF/(1.15^N)	Present Value of Cash Flow (discount rate 15%)	($125,000)	$48,696	$36,295	$28,405	$23,053	$24,020	$35,468
	NPV=sum of PV	Net Present value of the Project	$35,468