Question

Consider a $50,000 SUV that you expect to last for 10 years. The IRS uses an MACRS 5-year depreciation schedule on cars. It allows depreciating 20% in year 1, 32%, 19.2%, 11.52%, 11.52%, and 5.76% in the following years. You can finance this car yourself. You can produce sales of $100,000 per year with it. Maintenance costs will be $5,000 per year. Your income tax rate is 30% per annum. Your cost of capital is 12% per annum. 1. What are the income and cash-flow statements for this car? 2. What is the net present value of this car? 3. Show how you can infer the economic value of the car from the financials.

2, Repeat the previous question but assume you finance the entire car with a loan that charges 10% interest per annum. (The net present value now is the bundle “loan plus car,” of course.)

Answer 1

		Present Value (PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		i=Discount Rate=Cost of capital=12%=0.12
		N=Year of Cash Flow
	N	Year	0	1	2	3	4	5	6	7	8	9	10
	I	Initialcash Flow	($50,000)
	A	MACRS Depreciation Rate		20%	32%	19.20%	11.52%	11.52%	5.76%
	B=A*50000	Annual Depreciation		$        10,000	$16,000	$    9,600	$    5,760	$    5,760	$    2,880
	C	Annual   Sales		$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000	$100,000
	D	Maintenance Cost		$5,000	$5,000	$5,000	$5,000	$5,000	$5,000	$5,000	$5,000	$5,000	$5,000
	E=C-D-B	Income before tax		$85,000	$79,000	$85,400	$89,240	$89,240	$92,120	$95,000	$95,000	$95,000	$95,000
	F=E*0.3	Income tax expense		$25,500	$23,700	$25,620	$26,772	$26,772	$27,636	$28,500	$28,500	$28,500	$28,500
	G=E-F	Net Income		$59,500	$55,300	$59,780	$62,468	$62,468	$64,484	$66,500	$66,500	$66,500	$66,500
	H=G+B+I	Net Cash Flow	($50,000)	$69,500	$71,300	$69,380	$68,228	$68,228	$67,364	$66,500	$66,500	$66,500	$66,500	SUM
	PV=H/(1.12^N)	Present Value (PV) of Cash Flows:	($50,000)	$        62,054	$56,840	$49,383	$43,360	$38,714	$34,129	$30,081	$26,858	$23,981	$21,411	#######
	NPV=Sum of PVs	Net Present Value(NPV) of the car	$336,811
		Market Value of the car	$50,000
		Economic value of the Car =Present Value of future cash inflows
		Economic value of the Car =(336811+50000)	$386,811
	Part b)
		Interest on Loan per year	$5,000	(50000*0.1)
		Cash Flow frompart a:
	N	Year	0	1	2	3	4	5	6	7	8	9	10
	H	Net Cash Flow Frompart (a)	($50,000)	$69,500	$71,300	$69,380	$68,228	$68,228	$67,364	$66,500	$66,500	$66,500	$66,500
	J	Cash Flow for Loan	$50,000	($5,000)	($5,000)	($5,000)	($5,000)	($5,000)	($5,000)	($5,000)	($5,000)	($5,000)	($55,000)	Return of Principal +Interest
	K=H+J	Cash flow for bundle of car +Loan	$0	$64,500	$66,300	$64,380	$63,228	$63,228	$62,364	$61,500	$61,500	$61,500	$11,500	SUM
	PV=K/(1.12^N)	Present Value (PV) of Cash Flows:	$0	$        57,589	$         52,854	$    45,824	$        40,183	$              35,877	$             31,596	$        27,819	$            24,839	$           22,178	$              3,703	$342,462
	NPV=SUM of PVs	The net present value of the bundle “loan plus car,”	$342,462