Question

Q13.23 Consider purchasing 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 3290, 19.2%, 11.52%, 11.52%, and 5.76% in the following years. You can finance this car yourself. You can produce income 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. (a) What are the income and cash flow state ments for this car? (b) What is the economic value of this car? (c) Show how you can infer the economic value of the car from the financials.

Answer 1

Please see the table below. In the second column, i have explained the calculation for each of the rows.

Part (a)

Year, N		0	1	2	3	4	5	6	7	8	9	10
Initial investment	I	50000
MACRS depreciation schedule	d		20%	32%	19.20%	11.52%	11.52%	5.76%
Tax rate	t	30%
Part (a) Income Statement
Revenue from the car	R		100,000	100,000	100,000	100,000	100,000	100,000	100,000	100,000	100,000	100,000
[-] Maintenance Costs	M		5,000	5,000	5,000	5,000	5,000	5,000	5,000	5,000	5,000	5,000
[-] Depreciation	D = I x d		10,000	16,000	9,600	5,760	5,760	2,880	-	-	-	-
Operating income	OI = R - M - D		85,000	79,000	85,400	89,240	89,240	92,120	95,000	95,000	95,000	95,000
[-] Taxes	T = t x OI		25,500	23,700	25,620	26,772	26,772	27,636	28,500	28,500	28,500	28,500
Net Income	NI = OI - T		59,500	55,300	59,780	62,468	62,468	64,484	66,500	66,500	66,500	66,500
Part (a) Cash flow statement
[-] Initial investment	I	50,000
Net Income	NI		59,500	55,300	59,780	62,468	62,468	64,484	66,500	66,500	66,500	66,500
[+] Depreciation	D		10,000	16,000	9,600	5,760	5,760	2,880	-	-	-	-
Net cash flows	CF = NI + D - I	(50,000)	69,500	71,300	69,380	68,228	68,228	67,364	66,500	66,500	66,500	66,500
Part (b) Economic Value
NOPAT (same as net income)	NI		59,500	55,300	59,780	62,468	62,468	64,484	66,500	66,500	66,500	66,500
Cost of capital	R	12%
Charge on capital	CC = R x I		6,000	6,000	6,000	6,000	6,000	6,000	6,000	6,000	6,000	6,000
Economic value each year	NI - CC		53,500	49,300	53,780	56,468	56,468	58,484	60,500	60,500	60,500	60,500
Economic Value (Total)	Sum of all NI - CC above	570,000

Part (b)

Economic value of an item is the maximum price a buyer is willing to pay for the item. So, the economic value is the NOPAT in excess of the charge on the capital deployed. The economy value = $ 570,000

Part (c)

Economic Value = NOPAT - charge on the capital = NOPAT - cost of capital x Capital deployed

Based on the financials, one can infer economic value by following steps:

• Calculate the operating income
• Calculate taxes (= tax rate x operating income)
• Calculate net income (NOPAT = Operating income - taxes)
• Calculate charge on capital = Discount rate x capital deployed
• Calculat, the economic value in each year as = NOPAT - charge on the capital deployed.