Question

Determine the number of possible rate of return (i*) values for the cash flow below according to the rule of signs (Descartes’ rule).

Year	Annual Revenues, $	Annual Costs,$
0	$0	-$500
1	$350	-$500
2	$250	-$300
3	$450	-$350
4	$150	-$100
5	$350	-$150

		Four
		One
		Three
		Two

Answer 1

Cash Flows = Annual Revenue-Annual Cost

Year 0 = 0-5000 = -5000

Year 1 = 350-500 = -150

Year 2 = 250-300 = -50

Year 3 = 450-350 = 100

Year 4 = 150-100 = 50

Year 5 = 350-150 = 200

IRR is the Rate at which NPV = 0

Therefore,

-5000/[(1+IRR)^0] - 150/[(1+IRR)^1] - 50/[(1+IRR)^2] + 100/[(1+IRR)^3] + 50/[(1+IRR)^4] + 200/[(1+IRR)^5] = 0

Let 1/[1+IRR)] be x

Therefore, 200x⁵ + 50x⁴ + 100x³ - 50x² - 150x¹ - 5000 = 0

There is/are 1 sign change(s).

Descarte's Rule: Number of Possible Positive solutions for a polynomial are, Number of sign change or Number of sign change - 2 or (keep reducing by 2 until 1 or 0)

Therefore, As per Descarte's rule, there is/are 1 potential IRR(s)

Therefore, One