Question

A company has the opportunity to take over a redevelopment project in an industrial area of a city. No immediate investment is required, but it must raze the existing buildings over a four-year period and, at the end of the fourth year, invest $2,300,000 for new construction. It will collect all revenues and pay all costs for a period of 10 years, at which time the entire project, and properties thereon, will revert to the city. The net cash flows are estimated to be as shown on the right. Tabulate the PW versus the interest rate and determine whether multiple IRRs exist. If so, use the ERR method when ??6% per year to determine a rate of return Year End Net Cash Flow $540,000 300,000 80,000 -2,300,000 130,000 180,000 230,000 280,000 330,000 4 Click the icon to view the interest and annuity table for discrete compounding when the MARR is 6% per year There is/are two IRR value(s) for the given net cash-flow sequence The first IRR value is | %. (Round to one decimal place.)

Answer 1

The first IRR value = 7.6%
and second IRR value = 31.2%

	A	B	C	D	E	F
	Year	Net Cash flow	Interest rate	Present Worth Formula = NPV(C1,B1:10)	IRR = IRR( B1:B10,F1:F8)	Guess values
1	1	510,000	1%	$221,344.87	7.6%	5%
2	2	270,000	2%	$170,861.98	7.6%	10%
3	3	90,000	3%	$127,572.79	7.6%	15%
4	4	-2,390,000	4%	$90,615.85	31.2%	20%
5	5	150,000	5%	$59,232.26	31.2%	25%
6	6	210,000	6%	$32,752.99	31.2%	30%
7	7	270,000	7%	$10,587.79	31.2%	35%
8	8	330,000	8%	($7,784.34)	31.2%	40%
9	9	390,000	9%	($22,823.57)	31.2%	45%
10	10	450,000	10%	($34,936.56)

	A	B	C	D
	Year	Net Cash flow	Interest rate	Present value of expenses = C4/((1+C1)^4)	Future value of income = B1*(1+06%)^(10-A1)
1	1	510,000	6%	($1,893,103.86)	861634.27
2	2	270,000			430338.98
3	3	90,000			135326.72
4	4	-2,390,000			0.00
5	5	150,000			200733.84
6	6	210,000			265120.16
7	7	270,000			321574.32
8	8	330,000			370788.00
9	9	390,000			413400.00
10	10	450,000			450000.00
				Total FV	3448916.29

(PV of expenses discounnted at 6%) * (1+r)¹⁰ = (FV of revenues at 6%)
r = (FV/PV)^(1/10) -1 = 6.18%