Problem 5-47 (algorithmic) Question Help 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 $2,480,000 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 detemine whether multiple IRRs exist. If so, use the ERR method when -9% per year to determine a rate of return. Year Encd Net Cash Flow $500,000 270,000 100,000 -2,480,000 160,000 220,000 280,000 340,000 400,000 460,000 Click the icon to view the interest and annuity table for discrete compounding when the MARR is 9% per year. 10 There is/areIRR value(s) for the given net cash-flow sequence.
ANSWER:
We need to equate the pw of these cash flows to zero in order to find the irr, as there is only 1 negative cash flow , so there won\'t be multiple irr but instead one single irr.
pw = cash flow in year 1(p/f,i,n) + cash flow in year 2(p/f,i,n) + cash flow in year 3(p/f,i,n) + cash flow in year 4(p/f,i,n) + cash flow in year 5(p/f,i,n) + cash flow in year 6(p/f,i,n) + cash flow in year 7(p/f,i,n) + cash flow in year 8(p/f,i,n) + cash flow in year 9(p/f,i,n) + cash flow in year 10(p/f,i,n)
0 = 500,000(p/f,i,1) + 270,000(p/f,i,2) + 100,000(p/f,i,3) -2,480,000(p/f,i,4) + 160,000(p/f,i,5) + 220,000(p/f,i,6) + 280,000(p/f,i,7) + 340,000(p/f,i,8) + 400,000(p/f,i,9) + 460,000(p/f,i,10)
solving via trial and error for various values of i , we get i = 5.97%
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