Question

4.45. 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 $2,400,000 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 follows: Year End Net Cash Flow 1 $500,000 2 300,000 3 100,000 -2,400,000 5 150,000 200,000 250,000 300,000 350,000 400,000 Tabulate the PW versus the interest rate and determine whether multiple IRRs exist. If so, use the ERR method when ε = 8% per year to determine a rate of return.

Answer 1

SOLUTION IRR method: PW(i%) = 0 = $500,000(P/F,i'%,1) + $300,000(P/F,i'%,2) + [$100,000+ $100,000(P/A,i'%,7) + $50,000(P/G,it%,7)](P/F,i'%,3) - $2,500,000 (P/F,i'%,4) i% 1 2 3 4 5 Present Worth $103,331.55 63,694.68 30,228.14 2.175.18 -21,130.28 i'% 30 31 32 Present Worth -$12,186.78 -5,479.09 1,182.76

There are two internal rates of return: 4.09% and 31.8% per year. ERR Method: 1-$2,400,000|(P/F,8%,4)(F/P,i'%,10) = $500,000(F/P,8%,9) +$300,000(F/P,8%,8) + $100,000(F/P,8%,7) + $150,000(P/A,8%,6)(F/P,8%,6) + $50,000(P/G,8%,6)(F/P,8%,6) After solving, the external rate of return is 7.6% per year.