Your firm is considering a project that will cost $4.704 million up front, generate cash flows of $3.55 million per year for 3 years, and then have a cleanup and shutdown cost of $5.98 million in the fourth year. A.) How many IRRs does this project have? B.) Calculate a modified IRR for this project assuming a discount and compounding rate of 10.3%. C.) Using the MIRR and a cost of capital of 10.3%, would you take the project?
Cash flow :
Year 0 = - $4.704 Million
Year 1 = $3.55 Million
Year 2 = $3.55 Million
Year 3 = $3.55 Million
Year 4 = - $5.98 Million
Answer A.
Let IRR be i%
Therefore, 0 = -4,704,000 + 3,550,000/(1+i) + 3,550,000/(1+i)^2 + 3,550,000/(1+i)^3 - 5,980,000/(1+i)^4
I = 1.50%
Answer B.
Future Value of Inflow at t = 4 :
3,550,000*(1.103)^3 + 3,550,000*(1.103)^2 + 3,550,000*(1.103) = $12,998,426.98
Present Value of Outflow :
-4,704,000 - 5,980,000/(1+i)^4 = - $8,744,165.30
MIRR = (12,998,426.98/8,744,165.30)^(1/4) – 1 = 10.42%
Answer C.
Since, the MIRR is more than the cost of capital. Therefore, we should accept the project.
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