Question

A firm is considering two mutually exclusive projects, X and Y, with the following cash flows:

Answer 1

Answer: MIRR (project x ) = 3.42% , Project Y = 4.51%

Explanation:

Modified internal Rate of return

Project X

Period (n) = 4

Weighted Average Cost of equity(WACC) = 8.0%

Cash out flow = -$1000

Cash Inflows = $100 year 1 , $280 year 2 , 370 year 3 ,$700 year 4

Present Value Cash Inflows = PVCIF = Cash Inflow/(1+WACC)^n

PVCIF = 100/(1+0.08)^1 + 280/(1+0.08)^2 + 370/(1+0.08)^3 + $700/(1+0.08)^4

PVCIF = 95.592592593 + 240.05486968 + 293.71792918 + 514.5208969

Present Value of Cash inflows (PVCIF) = $1143.8862884

Present Value of Cash out flows(PVCOF) = -$1000

Modified Internal Rate of Return (MIRR) = $\sqrt[n]{\frac{PVCIF}{PVCOF} } -1$  

Modified Internal Rate of Return (MIRR) = $\sqrt[4]{\frac{1143.8862884}{10000} } -1$

Modified Internal Rate of Return (MIRR) = 0.034178971

Modified Internal Rate of Return (MIRR) = 3.41789971 = 3.42%

Project Y

Period (n) = 4

Weighted Average Cost of equity(WACC) = 8.0%

Cash out flow = -$1000

Cash Inflows = $1100 year 1 , $110 year 2 , $50 year 3 ,$55 year 4

Present Value Cash Inflows = PVCIF = Cash Inflow/(1+WACC)^n

PVCIF = $1100/(1+0.08)^1 + $110/(1+0.08)^2 + $50/(1+0.08)^3 + $55/(1+0.08)^4

PVCIF = 1018.5185185 + 94.307270233 + 39.691612051 + 40.42641904

Present Value of Cash inflows (PVCIF) = $10192.9438198

Present Value of Cash out flows(PVCOF) = -$1000

Modified Internal Rate of Return (MIRR) = $\sqrt[n]{\frac{PVCIF}{PVCOF} } -1$  

Modified Internal Rate of Return (MIRR) = $\sqrt[4]{\frac{1192.9438198}{10000} } -1$

Modified Internal Rate of Return (MIRR) = 0.0450931421

Modified Internal Rate of Return (MIRR) = = 4.50931421 = 4.51%