Question

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

Project X: CF0= -$1,000, CF1= $110, CF2= $300, CF3= $370, CF4= $750

Project Y: CF0= -$1,000, CF1= $900, CF2= $110, CF3= $50, CF4= $50

The projects are equally risky, and their WACC is 13%. What is the MIRR of the project that maximizes shareholder value? Round your answer to two decimal places. Do not round your intermediate calculations.

Answer 1

Project X
Discount rate	13.000%
Year	0	1	2	3	4
Cash flow stream	-1000	110	300	370	750
Discounting factor	1.000	1.130	1.277	1.443	1.630
Discounted cash flows project	-1000.000	97.345	234.944	256.429	459.989
NPV = Sum of discounted cash flows
NPV Project X =	48.71
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Project Y
Discount rate	13.000%
Year	0	1	2	3	4
Cash flow stream	-1000	900	110	50	50
Discounting factor	1.000	1.130	1.277	1.443	1.630
Discounted cash flows project	-1000.000	796.460	86.146	34.653	30.666
NPV = Sum of discounted cash flows
NPV Project Y =	-52.08
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Project X has higher NPV and maximizes share holder value therefore MIRR of project X =

Reinvestment Approach
All cash flows except the first are compounded to the last time period and IRR is calculated
Thus year 4 modified cash flow=(158.72)+(383.07)+(418.1)+(750)
=1709.89
Discount rate	13.000%
Year	0	1	2	3	4
Cash flow stream	-1000.000	110.000	300.000	370.000	750.000
Compound factor	1.000	1.443	1.277	1.130	1.000
Compounded cash flows	-1000.000	158.72	383.07	418.1	750
Modified cash flow	-1000.000	0	0	0	1709.890
Discounting factor (using MIRR)	1.000	1.144	1.308	1.495	1.710
Discounted cash flows	-1000.000	0.000	0.000	0.000	1000.000
NPV = Sum of discounted cash flows
NPV Discount rate =	0.00
MIRR is the rate at which NPV = 0
MIRR=	14.35%
Where
Compounding factor =	(1 + reinvestment rate)^(time of last CF-Corresponding period in years)
compounded Cashflow=	Cash flow stream*compounding factor