Question

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

0

1

2

3

4

Project X	-$1,000	$110	$280	$370	$650
Project Y	-$1,000	$1,100	$100	$55	$45

The projects are equally risky, and their WACC is 8%. 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	8.000%
Year	0	1	2	3	4
Cash flow stream	-1000	110	280	370	650
Discounting factor	1.000	1.080	1.166	1.260	1.360
Discounted cash flows project	-1000.000	101.852	240.055	293.718	477.769
NPV = Sum of discounted cash flows
NPV Project X =	113.39
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Project Y
Discount rate	8.000%
Year	0	1	2	3	4
Cash flow stream	-1000	1100	100	55	45
Discounting factor	1.000	1.080	1.166	1.260	1.360
Discounted cash flows project	-1000.000	1018.519	85.734	43.661	33.076
NPV = Sum of discounted cash flows
NPV Project Y =	180.99
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Project Y maximizes shareholders value as it has highest NPV, there fore its MIRR is:

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=(1385.68)+(116.64)+(59.4)+(45)
=1606.72
Discount rate	8.000%
Year	0	1	2	3	4
Cash flow stream	-1000.000	1100.000	100.000	55.000	45.000
Compound factor	1.000	1.260	1.166	1.080	1.000
Compounded cash flows	-1000.000	1385.68	116.64	59.4	45
Modified cash flow	-1000.000	0	0	0	1606.720
Discounting factor (using MIRR)	1.000	1.126	1.268	1.427	1.607
Discounted cash flows	-1000.000	0.000	0.000	0.000	999.999
NPV = Sum of discounted cash flows
NPV Discount rate =	0.00
MIRR is the rate at which NPV = 0
MIRR=	12.59%
Where
Compounding factor =	(1 + reinvestment rate)^(time of last CF-Corresponding period in years)
compounded Cashflow=	Cash flow stream*compounding factor