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	$100	$300	$400	$650
Project Y	-$1,000	$1,000	$110	$45	$55

The projects are equally risky, and their WACC is 10%. What is the MIRR of the project that maximizes shareholder value? Do not round intermediate calculations. Round your answer to two decimal places.

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Answer 1

Modified IRR:

It is similar to IRR. In IRR, we are assumed that intermediary cashflows are reinvested at IRR only. In MIRR, we assume that Intermediary CFs are reinvested at
Reinvestment Rate rather than at IRR.

Project X

ReInvestment rate	10%
Initial Investment	$   1,000.00
Time Period	4.00

Cash Flows for 4 Years
Year	Bal Years	CF	FVF @0.1	FV of CFs
1	3	$    100.00	1.3310	$      133.10
2	2	$    300.00	1.2100	$      363.00
3	1	$    400.00	1.1000	$      440.00
4	0	$    650.00	1.0000	$      650.00
Future Value of CFs	$   1,586.10
Thus $1000 has become $1586.1 over a period of 4 Years
Future Value = Cash Flow * ( 1 + r )^n
$ 1586.1 = $ 1000 ( 1 + r) ^ 4
( 1 + r) ^ 4 = $1586.1 / $ 1000
( 1 + r) ^ 4 = 1.5861
( 1 + r) = 1.5861 ^ ( 1 / 4 )
( 1 + r) = 1.1222
r = 1.1222 -1
r = 0.1222
i.e MIRR is 12.22 %

FVF = (1+r)n

r = Interest rate

n= time gap

Project Y

Cash Flows for 4 Years
Year	Bal Years	CF	FVF @0.1	FV of CFs
1	3	$ 1,000.00	1.3310	$   1,331.00
2	2	$    110.00	1.2100	$      133.10
3	1	$      45.00	1.1000	$         49.50
4	0	$      55.00	1.0000	$         55.00
Future Value of CFs	$   1,568.60
Thus $1000 has become $1568.6 over a period of 4 Years
Future Value = Cash Flow * ( 1 + r )^n
$ 1568.6 = $ 1000 ( 1 + r) ^ 4
( 1 + r) ^ 4 = $1568.6 / $ 1000
( 1 + r) ^ 4 = 1.5686
( 1 + r) = 1.5686 ^ ( 1 / 4 )
( 1 + r) = 1.1191
r = 1.1191 -1
r = 0.1191
i.e MIRR is 11.91 %

Project X has higher MIRR i.e., 12..22 % that maximizes the share holder's value

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