Question

Project A requires an initial outlay at t = 0 of $1,000, and its cash flows are the same in Years 1 through 10. Its IRR is 15%, and its WACC is 8%. What is the project's MIRR? Do not round intermediate calculations. Round your answer to two decimal places. %

(the answer is not 2.947919%)

Answer 1

IRR is the rate at which PV of cash Inflows are equal to PV of Cash Outflows.

Let X be the CF per year.

$ 1000 = X * PVAF(15%,10)

= X * 5.0188

X = $ 1000 / 5.0188

= $ 199.25

in IRR it is assumed that intermediary CFs are reinvested at IRR. in MIRR it is assumed that intermediary CFs are reinvested at WACC.

Year	Bal Years	CF	FVF @8%	FV of CFs
1	9	$ 199.25	1.9990	$    398.31
2	8	$ 199.25	1.8509	$    368.80
3	7	$ 199.25	1.7138	$    341.48
4	6	$ 199.25	1.5869	$    316.19
5	5	$ 199.25	1.4693	$    292.77
6	4	$ 199.25	1.3605	$    271.08
7	3	$ 199.25	1.2597	$    251.00
8	2	$ 199.25	1.1664	$    232.41
9	1	$ 199.25	1.0800	$    215.19
10	0	$ 199.25	1.0000	$    199.25
FV of CFs				$ 2,886.48

Thus $ 1000 has become 2886.48 in 10 Years.

FV = PV (1+r)^n

$ 2886.48 = $ 1000 (1+r)^10

(1+r)^10 = 2886.48 / 1000

= 2.8865

1+r = 2.8865 ^ ( 1/10)

= 1.1118

r = 1.1118 - 1

= 0.1118 i.e 11.18%

MIRR is 11.18%