Question

AAA Inc. has four potential independent projects. The information for each project​ (Cash flows each​ period, NPV,​ IRR, MIRR, and​ PI) is presented in the table below but unfortunately some is missing. For your​ convenience, PVIF and FVIF for years 1 to 5 are also presented in the last two columns of the table. The discount rate is​ 10%,

Year	Project I	Project II	Project III	Project IV	PVIF	FVIF
0	​-300,000	​-5,000	​-100,000	​-100,000	1
1	​10,000	​15,000	​200,000	​10,000	0.9091	1.4641
2	​150,000	​15,000	​15,000	​150,000	0.8265	1.331
3	​150,000	​15,000	​15,000	​150,000	0.7513	1.21
4	​150,000	​15,000	​15,000	​150,000	0.6830	1.1
5	​150,000	​15,000	​15,000	​150,000	0.6209	1
NPV	​141,345	​???	​???	​341,345
IRR	23.86	​???	​112.66%	​79.87%
MIRR	​???	​???	​29.37%	48.03
PI	1.47	11.37	​???	4.41

What is the MIRR for project I (answer in percentage with two digits. for example if your solution is 0.094692 then enter 9.47​)​? The MIRR for project I is ____ ​%.

Answer 1

Reinvestment Approach

All cash flows except the first are compounded to the last time period and IRR is calculated

Thus year 5 modified cash flow=(14641)+(199650)+(181500)+(165000)+(150000)

=710791

Discount rate	10.000%
Year	0	1	2	3	4	5
Cash flow stream	-300000.000	10000.000	150000.000	150000.000	150000.000	150000.000
Compound factor (Using discount rate)	1.000	1.464	1.331	1.210	1.100	1.000
Compounded cash flows	-300000.000	14641	199650	181500	165000	150000
Modified cash flow	-300000.000	0	0	0	0	710791.000
Discounting factor (using MIRR)	1.000	1.188	1.412	1.678	1.994	2.369
Discounted cash flows	-300000.000	0.000	0.000	0.000	0.000	300000.000
NPV = Sum of discounted cash flows
NPV =	0.00
MIRR is the rate at which NPV = 0
MIRR=	18.83%
Where
Compounding factor =	(1 + discount rate)^(time of last CF-Corresponding period in years)
Discounted Cashflow=	Cash flow stream*discounting factor