Question

Solo Corp. is evaluating a project with the following cash flows: Year Cash Flow 0 –$30,000 1 12,200 2 14,900 3 16,800 4 13,900 5 –10,400

The company uses an interest rate of 8 percent on all of its projects.

Calculate the MIRR of the project using all three methods. a. MIRR using the discounting approach.

b. MIRR using the reinvestment approach.

c. MIRR using the combination approach.

Answer 1

a

Discounting Approach
All negative cash flows are discounted back to the present at the required return and added to the initial cost
Thus year 0 modified cash flow=-30000-7078.07
=-37078.07
Year	0	1	2	3	4	5
Cash flow stream	-30000.000	12200.000	14900.000	16800.000	13900.000	-10400.000
Discounting factor (Using discount rate)	1.000	1.080	1.166	1.260	1.360	1.469
Discounted cash flows	-30000.000	11296.296	12774.348	13336.382	10216.915	-7078.065
Modified cash flow	-37078.065	12200.000	14900.000	16800.000	13900.000	0.000
Discounting factor (using MIRR)	1.000	1.198	1.435	1.720	2.060	2.469
Discounted cash flows	-37078.065	10182.873	10380.238	9768.791	6746.163	0.000
NPV = Sum of discounted cash flows
NPV Reinvestment rate =	0.00
MIRR is the rate at which NPV = 0
MIRR=	19.81%
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
b
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=(16597.97)+(18769.71)+(19595.52)+(15012)+(-10400)
=59575.2
Discount rate	8.000%
Year	0	1	2	3	4	5
Cash flow stream	-30000.000	12200.000	14900.000	16800.000	13900.000	-10400.000
Compound factor	1.000	1.360	1.260	1.166	1.080	1.000
Compounded cash flows	-30000.000	16597.97	18769.71	19595.52	15012	-10400
Modified cash flow	-30000.000	0	0	0	0	59575.200
Discounting factor (using MIRR)	1.000	1.147	1.316	1.509	1.731	1.986
Discounted cash flows	-30000.000	0.000	0.000	0.000	0.000	30000.000
NPV = Sum of discounted cash flows
NPV Discount rate =	0.00
MIRR is the rate at which NPV = 0
MIRR=	14.71%
Where
Compounding factor =	(1 + reinvestment rate)^(time of last CF-Corresponding period in years)
compounded Cashflow=	Cash flow stream*compounding factor
c
Combination approach
All negative cash flows are discounted back to the present and all positive cash flows are compounded out to the end of the project’s life
Thus year 5 modified cash flow=(16597.97)+(18769.71)+(19595.52)+(15012)
=69975.2
Thus year 0 modified cash flow=-30000-7078.07
=-37078.07
Discount rate	8.000%
Year	0	1	2	3	4	5
Cash flow stream	-30000.000	12200.000	14900.000	16800.000	13900.000	-10400.000
Discount factor	1.000	1.080	1.166	1.260	1.360	1.469
Compound factor	1.000	1.360	1.260	1.166	1.080	1.000
Discounted cash flows	-30000.000	0	0	0	0	-7078.07
Compounded cash flows	0.000	16597.97	18769.71	19595.52	15012	0
Modified cash flow	-37078.070	0	0	0	0	69975.200
Discounting factor (using MIRR)	1.000	1.135	1.289	1.464	1.662	1.887
Discounted cash flows	-37078.070	0.000	0.000	0.000	0.000	37078.070
NPV = Sum of discounted cash flows
NPV=	0.00
MIRR is the rate at which NPV = 0
MIRR=	13.54%
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Compounding factor =	(1 + reinvestment rate)^(time of last CF-Corresponding period in years)
Compounded Cashflow=	Cash flow stream*compounding factor