Question

Solo Corp. is evaluating a project with the following cash flows: Year Cash Flow 0 –$12,000 1 5,800 2 6,500 3 6,200 4 5,100 5 –4,300 The company uses a disount rate of 11 percent and a reinvestment rate of 8 percent on all of its projects. Calculate the MIRR of the project using all three methods using these interest rates.

a. MIRR using the discounting approach.

b. MIRR using the reinvestment approach.

  

c. MIRR using the combination approach.

Answer 1

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=-12000-2551.84
=-14551.84
Year	0	1	2	3	4	5
Cash flow stream	-12000.000	5800.000	6500.000	6200.000	5100.000	-4300.000
Discounting factor (Using discount rate)	1.000	1.110	1.232	1.368	1.518	1.685
Discounted cash flows	-12000.000	5225.225	5275.546	4533.387	3359.528	-2551.841
Modified cash flow	-14551.841	5800.000	6500.000	6200.000	5100.000	0.000
Discounting factor (using MIRR)	1.000	1.231	1.515	1.864	2.295	2.824
Discounted cash flows	-14551.841	4712.526	4291.063	3325.592	2222.661	0.000
NPV = Sum of discounted cash flows
NPV Reinvestment rate =	0.00
MIRR is the rate at which NPV = 0
MIRR=	23.08%
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
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=(7890.84)+(8188.13)+(7231.68)+(5508)+(-4300)
=24518.65
Discount rate	11.000%
Year	0	1	2	3	4	5
Cash flow stream	-12000.000	5800.000	6500.000	6200.000	5100.000	-4300.000
Compound factor	1.000	1.360	1.260	1.166	1.080	1.000
Compounded cash flows	-12000.000	7890.84	8188.13	7231.68	5508	-4300
Modified cash flow	-12000.000	0	0	0	0	24518.650
Discounting factor (using MIRR)	1.000	1.154	1.331	1.535	1.771	2.043
Discounted cash flows	-12000.000	0.000	0.000	0.000	0.000	12000.000
NPV = Sum of discounted cash flows
NPV Discount rate =	0.00
MIRR is the rate at which NPV = 0
MIRR=	15.36%
Where
Compounding factor =	(1 + reinvestment rate)^(time of last CF-Corresponding period in years)
compounded Cashflow=	Cash flow stream*compounding factor
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=(7890.84)+(8188.13)+(7231.68)+(5508)
=28818.65
Thus year 0 modified cash flow=-12000-2551.84
=-14551.84
Discount rate	11.000%
Year	0	1	2	3	4	5
Cash flow stream	-12000.000	5800.000	6500.000	6200.000	5100.000	-4300.000
Discount factor	1.000	1.110	1.232	1.368	1.518	1.685
Compound factor	1.000	1.360	1.260	1.166	1.080	1.000
Discounted cash flows	-12000.000	0	0	0	0	-2551.84
Compounded cash flows	0.000	7890.84	8188.13	7231.68	5508	0
Modified cash flow	-14551.840	0	0	0	0	28818.650
Discounting factor (using MIRR)	1.000	1.146	1.314	1.507	1.727	1.980
Discounted cash flows	-14551.840	0.000	0.000	0.000	0.000	14551.840
NPV = Sum of discounted cash flows
NPV=	0.00
MIRR is the rate at which NPV = 0
MIRR=	14.64%
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