Question

RAK Corp. is evaluating a project with the following cash flows: Year Cash Flow 0 –$ 28,900 1 11,100 2 13,800 3 15,700 4 12,800 5 – 9,300 The company uses an interest rate of 9 percent on all of its projects. Calculate the MIRR of the project using the discounting approach. Calculate the MIRR of the project using the reinvestment approach. Calculate the MIRR of the project 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=-28900-6044.36
=-34944.36
Year	0	1	2	3	4	5
Cash flow stream	-28900.000	11100.000	13800.000	15700.000	12800.000	-9300.000
Discounting factor (Using discount rate)	1.000	1.090	1.188	1.295	1.412	1.539
Discounted cash flows	-28900.000	10183.486	11615.184	12123.281	9067.843	-6044.362
Modified cash flow	-34944.362	11100.000	13800.000	15700.000	12800.000	0.000
Discounting factor (using MIRR)	1.000	1.188	1.410	1.675	1.989	2.362
Discounted cash flows	-34944.362	9347.184	9785.764	9375.040	6436.374	0.000
NPV = Sum of discounted cash flows
NPV Reinvestment rate =	0.00
MIRR is the rate at which NPV = 0
MIRR=	18.75%
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=(15668.56)+(17871.4)+(18653.17)+(13952)+(-9300)
=56845.13
Discount rate	9.000%
Year	0	1	2	3	4	5
Cash flow stream	-28900.000	11100.000	13800.000	15700.000	12800.000	-9300.000
Compound factor	1.000	1.412	1.295	1.188	1.090	1.000
Compounded cash flows	-28900.000	15668.56	17871.4	18653.17	13952	-9300
Modified cash flow	-28900.000	0	0	0	0	56845.130
Discounting factor (using MIRR)	1.000	1.145	1.311	1.501	1.718	1.967
Discounted cash flows	-28900.000	0.000	0.000	0.000	0.000	28900.000
NPV = Sum of discounted cash flows
NPV Discount rate =	0.00
MIRR is the rate at which NPV = 0
MIRR=	14.49%
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=(15668.56)+(17871.4)+(18653.17)+(13952)
=66145.13
Thus year 0 modified cash flow=-28900-6044.36
=-34944.36
Discount rate	9.000%
Year	0	1	2	3	4	5
Cash flow stream	-28900.000	11100.000	13800.000	15700.000	12800.000	-9300.000
Discount factor	1.000	1.090	1.188	1.295	1.412	1.539
Compound factor	1.000	1.412	1.295	1.188	1.090	1.000
Discounted cash flows	-28900.000	0	0	0	0	-6044.36
Compounded cash flows	0.000	15668.56	17871.4	18653.17	13952	0
Modified cash flow	-34944.360	0	0	0	0	66145.130
Discounting factor (using MIRR)	1.000	1.136	1.291	1.466	1.666	1.893
Discounted cash flows	-34944.360	0.000	0.000	0.000	0.000	34944.360
NPV = Sum of discounted cash flows
NPV=	0.00
MIRR is the rate at which NPV = 0
MIRR=	13.61%
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