Question

Doak Corp. is evaluating a project with the following cash flows: Year Cash Flow 0 –$ 15,300 1 6,400 2 7,600 3 7,200 4 6,000 5 – 3,400 The company uses an interest rate of 9 percent on all of its projects. Calculate the MIRR of the project using all three methods.

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=-15300-2209.77
=-17509.77
Year	0	1	2	3	4	5
Cash flow stream	-15300.000	6400.000	7600.000	7200.000	6000.000	-3400.000
Discounting factor (Using discount rate)	1.000	1.090	1.188	1.295	1.412	1.539
Discounted cash flows	-15300.000	5871.560	6396.768	5559.721	4250.551	-2209.767
Modified cash flow	-17509.767	6400.000	7600.000	7200.000	6000.000	0.000
Discounting factor (using MIRR)	1.000	1.205	1.452	1.749	2.108	2.539
Discounted cash flows	-17509.767	5311.699	5235.047	4116.167	2846.854	0.000
NPV = Sum of discounted cash flows
NPV Reinvestment rate =	0.00
MIRR is the rate at which NPV = 0
MIRR=	20.49%
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=(9034.12)+(9842.22)+(8554.32)+(6540)+(-3400)
=30570.66
Discount rate	9.000%
Year	0	1	2	3	4	5
Cash flow stream	-15300.000	6400.000	7600.000	7200.000	6000.000	-3400.000
Compound factor	1.000	1.412	1.295	1.188	1.090	1.000
Compounded cash flows	-15300.000	9034.12	9842.22	8554.32	6540	-3400
Modified cash flow	-15300.000	0	0	0	0	30570.660
Discounting factor (using MIRR)	1.000	1.148	1.319	1.515	1.740	1.998
Discounted cash flows	-15300.000	0.000	0.000	0.000	0.000	15300.000
NPV = Sum of discounted cash flows
NPV Discount rate =	0.00
MIRR is the rate at which NPV = 0
MIRR=	14.85%
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=(9034.12)+(9842.22)+(8554.32)+(6540)
=33970.66
Thus year 0 modified cash flow=-15300-2209.77
=-17509.77
Discount rate	9.000%
Year	0	1	2	3	4	5
Cash flow stream	-15300.000	6400.000	7600.000	7200.000	6000.000	-3400.000
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	-15300.000	0	0	0	0	-2209.77
Compounded cash flows	0.000	9034.12	9842.22	8554.32	6540	0
Modified cash flow	-17509.770	0	0	0	0	33970.660
Discounting factor (using MIRR)	1.000	1.142	1.304	1.488	1.699	1.940
Discounted cash flows	-17509.770	0.000	0.000	0.000	0.000	17509.770
NPV = Sum of discounted cash flows
NPV=	0.00
MIRR is the rate at which NPV = 0
MIRR=	14.17%
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