Year Cash Flow 0 –$ 15,900 1 7,930 2 9,490 3 8,970 4 7,210 5 –...

Year Cash Flow 0 –$ 15,900 1 7,930 2 9,490 3 8,970 4 7,210 5 – 3,580 Required: The company uses an interest rate of 12 percent on all of its projects. Calculate the MIRR of the project using all three methods. (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).) MIRR Discounting approach % Reinvestment approach % Combination approach %

Expert Solution

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=-15900-2031.39
=-17931.39

Year	0	1	2	3	4	5
Cash flow stream	-15900.000	7930.000	9490.000	8970.000	7210.000	-3580.000
Discounting factor (Using discount rate)	1.000	1.120	1.254	1.405	1.574	1.762
Discounted cash flows	-15900.000	7080.357	7565.370	6384.669	4582.085	-2031.388
Modified cash flow	-17931.388	7930.000	9490.000	8970.000	7210.000	0.000
Discounting factor (using MIRR)	1.000	1.313	1.724	2.264	2.973	3.903
Discounted cash flows	-17931.388	6039.348	5504.272	3962.260	2425.508	0.000
NPV = Sum of discounted cash flows
NPV Reinvestment rate =	0.00
MIRR is the rate at which NPV = 0
MIRR=	31.31%
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=(12478.01)+(13332.77)+(11251.97)+(8075.2)+(-3580)
=41557.95

Discount rate	12.000%
Year	0	1	2	3	4	5
Cash flow stream	-15900.000	7930.000	9490.000	8970.000	7210.000	-3580.000
Compound factor	1.000	1.574	1.405	1.254	1.120	1.000
Compounded cash flows	-15900.000	12478.01	13332.77	11251.97	8075.2	-3580
Modified cash flow	-15900.000	0	0	0	0	41557.950
Discounting factor (using MIRR)	1.000	1.212	1.469	1.780	2.157	2.614
Discounted cash flows	-15900.000	0.000	0.000	0.000	0.000	15900.001
NPV = Sum of discounted cash flows
NPV Discount rate =	0.00
MIRR is the rate at which NPV = 0
MIRR=	21.19%
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=(12478.01)+(13332.77)+(11251.97)+(8075.2)
=45137.95
Thus year 0 modified cash flow=-15900-2031.39
=-17931.39


Discount rate	12.000%
Year	0	1	2	3	4	5
Cash flow stream	-15900.000	7930.000	9490.000	8970.000	7210.000	-3580.000
Discount factor	1.000	1.120	1.254	1.405	1.574	1.762
Compound factor	1.000	1.574	1.405	1.254	1.120	1.000
Discounted cash flows	-15900.000	0	0	0	0	-2031.39
Compounded cash flows	0.000	12478.01	13332.77	11251.97	8075.2	0
Modified cash flow	-17931.390	0	0	0	0	45137.950
Discounting factor (using MIRR)	1.000	1.203	1.447	1.740	2.093	2.517
Discounted cash flows	-17931.390	0.000	0.000	0.000	0.000	17931.390
NPV = Sum of discounted cash flows
NPV=	0.00
MIRR is the rate at which NPV = 0
MIRR=	20.28%
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

jeff jeffy answered 10 months ago

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