Question

Slow Ride Corp. is evaluating a project with the following cash flows:

Year	Cash Flow
0	–$13,200
1	5,900
2	6,600
3	6,300
4	5,200
5	–5,700

The company uses a 11 percent discount rate and an 8 percent reinvestment rate on all of its projects. Calculate the MIRR of the project using all three methods using these interest rates.

Required:
(a)	MIRR using the discounting approach.
	(Click to select)17.31%16.12%15.46%17.82%16.97%

  

(b)	MIRR using the reinvestment approach.
	(Click to select)11.71%12.95%14.36%12.33%12.58%

(c)	MIRR using the combination approach.
	(Click to select)12.3%11.46%12.66%13.04%12.06%

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=-13200-3382.67
=-16582.67
Year	0	1	2	3	4	5
Cash flow stream	-13200.000	5900.000	6600.000	6300.000	5200.000	-5700.000
Discounting factor (Using discount rate)	1.000	1.110	1.232	1.368	1.518	1.685
Discounted cash flows	-13200.000	5315.315	5356.708	4606.506	3425.401	-3382.673
Modified cash flow	-16582.673	5900.000	6600.000	6300.000	5200.000	0.000
Discounting factor (using MIRR)	1.000	1.170	1.368	1.600	1.872	2.190
Discounted cash flows	-16582.673	5044.081	4823.963	3936.685	2777.944	0.000
NPV = Sum of discounted cash flows
NPV Reinvestment rate =	0.00
MIRR is the rate at which NPV = 0
MIRR=	16.97%
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=(8026.88)+(8314.1)+(7348.32)+(5616)+(-5700)
=23605.3
Discount rate	11.000%
Year	0	1	2	3	4	5
Cash flow stream	-13200.000	5900.000	6600.000	6300.000	5200.000	-5700.000
Compound factor	1.000	1.360	1.260	1.166	1.080	1.000
Compounded cash flows	-13200.000	8026.88	8314.1	7348.32	5616	-5700
Modified cash flow	-13200.000	0	0	0	0	23605.300
Discounting factor (using MIRR)	1.000	1.123	1.262	1.417	1.592	1.788
Discounted cash flows	-13200.000	0.000	0.000	0.000	0.000	13200.000
NPV = Sum of discounted cash flows
NPV Discount rate =	0.00
MIRR is the rate at which NPV = 0
MIRR=	12.33%
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=(8026.88)+(8314.1)+(7348.32)+(5616)
=29305.3
Thus year 0 modified cash flow=-13200-3382.67
=-16582.67
Discount rate	11.000%
Year	0	1	2	3	4	5
Cash flow stream	-13200.000	5900.000	6600.000	6300.000	5200.000	-5700.000
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	-13200.000	0	0	0	0	-3382.67
Compounded cash flows	0.000	8026.88	8314.1	7348.32	5616	0
Modified cash flow	-16582.670	0	0	0	0	29305.300
Discounting factor (using MIRR)	1.000	1.121	1.256	1.407	1.577	1.767
Discounted cash flows	-16582.670	0.000	0.000	0.000	0.000	16582.670
NPV = Sum of discounted cash flows
NPV=	0.00
MIRR is the rate at which NPV = 0
MIRR=	12.06%
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