Mittuch Corp. is evaluating a project with the following cash flows. The company
ID: 2779611 • Letter: M
Question
Mittuch Corp. is evaluating a project with the following cash flows. The company uses a discount rate of 9 percent and a reinvestment rate of 6 percent on all of its projects. Year Cash Flow 0 -$16,700 7,800 9,000 8,600 7,400 5 4,800 2 4 Calculate the MIRR of the project using all three methods with these interest rates. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) MIRR Discounting approach Reinvestment approach Combination approach 14.78 %Explanation / Answer
In the discounting approach, we find the value of all cash outflows at Time 0, while any cash inflows remain at the time at which they occur. So, discounting the cash outflows at Time 0, we find:
Cash flow at time: 0
CF0 = -16,700 - 4,800/(1.09)5
CF0 = -19,819.67
Discount Rate = 9%
0 = -19,819.67 + 7,800/ (1 + MIRR) + 9,000/ (1 + MIRR)2 + 8,600/ (1 + MIRR)3 + 7,400/ (1 + MIRR)4
MIRR = 23.90%
Reinvestment approach:
In the reinvestment approach, we find the future value of all cash, except the initial cash flow, at the end of the project. So, reinvesting the cash flows to Time 5, we find:
Time 5 Cash flow = 7,800 * (1.06)4 + 9,000 * (1.06)3 + 8,600 * (1.06)2 + 7,400 * (1.06)1 - 4,800
Time 5 Cash flow = 33,273.42
So, the MIRR using the reinvestment approach is:
0 = -16,700 + 33,273.42/(1 + MIRR)5
16,700 = 33,273.42/(1 + MIRR)5
MIRR = 14.78%
Combination approach:
In the combination approach, we find the value of all cash outflows at Time 0, and the value of all cash inflows at the end of the project. So, the value of the cash flows is
CF0 = -16,700 - 4,800/(1.09)5
CF0 = -19,819.67
Time 5 Cash flow = 7,800 * (1.06)4 + 9,000 * (1.06)3 + 8,600 * (1.06)2 + 7,400 * (1.06)1
Time 5 Cash flow = 38,073.42
MIRR is:
0 = -19,819.67 + 38,073.42/(1 + MIRR)5
38,073.42/(1 + MIRR)5 = 19,819.67
(1 + MIRR)5 = 1.920992
MIRR = 1.9209920.2 - 1
MIRR = 13.95%