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

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

Year	Cash Flow
0	–$	28,400
1		10,600
2		13,300
3		15,200
4		12,300
5	–	8,800

  

The company uses an interest rate of 8 percent on all of its projects.

  

Calculate the MIRR of the project using the discounting approach. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

  

MIRR

%

  

Calculate the MIRR of the project using the reinvestment approach. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

  

MIRR

%

Calculate the MIRR of the project using the combination approach. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

  

MIRR

%

 

Explanation:

The MIRR for the project with all three approaches is:

Discounting approach:

In the discounting approach, we find the value of all negative cash outflows at Time 0, while any positive cash inflows remain at the time at which they occur. So, discounting the cash outflows to Time 0, we find:

Time 0 cash flow = –$28,400 – $8,800 / 1.085

Time 0 cash flow = –$34,389.13

   

So, the MIRR using the discounting approach is:

0 = –$34,389.13 + $10,600 / (1 + MIRR) + $13,300 / (1 + MIRR)2 + $15,200 / (1 + MIRR)3          + $12,300 / (1 + MIRR)4

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find:

MIRR = 17.63%

  

Reinvestment approach:

In the reinvestment approach, we find the future value of all cash flows, 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 = $10,600(1.084) + $13,300(1.083) + $15,200(1.082) + $12,300(1.08) – $8,800

Time 5 cash flow = $53,388.63

So, the MIRR using the reinvestment approach is:

0 = –$28,400 + $53,388.63 / (1 + MIRR)5

$53,388.63 / $28,400 = (1 + MIRR)5

MIRR = ($53,388.63 / $28,400)1/5 – 1

MIRR = .1346, or 13.46%

  

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:

Time 0 cash flow = –$28,400 – $8,800 / 1.085

Time 0 cash flow = –$34,389.13

Time 5 cash flow = $10,600(1.084) + $13,300(1.083) + $15,200(1.082) + $12,300(1.08)

Time 5 cash flow = $62,188.63

So, the MIRR using the combination approach is:

0 = –$34,389.13 + $62,188.63 / (1 + MIRR)5

$62,188.632 / $34,389.13 = (1 + MIRR)5

MIRR = ($62,188.63 / $34,389.13)1/5 – 1

MIRR = .1258, or 12.58%