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

Question

Slow Ride Corp. is evaluating a project with the following cash flows: Year Cash Flow 0 –$ 28,700 1 10,900 2 13,600 3 15,500 4 12,600 5 – 9,100 The company uses an interest rate of 8 percent on all of its projects. Calculate the MIRR of the project using the discounting approach method. (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) MIRR % Calculate the MIRR of the project using the reinvestment approach method. (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) MIRR % Calculate the MIRR of the project using the combination approach method. (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) MIRR %

Explanation / Answer

Discounting approach:

In the discounting approach, we find the value of all cash outflows at time 0 using the discount rate, while any cash inflows remain at the time at which they occur.

So, discounting the cash outflows at time 0, we find:

Time 0 cash flow = –$28,700 – $9,100 /1.08^5

Time 0 cash flow = –$22506.69

So, the MIRR using the discounting approach is: 0 = –22506.69 + 10900 /(1+MIRR) + 13600/(1+MIRR)^2 + 15,500/(1+MIRR)^3 + 12600/(1+MIRR)^4

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

we find that: MIRR = 43.24%

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 using the reinvestment rate.

So, reinvesting the cash flows to time 5, we find:

Time 5 cash flow = 10900(1.08^4) + 13,600(1.05^3) + 15500(1.05^2) + 12600(1.05) – 9100

Time 5 cash flow = 51791.779

So, the MIRR using the reinvestment approach is: 0 = –28700 + 51791.779 /(1+MIRR)^5

51791.779 / 28700 = (1+MIRR)^5

MIRR = (51791.779 / 28700)^1/5 – 1

MIRR = 0.1253 or 12.53%

Combination approach:

In the combination approach, we find the value of all cash outflows at time 0 using the discount rate, and the value of all cash inflows at the end of the project using the reinvestment rate. So, the value of the cash flows is:

Time 0 cash flow = –$28,700 – $9,100 /1.08^5

Time 0 cash flow = –$22506.69

Time 5 cash flow = 10900(1.08^4) + 13,600(1.05^3) + 15500(1.05^2) + 12600(1.05)

Time 5 cash flow = 60891.779

So, the MIRR using the combination approach is: 0 = –22506.69 + 60891.779 /(1+MIRR)^5

60891.779 / 22506.69 = (1+MIRR) 5

MIRR = (60891.779 / 22506.69)^1/5 – 1

MIRR = 0.22025 or 22.03%

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