The Caffeine Coffee Company uses the modified internal rate of return. The firm has a cost of capital of 13 percent. The project being analyzed is as follows ($32,000 investment):
Year Cash Flow
1 $19,000
2 $15,000
3 $10,000
What is the modified internal rate of return?
Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.
Answer (2)
Calculate the future value of each cash inflow at the cost of capital (13%).
Sum the future values to find the total future value: T o t a l _ F V = $51 , 211.10 .
Calculate the MIRR using the formula: M I RR = ( P V T o t a l _ F V ) n 1 − 1 .
The modified internal rate of return (MIRR) for the project is approximately 16.97% .
Explanation
Understanding the Problem We need to calculate the modified internal rate of return (MIRR) for a project with an initial investment of $32,000 and the following cash flows:
Year 1: $19,000 Year 2: $15,000 Year 3: $10,000
The firm's cost of capital is 13 percent. The MIRR calculation involves finding the future value of the cash inflows, discounting them back to the present, and then calculating the rate of return.
Calculating Future Values First, we calculate the future value (FV) of each cash inflow at the cost of capital (13%).
Year 1 Cash Flow: $19,000 will earn interest for 2 years. F V 1 = 19000 × ( 1 + 0.13 ) 2 = 19000 × ( 1.13 ) 2 = 19000 × 1.2769 = $24 , 261.10
Year 2 Cash Flow: $15,000 will earn interest for 1 year. F V 2 = 15000 × ( 1 + 0.13 ) 1 = 15000 × 1.13 = $16 , 950
Year 3 Cash Flow: $10,000 will not earn any interest as it is received at the end of the project. F V 3 = $10 , 000
Now, we sum these future values to find the total future value: T o t a l _ F V = F V 1 + F V 2 + F V 3 = 24261.10 + 16950 + 10000 = $51 , 211.10
Determining Present Value Next, we have the present value (PV) of the initial investment, which is simply the initial investment itself: P V = $32 , 000
Calculating MIRR Now we calculate the MIRR using the formula: M I RR = ( P V T o t a l _ F V ) n 1 − 1 Where: T o t a l _ F V = $51 , 211.10 P V = $32 , 000 n = 3 (number of years)
M I RR = ( 32000 51211.10 ) 3 1 − 1 = ( 1.600346875 ) 3 1 − 1 M I RR = 1.169691611565564 − 1 = 0.169691611565564
To express MIRR as a percentage rounded to two decimal places: M I RR % = 0.169691611565564 × 100 = 16.9691611565564 ≈ 16.97%
Final Answer The modified internal rate of return (MIRR) for the project is approximately 16.97%.
Examples
Modified Internal Rate of Return (MIRR) is a crucial metric in financial analysis, especially when comparing different investment opportunities. For instance, imagine you're deciding between two coffee shop franchises. MIRR helps you determine which franchise provides a better return on investment, considering the time value of money and reinvestment rates. By calculating the future value of cash inflows and comparing it to the initial investment, MIRR offers a clear percentage that aids in making informed investment decisions. It ensures that you're not just looking at the total profit, but also how efficiently the investment generates returns over time, making it a practical tool for business owners and investors.
The Modified Internal Rate of Return (MIRR) for the project, after calculating future cash flows at a cost of capital of 13%, is approximately 16.97%. This value reflects the project's efficiency in generating returns related to the initial investment. Calculating MIRR helps assess the profitability of the investment over its duration.
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