Cost accounting and financial management

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Khushbu Modi (Querist)
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22 March 2012 Hello sir, i am a student of CA IPCC n i am appearning exam in may '12. I have a query in financial mgt in RTP question no. 3 investment decision. How to calculate MIRR in that question? Give me full answer.

Khushbu Modi

Khushbu Modi (Querist)
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22 March 2012 I want to know how to calculate MIRR in investment decision of financial mgt in IPCC

Aashok Kumar Sharma

Aashok Kumar Sharma (Expert)
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20 July 2024 To calculate the Modified Internal Rate of Return (MIRR), you follow these steps:

### Step-by-Step Calculation of MIRR

1. **Understand the Scenario:**
Typically, in an investment decision context, MIRR is used when there are multiple cash flows including both investment outflows (negative cash flows) and investment inflows (positive cash flows).

2. **Calculate Future Value (FV) of Positive Cash Flows:**
- Identify all positive cash flows (inflows) and their respective timings.
- Determine the future value of these cash flows at the end of the investment period using a reinvestment rate (often the cost of capital or another specified rate).

3. **Calculate Present Value (PV) of Negative Cash Flows:**
- Identify all negative cash flows (outflows) and their respective timings.
- Determine the present value of these cash flows at the beginning of the investment period using the initial cost of capital (often the cost of capital or another specified rate).

4. **Calculate MIRR Formula:**
- MIRR formula adjusts for both the cost of financing the investment (outflows) and the return on reinvestment (inflows).

\[
MIRR = \left( \frac{\text{FV of positive cash flows}}{\text{PV of negative cash flows}} \right)^{\frac{1}{n}} - 1
\]

Where:
- \( \text{FV of positive cash flows} \) = Sum of all future values of inflows (reinvested at the reinvestment rate).
- \( \text{PV of negative cash flows} \) = Sum of all present values of outflows (initial investment at the cost of capital).
- \( n \) = Number of periods (years) involved in the investment decision.

### Example Calculation

Let's assume an example scenario with hypothetical cash flows:

- Initial investment (outflow) = Rs. 100,000 at time 0 (cost of capital rate 10%)
- Inflows over 5 years:
- Year 1: Rs. 20,000
- Year 2: Rs. 30,000
- Year 3: Rs. 40,000
- Year 4: Rs. 50,000
- Year 5: Rs. 60,000
- Reinvestment rate = 12%

**Step-by-Step Calculation:**

1. **Calculate Future Value of Inflows:**
- Use the reinvestment rate (12%) to calculate the future value of each cash inflow at the end of Year 5.
- For example, Year 1 inflow future value = Rs. 20k * (1 + 0.12)^4 = Rs. 20k * 1.5735 = Rs. 31,470

Calculate the future value for all inflows and sum them up.

\[
\text{FV of positive cash flows} = \sum \text{Future values of inflows}
\]

2. **Calculate Present Value of Outflow:**
- Use the cost of capital rate (10%) to calculate the present value of the initial investment outflow (Rs. 100,000) at time 0.

\[
\text{PV of negative cash flows} = \text{Present value of initial outflow}
\]

3. **Apply the MIRR Formula:**

\[
MIRR = \left( \frac{\text{FV of positive cash flows}}{\text{PV of negative cash flows}} \right)^{\frac{1}{n}} - 1
\]

Substitute the calculated values into the formula to get the MIRR.

### Conclusion

This method of calculating MIRR incorporates both the cost of capital and the reinvestment rate, providing a comprehensive measure of the investment's profitability that takes into account the timing and magnitude of cash flows.

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