17. Find the IRR of an investment having initial cash outflow of Rs. 213,000. The cash inflows during the first, second, third and fourth years are expected to be Rs. 65,200, Rs. 96,000, Rs. 73,100 and Rs. 55,400 respectively. A) $$ 12.76 \% $$ B) $$ 14.05 \% $$ C) $$ 0.1276 \% $$ D) $$ 0.1405 \% $$

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UpStudy AI · Accepted Answer

To determine the Internal Rate of Return (IRR) for the given investment, we'll use the cash flow data provided and apply the IRR concept, which is the discount rate that makes the Net Present Value (NPV) of all cash flows equal to zero.

### Given:
- **Initial Investment (Year 0):** Rs. 213,000 (Outflow)
- **Cash Inflows:**
  - **Year 1:** Rs. 65,200
  - **Year 2:** Rs. 96,000
  - **Year 3:** Rs. 73,100
  - **Year 4:** Rs. 55,400

### IRR Calculation Steps:

1. **NPV Formula:**
   $$
   NPV = -213,000 + \frac{65,200}{(1 + r)^1} + \frac{96,000}{(1 + r)^2} + \frac{73,100}{(1 + r)^3} + \frac{55,400}{(1 + r)^4} = 0
   $$
   Here, $$ r $$ is the IRR we need to find.

2. **Trial and Error Method:**
   - **At 12%:**
     $$
     NPV \approx +9,010 \quad (\text{Positive})
     $$
   - **At 14%:**
     $$
     NPV \approx +300 \quad (\text{Close to Zero})
     $$
   - **At 15%:**
     $$
     NPV \approx -3,989 \quad (\text{Negative})
     $$
   
   Since the NPV changes from positive to negative between 14% and 15%, the IRR lies within this range.

3. **Linear Interpolation:**
   To pinpoint the IRR more accurately:
   $$
   IRR \approx 14\% + \left(\frac{0 - 300}{-3,989 - 300}\right) \times 1\% \approx 14.07\%
   $$
   
   This calculation aligns closely with **14.05%**.

### **Conclusion:**
The IRR for the investment is approximately **14.05%**.

**Answer:**  
B) $$ 14.05 \% $$
The Internal Rate of Return (IRR) for the investment is approximately **14.05%**. **Answer:** B) $$ 14.05 \% $$

Find the IRR of an investment having initial cash outflow of Rs. 213,000. The cash inflows during the first, second, third and fourth years are expected to be Rs. 65,200, Rs. 96,000, Rs. 73,100 and Rs. 55,400 respectively.
A)
B)
C)
D)

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Find the IRR of an investment having initial cash outflow of Rs. 213,000. The cash inflows during the first, second, third and fourth years are expected to be Rs. 65,200, Rs. 96,000, Rs. 73,100 and Rs. 55,400 respectively. A) B) C) D)