Calculate the IRR of an investment of ₹1,36,000 which yields the following cash inflows: 1st year: ₹30,000 2nd year: ₹40,000 3rd year: ₹60,000 4th year: ₹30,000 5th year: ₹20,000 Calculate the IRR of an investment of ₹1,36,000 which yields the following cash inflows: 1st year: ₹30,000 2nd year: ₹40,000 3rd year: ₹60,000 4th year: ₹30,000 5th year: ₹20,000 Read more

Steps to Solve

1. Understanding Internal Rate of Return (IRR)

IRR is the discount rate at which the net present value (NPV) of an investment equals zero. It helps determine the profitability of a potential investment. We will use trial and error to find the IRR, since we can't directly solve for it in this case.

2. Setting up the NPV equation

The Net Present Value (NPV) is calculated as follows.

$NPV = \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t} - Initial Investment$

Where : $CF_t$ = Cash flow at period t $r$ = Discount rate $n$ = Number of periods

We want to find the $r$ (IRR) that makes the $NPV = 0$:

$0 = \frac{30000}{(1+r)^1} + \frac{40000}{(1+r)^2} + \frac{60000}{(1+r)^3} + \frac{30000}{(1+r)^4} + \frac{20000}{(1+r)^5} - 136000$

3. First Trial Rate

Let's start with a rate of 5% (0.05). $NPV = \frac{30000}{(1+0.05)^1} + \frac{40000}{(1+0.05)^2} + \frac{60000}{(1+0.05)^3} + \frac{30000}{(1+0.05)^4} + \frac{20000}{(1+0.05)^5} - 136000$ $NPV = \frac{30000}{1.05} + \frac{40000}{1.1025} + \frac{60000}{1.157625} + \frac{30000}{1.21550625} + \frac{20000}{1.2762815625} - 136000$ $NPV = 28571.43 + 36281.18 + 51829.55 + 24679.86 + 15661.54 - 136000 = 21023.56$

Since the NPV is positive, we need to try higher rates.

4. Second Trial Rate

Let's try 10% (0.10).

$NPV = \frac{30000}{(1+0.10)^1} + \frac{40000}{(1+0.10)^2} + \frac{60000}{(1+0.10)^3} + \frac{30000}{(1+0.10)^4} + \frac{20000}{(1+0.10)^5} - 136000$ $NPV = \frac{30000}{1.1} + \frac{40000}{1.21} + \frac{60000}{1.331} + \frac{30000}{1.4641} + \frac{20000}{1.61051} - 136000$ $NPV = 27272.73 + 33057.85 + 45078.89 + 20490.40 + 12418.43 - 136000 = 23018.30$

The NPV is still positive, so let's increase the rate further.

5. Third Trial Rate

Let's try 15% (0.15).

$NPV = \frac{30000}{(1+0.15)^1} + \frac{40000}{(1+0.15)^2} + \frac{60000}{(1+0.15)^3} + \frac{30000}{(1+0.15)^4} + \frac{20000}{(1+0.15)^5} - 136000$ $NPV = \frac{30000}{1.15} + \frac{40000}{1.3225} + \frac{60000}{1.520875} + \frac{30000}{1.74900625} + \frac{20000}{2.0113571875} - 136000$ $NPV = 26086.96 + 30245.03 + 39450.74 + 17152.76 + 9943.53 - 136000 = -13120.98$

The NPV is now negative. This means the IRR is between 10% and 15%.

6. Fourth Trial Rate

Let's try 13% (0.13).

$NPV = \frac{30000}{(1+0.13)^1} + \frac{40000}{(1+0.13)^2} + \frac{60000}{(1+0.13)^3} + \frac{30000}{(1+0.13)^4} + \frac{20000}{(1+0.13)^5} - 136000$ $NPV = \frac{30000}{1.13} + \frac{40000}{1.2769} + \frac{60000}{1.442897} + \frac{30000}{1.63047361} + \frac{20000}{1.84243518} - 136000$ $NPV = 26548.67 + 31325.94 + 41581.64 + 18400.46 + 10855.28 - 136000 = 2711.99$

The NPV is now positive. This means the IRR is between 13% and 15%.

7. Fifth Trial Rate

Let's try 14% (0.14).

$NPV = \frac{30000}{(1+0.14)^1} + \frac{40000}{(1+0.14)^2} + \frac{60000}{(1+0.14)^3} + \frac{30000}{(1+0.14)^4} + \frac{20000}{(1+0.14)^5} - 136000$ $NPV = \frac{30000}{1.14} + \frac{40000}{1.2996} + \frac{60000}{1.481544} + \frac{30000}{1.68896016} + \frac{20000}{1.9254145824} - 136000$ $NPV = 26315.79 + 30779.16 + 40500.32 + 17762.06 + 10387.31 - 136000 = -10255.36$

The NPV is now negative. This means the IRR is between 13% and 14%. By interpolating, since 2711.99 is closer to zero than -10255.36, we can estimate the solution as somewhere between 13% and 13.5%, but in order to simplify, an estimate is required.

8. Estimation

Without further interpolation, we can estimate the IRR to be closer to 13% than 14%. We can round the estimate to 13%.