**Introduction**

Decision-making process is always future-oriented i.e. we consider alternatives and make choices for our future actions. All the things we consider for future decisions contain some level of uncertainty and risk. Financial decision making has also a future orientation and involves high uncertainty and such decisions are always a trade-off between risk and return. Certainty Equivalent is an important concept in capital budgeting and a crucial approach in financial decision making.

**Certainty Equivalent Approach (CEA)**, in the capital budgeting context, deals with risk factors involved where risky future cash flows are expressed in terms of the certain cash flows investors will accept today. Certainty Equivalent is essential for evaluating risk.

It is evident that investors expect the return on their investment equivalent to the risk she/he takes, which means, higher the risk, equivalent is the expected return on that investment.

Uncertain cash flows are converted into certain cash flows by multiplying it with probability of occurrence i.e. certainty coefficient. Certainty coefficient lies between 0 and 1.

**Illustration I**

The following table presents 5 years cash inflows. The certainty coefficient for the cash flows are also given which presents the probability of the occurrence of cash flows.

Year | Cash Inflows | Certainty Coefficient |

1 | Rs. 100,000 | 0.9 |

2 | Rs. 250,000 | 0.7 |

3 | Rs. 90,000 | 0.5 |

4 | Rs. 120,000 | 0.6 |

5 | Rs. 50,000 | 0.2 |

The Initial cost of investment is Rs. 300,000 And the discount rate is 9% annually. With the help of a certainty equivalent method, find out the NPV and analyze it.

**Solution**

**Net Present Value (NPV)** = Present Values of all the cash inflows- Initial cost of investment.

Now, for the calculation of present value of the cash inflows considered;

Year | Cash Inflows | Certainty Coefficient | Certainty Equivalent Cash Flow | Present Value @ 9% | |

1 | Rs. 100,000 | 0.9 | Rs. 90,000 | Rs. 82568.81 | |

2 | Rs. 250,000 | 0.7 | Rs. 175,000 | Rs. 147,293.99 | |

3 | Rs. 90,000 | 0.5 | Rs. 45,000 | Rs. 34,748.26 | |

4 | Rs. 120,000 | 0.6 | Rs. 72,000 | Rs. 51,006.61 | |

5 | Rs. 50,000 | 0.2 | Rs. 10,000 | Rs. 6,499.31 | |

Total | – | – | Rs. 322,116.98 | ||

Net Present Value: Present Value of Cash Inflows – Initial cost of Investment

Here,

NPV = Rs. 322,116.98 -Rs. 300,000

= Rs. 22,116.98

Here, NPV is positive which means the project is viable in terms of cash flow. Therefore, project is accepted

**Internal Rate of Return (IRR) Method**

**Let us assume, **the discount rate is 13% then the impact on NPV will be.

Year | Cash Inflows | Certainty Coefficient | Certainty Equivalent Cash Flow | Present Value @ 13 % | |

1 | Rs. 100,000 | 0.9 | Rs. 90,000 | Rs. 79,646.02 | |

2 | Rs. 250,000 | 0.7 | Rs. 175,000 | Rs. 137,050.67 | |

3 | Rs. 90,000 | 0.5 | Rs. 45,000 | Rs. 31,187.28 | |

4 | Rs. 120,000 | 0.6 | Rs. 72,000 | Rs. 44,158.95 | |

5 | Rs. 50,000 | 0.2 | Rs. 10,000 | Rs. 5,427.59 | |

Total | – | – | Rs. 297,470.51 | ||

Net Present Value = Present value of Cash Inflows- Initial Cost of Investment

= Rs. 297,470.51 – Rs. 300,000

= **– Rs. 2529.49**

We calculate the NPV at the discount rate of 12%,

Year | Cash Inflows | Certainty Coefficient | Certainty Equivalent Cash Flow | Present Value @ 12 % | |

1 | Rs. 100,000 | 0.9 | Rs. 90,000 | Rs. 80,357.14 | |

2 | Rs. 250,000 | 0.7 | Rs. 175,000 | Rs. 139,508.93 | |

3 | Rs. 90,000 | 0.5 | Rs. 45,000 | Rs. 32,030.11 | |

4 | Rs. 120,000 | 0.6 | Rs. 72,000 | Rs. 45,757.30 | |

5 | Rs. 50,000 | 0.2 | Rs. 10,000 | Rs. 5,674.29 | |

Total | – | – | Rs. 303,327.77 | ||

NPV = Present value of the cash inflows – Initial cost of investment

= Rs. 303,327.77- Rs. 300,000

**= Rs. 3,327.77**

**For Internal Rate of Return (IRR)**

**IRR = Lower Rate + ((NPV at LR)/(NPV at LR- NPV at HR)* (HR-LR)**

**= **12+ ( 3,327.77/(3327.77+2529.49)*(13-12)

= 12+ ( 3,327.77/5857.26)

= 12+0.57

= 12.57 %

Here, Internal rate of return (IRR) is 12.57% which is greater than the discount rate i.e. 9 %. Therefore, the project is accepted.