Question

With the NPV, we are looking for a number; whereas with the IRR, we are looking for the return. NPV can be calculated on a financial calculator, in excel, or by hand. NPV is very simply the present value (PV) of Cash inflows minus the present value (PV) of Cash outflows. Let’s look at an example. Let’s assume that you want to consider an investment of $5,000, and you are currently making 11% on that money. The payments that you will receive over the next 5 years are:

Year 1 $1500

Year 2 $1000

Year 3 $ 500

Year 4 $ 500

Year 5 $4000

Total $7500

So in total you will receive $7500.

Payments Required rate of return Formula Present Value 0 1 1500 11% =1500/(1.11) 1,351.35 2 1000 11% =1000/(1.11)(1.11) 811.62 3 500 11% =500/(1.11)(1.11)(1.11) 365.60 4 500 11% =500/(1.11)(1.11)(1.11)(1.11) 329.37 5 4000 11% =4000/(1.11)(1.11)(1.11)(1.11)(1.11) 2,373.81 5231.74 So the total present value (PV) of the cash inflows is $5,231.74. Now you need to calculate the present value of the outflows. Since the outflow happened right at the beginning, there is nothing to calculate because it is already in today’s dollars.

PV of cash inflows $5231.74

Minus PV of cash outflows (5000.00)

Net present value 231.74

So what does this mean?

When the NPV is positive, it means that the internal rate of return is greater than the required rate of return, and therefore the investment should be accepted. If our required rate of return in this example, were 15%, then the net present value would calculate out to be ($336.17) or $4663.82 minus $5000. In that case you would not accept the investment because you aren’t going to achieve your desired result.

Payments Required rate of return Present Value 0 - 1 1500 15% 1,304.35 2 1000 15% 756.14 3 500 15% 328.76 4 500 15% 285.88 5 4000 15% 1,988.71 4,663.83

In excel, you enter the formula below: ? Rate is the required rate of return ? Value1… are the payments =NPV(rate,value1,value2,value3…) =NPV(11%,1500,1000,500,500,4000) $5,231.74

Please note that excel is giving you the present value of the cash inflows, you still need to subtract the present value of the cash outflow.

Take the value calculated above and subtract the PV of the cash outflow 5231.74 -5000 NPV = 231.74

In the notes that I prepared for you in the Module 10: media and resources section, I gave you an example of calculating NPV. I want you to use that example and calculate what the PV would be if the payments were an equal amount and tell me which one is better and why? Please use the example with 11% required return.

Answer #1

**Calculation of
NPV**

Total cash inflows are $7,500 for 5 years. Hence equal annual cash inflow will be 7,500/5 = $ 1,500

Year | Cash inflow | PVF(_{11% , 5} ) |
Present value of cash inflows |

1 | 1,500 | 0.901 | 1,351.5 |

2 | 1,500 | 0.812 | 1,218 |

3 | 1,500 | 0.731 | 1,096.5 |

4 | 1,500 | 0.659 | 988.5 |

5 | 1,500 | 0.593 | 889.5 |

Total | 5,544 |

NPV = Present value of cash inflows - Present value of cash outflows

= 5,544 - 5,000

= $ 544

If cash inflows are evenly spread during the period of 5 years, then NPV is $544 which is higher than the NPV when cash flows are not even. Hence when cash flows are an equal amount, it is better since higher NPV means higher wealth to the common stockholders. Higher NPV adds more to the wealth of the stockholders.

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