Present worth (PW) analysis is an equivalence method of analysis of investment decisions in which a project's cash flows are presented as a single present value. PW is one of the most basic and efficient methods available for determining the acceptability of a project on an economic basis.

PW analysis takes two forms: *simple payback*, which ignores the time-value of money, and *discounted payback*, which accounts for the time-value of money. PW analysis results in a single criterion. For simple payback, that criterion is the investment payback period. For discounted payback, that criterion is whether the PW is greater than zero. If the investment passes the criterion, the investment is good.

# Net Present Worth

The present worth of all incoming cash flows is compared with all the outgoing cash flows and the difference in the two flows is the net present worth. This net present worth is a basic tool for determining whether an investment is a good one.

### The Effect of Choice Environment on Present Worth

#### Present Worth Criteria in an Unconstrained Choice Environment

You may be presented with a variety of investment choices, and on top of this, each choice may each have different options available. In this case we should adhere to the following rule: **Choose ALL investments that have a present worth greater than or equal to 0.**

Since this is unconstrained choice we are free to choose as many investment choices as we deem worthy by present worth analysis, but we can only have one option per investment.

##### Why Present Worth Criteria in an Unconstrained Choice Environment Works

Download audio here.

At one point in the audio the criteria is misspoken as PW>1, it should be PW>0

This rule works under the assumption that the money is not doing anything else if not invested. Unconstrained choice allows us to see all of our options and invest in all that are greater than or equal to zero. In a close run one single choice may not be sufficient so unconstrained choice takes care of this problem and displays our options.

##### Example: Present Worth Analysis in an Unconstrained Choice Environment

For this example assume MARR = 10%.

Year | Option A | Option B |

0 | -10 | -10 |

1 | 15 | 11 |

PW(10%) | 3.63 | 0 |

Sample Calculations for PW:

A: -10 + (15 / (1 + 0.1)^1 ) = 3.63

B: -10 + (11 / (1 + 0.1)^1 ) = 0

Analysis results: Both options should be purchased since the PW of both investments is greater than or equal to 0.

#### Present Worth Criteria in an Exclusive Choice Environment

Exclusive choice differs from unconstrained choice in that we only want to choose one investment option. An example would be choosing an investment for a business, such as building a house. The house can be built more durable but it takes longer to build or less durable but built much more quickly. You can't choose both options, you must choose only one.

In the case of exclusive choice, we should adhere to the following rule:

**We choose the single option that has the largest present worth.**

##### Why Present Worth Criteria in an Exclusive Choice Environment Works

Video Transcript Available here

This rule also works because money is not doing anything if it's not being invested. Unlike unconstrained choice it looks at a list of different things that are needed and finds the one with the greatest benefit.

##### The Phone Lines Example

Video Transcript Available here

Continuing the example with some calculations

Video Transcript Available here

Why the answer is the answer

Video Transcript Available here

##### Example 2

This is a pretty cool and quick analysis. It goes pretty fast.

##### Example 3

Assume that MARR = 10%

Year | A | B | C | D |

0 | -10 | -20 | -200 | -1 |

1 | 15 | 30 | 215 | 4 |

PW(10%) | 3.63 | 7.27 | -4.34 | 2.63 |

Sample Calculations for PW:

A: -10 + (15 / (1 + 0.1)^1 ) = 3.63

B: -20 + (30 / (1 + 0.1)^1 ) = 7.27

C: -200 + (215 / (1 + 0.1)^1 ) = -4.34

D: -1 + (4 / (1 + 0.1)^1 ) = 2.63

Investment option B is the winner for exclusive choice because it has the highest present worth.

##### Example 4

MARR = 10%

YEAR | A | B | C |

0 | 10 | 10 | 10 |

1 | 0 | 0 | -3 |

2 | 0 | 0 | -3 |

3 | 0 | -15 | -3 |

4 | 0 | 0 | -3 |

5 | -15 | 0 | 0 |

PW | 0.686 | -1.269 | 0.49 |

PW(A)= 10+(-15/1.1^{5}) = 0.686

PW(B)= 10+(-15/1.1^{3}) = -1.269

PW(C)=10-3(P\A, i=0.10, n=4)

PW(C)=10-3((1.1^{4}-1)/(0.10(1.1)^{4}))= 0.49

Remember:

**Assets** - as many as you want with one choice from each category, choose non-negative values.

**Asset** - choose *one* highest positive value.

Q1: Which assets would you choose?

A: Assets A and C

Q2: Which asset would you choose?

A: Asset A