## 1553 Financial Analysis Methods Sample Calculations

Chapter 4 offers a complete discussion of the various types of financial analyses commonly used in industry. A review of that material is suggested here, as the methods discussed below rely on this basic understanding.

To select the proper financial analysis requires an understanding of the degree of sophistication required by the decision maker. In some cases, a quick estimate of profitability is all that is required. At other times, a very detailed cash flow analysis is in order. The important point is to determine what level of analysis is desired and then seek to communicate at that level. Following is an abbreviated discussion of four primary methods of evaluating an insulation investment: (1) simple payback; (2) discounted payback; (3) minimum annual cost using a level annual equivalent; and (4) present-value cost analysis using discounted cash flows.

### Economic Calculations

Basically, a simple payback period is the time required to repay the initial capital investment with the operating savings attributed to that investment. For example, consider the possibility of upgrading a present insulation thickness standard.

Thickness Current Standard

Upgraded

Thickness Difference

Insulation investment ($) 225,000 275,000 Annual fuel cost ($) 40,000 30,000

Simple payback =

investment difference 50,000

annual fuel saving 10,000

50,000 10,000

This calculation represents the incremental approach, which determines the amount of time to recover the additional $50,000 of investment.

In the following table, the full thickness analysis is similar except that the upgraded thickness numbers are now compared to an uninsulated system with zero insulation investment.

Uninsulated Upgraded

System Thickness Difference

Insulation investment ($) 0 275,000 275,000

Annual fuel cost ($) 340,000 30,000 310,000

Simple payback =

275,000 310,000

The magnitude of the difference points out the danger in talking about payback without a proper definition of terms. If in the second example, management had a payback requirement of 3 years, the full insulation investment easily complies, whereas the incremental investment does not. Therefore, it is very important to understand the intent and meaning behind the payback requirement.

Although simple payback is the easiest financial calculation to make, its use is normally limited to rough estimating and the determination of a level of financial risk for a certain investment. The main drawback with this simple analysis is that it does not take into account the time value of money, a very important financial consideration.

### Time Value of Money

Again, see Chapter 4. The significance of the cost of money is often ignored or underestimated by those who are not involved in their company's financial mainstream. The following methods of financial analysis are all predicated on the use of discount factors that reflect the cost of money to the firm. Table 15.9 is an abbreviated table of present-value factors for a steady income stream over a number of years. Complete tables are found in Chapter 4.

### Discounted Payback

Although similar to simple payback, the utilization of the discount factor makes the savings in future years worth less in present-value terms. For discounted payback, then, the annual savings times the discount factor must now equal the investment to achieve payback in present-value dollars. Using the same example:

Thickness Current standard

Insulation investment ($) 225,000 Annual fuel cost ($) 40,000

upgraded

Thickness Difference

275,000 30,000

50,000 10,000

Now, payback occurs when:

investment = discount factor x annual savings 50,000 = (discount factor) x 10,000 so solving for the discount factor, investment 50,000

discount factor =

annual savings 10,000

money of only 5%, the payback is achieved in about 6 years. Obviously, a 0% cost of money would be the same as the simple payback calculation of 5 years.

### Minimum Annual Cost Analysis

As previously discussed, an insulation investment must involve a lump-sum cost for insulation as well as a stream of fuel costs over the many years. One method of putting these two sets of costs into the same terms is to spread out the insulation investment over the life of the project. This is done by dividing the initial investment by the appropriate discount factor in Table 15.9. This produces a "level annual equivalent" of the investment for each year which can then be added to the annual fuel cost to arrive at a total annual cost.

utilizing the same example with a 20-year project life and 10% cost of money:

Thickness Current upgraded standard Thickness

Insulation investment ($) |
225,000 |
275,000 |

For 20 years at 10%, the discount factor is 8 |
.514 (Table | |

15.9), so |

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