The Art of Mathematics in Business. Dr Jae K Shim
comparing actual to budgeted amounts, the owner can determine whether the business plans are sound. If not, improvements in the planning process are needed. Perhaps the planning is over-optimistic or unrealistic. On the other hand, the problem may lie with an inclination to overspend and/or waste. The expense deviation should be related to that of sales. Perhaps all that has happened is simply that expenses went up because sales revenue increased. In that case, the result is expected and no negative sign exists.
15. Projecting Financing Needs
Introduction
Forecasts of the future sales and their related expenses provide the firm with the information needed to project its future needs for financing. Percentage of sales is the most widely used method for projecting a company’s financing needs. This method involves estimating the various expenses, assets, and liabilities for a future period as a percent of the sales forecast and then using these percentages, together with the projected sales, to construct pro-forma balance sheets.
How is it computed?
The basic steps involved in projecting financing needs are as follows:
1.Project the first firm’s sales. The sales forecast is the most important initial step. Most other forecasts (budgets) follow the sales forecast.
2.Project additional variables such as expenses.
3.Estimate the level of investment in current and fixed assets required to support the projected sales.
4.Calculate the firm’s financing needs.
The following example illustrates ,how to develop a pro-forma balance sheet and determine the amount of external financing needed.
Example
Assume that sales for 20×7=$20, projected sales for 20×8 = $24, net income = 5 percent of sales, and the dividend payout ratio = 40 percent. The steps for the computations are outlined as follows, with the results shown in Exhibit 15.1:
Step 1: Express those balance sheet items that vary directly with sales as a percentage of sales. Any item such as long term debt that does not vary directly with sales is designed “n.a.,” or “not applicable.”
Step 2: Multiply these percentages by the 20×8 projected sales = $24 to obtain the projected amounts as shown in the last column.
Step 3: Insert figures for long-term debt, common stock, and paid-in-capital from the 20×1 balance sheet.
Step 4: Compute 20×8 retained earnings as shown in Note b.
Step 5: Sum the asset accounts, obtaining total projected assets of 47.2, and also add projected liabilities and equity to obtain $7.12, the total financing provided. Since there is a short fall of $0.08 “external financing needed.” Any external financing needed may be raised by issuing notes payable, bonds, stocks, or any combination of these financing sources.
Figure 15.1: Pro Forma Balance Sheet in Millions of Dollars
20×8 retained earnings = 20×7 retained earnings + projected net income − cash dividends paid = $1.2 + 5%($24) - 40%[5%($24)] = $1.2 + $1.2 - $0.48 = $2.4 - $0.48 = $1.92
External financing needed projected total assets - (projected total liabilities + projected equity) = $7.2 - ($4.9 + $2.22) = $7.2 - $7.12 = $0.08
How is it used and applied?
Financial officers and business owners need to determine the portion of the next year’s funding requirements that has to be raised externally. By doing so, they can get a head start in arranging a least-cost financing plan.
The major advantage of the percent-of-sales method of financial forecasting is that it is simple and inexpensive to use. To obtain a more precise projection of the firm’s future financing needs, however, the preparation of a cash budget is required. One important assumption behind the use of the method is that the firm is operating at full capacity. This means that the business has no production capacity to absorb a projected increase in sales, and thus requires an additional investment in assets.
16. Naive Forecasting Models
Introduction
Naive forecasting models are based exclusively on historical observation of sales or other variables such as earnings and cash flows being forecast. They do not attempt to explain the underlying causal relationships that produce the variables being forecast. Naive models may be classified into two groups. One group consists of simple projection models. These models require inputs of data from recent observations, but no statistical analysis is performed. The second group is comprised of models that, while naive, are complex enough to require a computer. Traditional methods such as classical decomposition, moving average, and exponential smoothing models are some examples. (See Sec. 17, Moving Averages, and Sec. 18, Exponential Smoothing.)
The advantages of naive forecasting models are that they are inexpensive to develop, store data, and operate. The disadvantages are that they do not consider possible causal relationships that underlie the forecasted variable.
How is it computed?
A simple example of a naive model type is to use the actual sales of the current period as the forecast for the next period. Let us use F as the forecast value and the symbol At as the actual value. Then:
F = At
If trends are considered, then:
F = At + (At − At-1)
This model adds the latest observed absolute period-to-period change to the most recent observed level of the variable.
If it is desirable to incorporate the rate of change rather than the absolute amount, then:
Example
Consider the following monthly sales data for 20×7:
| Month | Monthly sales of product |
| 1 | $5,504 |
| 2 | 5,810 |
| 3 | 6,100 |
Forecasts will be developed for the fourth month of 20×7, using the three models:
F = At = $6, 100
F = At + (At − At-1) = $6, 100 + ($6, 100 − $5,810) = $6, 100 + $290 = $6,390
How is it used and applied?
Naive models can be applied, with very little need of a computer, to develop forecasts for sales, earnings, and cash flows. These models, however, must be used in conjunction with more complex naive models such as classical decomposition and exponential smoothing and more sophisticated models such as regression analysis. The object is to pick the model (or models) that will best forecast performance.
17. Moving Averages
Introduction
A moving average is an average that is updated as new information is received. A manger employs the most recent observations to calculate an average, which is used as the forecast for the next period.
How is it computed?
For a moving average, simply take the most recent observations and calculate an average. Moving averages are updated continually as new data are available.
Example