ThinkingApplied.com Mind Tools: Applications and Solutions

Understanding Banks' Earnings:
An Evaluation & Forecasting Technique
Part 3

Lee Humphries

# The EPS Effect of a Ratio's 1% Improvement

It is important to understand each ratio's capacity to improve future EPS.  Exhibit 7 shows the EPS impact of a 1% improvement over our example bank's latest year ratio values.  When a lower value is better, the improved value is 99% of the original; when a higher value is better, the improved value is 101% of the original.

Ratio 1: interest expense ÷ average liabilities

A 1% decrease in the average interest rate paid on average liabilities would add about 5 cents to EPS.

Ratio 2: provision for loan losses ÷ interest income

A 1% decrease in the loan loss provision rate would add about 6/10 of a cent to EPS.

Ratio 3: interest income ÷ total revenue

Since non-interest income avoids the loan loss provision expense that burdens interest income, non-interest income typically has a higher profit margin.  A 1% increase in the proportion of total revenue coming from non-interest income would add just about 2/10 of a cent to EPS.  This assumes that the dollar amount of total revenue, the loss provision rate, and the tax rate stay constant.

Ratio 4: non-interest expense ÷ total revenue less interest expense

A 1% decrease in the efficiency ratio would add almost 7 cents to EPS.

Ratio 5: income tax ÷ pretax earnings

A 1% decrease in the effective tax rate would add about 1 and 4/10 cents per share.

Ratio 6: total revenue ÷ average assets

A 1% increase in the rate of asset turnover would add about 9 and 3/4 cents to EPS.  This assumes that the dollar amount of non-interest expense remains constant.

Ratio 7: average common equity ÷ average assets

The ratio of average common equity to average assets can be variously adjusted, both alone and in conjunction with the book value, to compare the EPS effects of alternative capital structures.

     A 1% increase in dollar liabilities while dollar common and preferred equity are unchanged would add about 2 and 1/2 cents to EPS.

     A 1% increase in dollar common equity while dollar preferred equity and dollar liabilities are unchanged would add about 3/10 of a cent to EPS.

     A 1% increase in dollar common equity replacing an equal dollar amount of liabilities would add about 1/10 of a cent to EPS.

     A 1% increase in dollar assets consisting solely of an increase in liabilities would add about 2 and 3/4 cents to EPS.

Ratio 8: Preferred charges ÷ average common equity

A 1% decrease in the ratio of preferred charges to common equity would add about 1/10 of a cent to EPS.

Ratio 9: average common equity ÷ average common shares outstanding.  Adjustments to book value alone can also provide useful information.

     A 1% increase in dollar assets while the preferred and common equity ratios are unchanged would add about 2 and 3/4 cents to EPS.

     A 1% decrease in the number of common shares outstanding would likewise add about 2 and 3/4 cents to EPS.

Comparing these figures we see that our bank's major earnings driver is asset turnover (about 9 and 3/4 cents per share), followed by its efficiency ratio (almost 7 cents per share), and then the average interest rate it pays on average liabilities (almost 5 cents per share).  One percent improvements in these items would have the greatest positive effects on EPS.  Next most important are the dollar amount of the assets and the number of common shares outstanding, where the effects of various 1% improvement are approximately the same (slightly more than 2 and 3/4 cents per share).

Had we started from different ratio values, the relative influence of the nine critical ratios on EPS improvement would likewise have been different.

Setting Up a Spreadsheet to Evaluate 1% Improvements

To calculate the EPS effect of a ratio's 1% improvement, we use Exhibit 8.  Exhibit 8 is an expanded version of Exhibit 6, Part 1; two additional columns, E and F, are added.

Column E. Column E will be used to make 1% improvements in the values of Column C.

     Initially, all of Column E's cells except E2 and E6 are set equal to the corresponding cells of Column C.  For example, Cell E1 reads = C1.

     Cell E2 is set equal to [100% - E9 - E10)] ÷ E8.

     Cell E6 is set equal to [100% - F2].  (The formulas in E2 and E6 correspond to those entered earlier in Exhibit 6, Part 3 cells I2 and I6.  Refer back to Section II for an explanation.)

Column F.  Column F is similar to Column D.  Cells F1 through F15 bear the same relationship to the cells of Column E as the corresponding cells of Column D bear to the cells of Column C.

    Cell F15 is re-labeled Improved EPS.

    A new cell, F16, is added.  It contains the Latest Year's EPS (which we enter by hand).

    Another new cell, F17, is added and set to equal F15 minus F16.  This cell shows the EPS increase when a value is improved.

## Calculating the EPS Effect of a Critical Ratio's 1% Improvement

To determine the EPS effect of a 1% improvement in a particular ratio, we adjust the current value of one of its associated cells, usually multiplying or dividing that cell's value by an improvement factor, as shown in Exhibit 7.  Before moving on to another ratio, we always restore the adjusted cell to its original value.

In most cases we use Column E to adjust a ratio directly.  We set the ratio's cell in Column E equal to the combination of: (1) its corresponding cell in Column C and (2) the mathematical operation that will produce a 1% improvement.  However in the first instance below, the average interest rate, we must adjust the ratio indirectly, operating on a dollar value in Column A that feeds into it.

Average interest rate paid on average liabilities. Adjust the average interest rate indirectly.  In cell A1 multiply the original dollar interest expense times the factor .99.  We make the adjustment in this cell because a change in interest expense alters not only the average interest rate (C1 and E1), but also the efficiency ratio (C5 and E5).  (Directly adjusting the average interest rate at E1 would leave the efficiency ratio unchanged, thus understating the EPS improvement.)  After you have noted the improvement's effect on EPS (cell F16), return A1 to its original value.

Loan loss provision rate. Adjust the loan loss provision rate in cell E3, making it equal to C3 times .99.  Note the improvement in F16, then reset E3 to equal C3.

Non-interest income as a percent of total revenue. As previously explained, the profit margin is normally higher on non-interest income than on interest income.  An increase in the percent of non-interest income means a complementary decrease in the percent of interest income.  The earnings equation uses the ratio of interest income to total revenue, so to show a 1% increase in non-interest income we must reduce the percentage of interest income by a complementary amount.  Set E4 equal to C4 times 1.01 and from that product subtract .01, that is, E4 = [(C4 * 1.01) - .01].  Note the improvement in F16, then reset E4 to equal C4.

Efficiency ratio. Adjust the efficiency ratio in cell E5, setting it equal to C5 times .99.  Note the improvement in F16, then reset E5 to equal C5.  This adjustment gives the EPS effect of a 1% reduction in non-interest expense.  (A reduction in non-interest expense changes the efficiency ratio's numerator, whereas a reduction in interest expensemade when we were considering the average interest ratechanges the efficiency ratio's denominator.)

Tax rate. Adjust the tax rate in cell E7, setting it equal to C7 times .99.  Note the improvement in F16, then reset E7 equal to C7.  (Up to this point, the tax rate has been unaffected by ratio improvements: its denominator, pretax earnings, was entered by hand from the Income Statementmaking it immune to previous adjustments in expensesand its numerator, dollar taxes paid, has not been altered.)

Asset turnover. The EPS effect of an improvement in asset turnover can't be determined without adjusting two ratios at once.  (This is also true for certain equity ratio and book value improvements.)  To adjust the asset turnover rate, perform the following steps:

     Set F4 (adjusted non-interest revenue consumption) equal to D4 (original non-interest revenue consumption) divided by 1.01.  This operation holds dollar non-interest expense constant.

     Set cell F8 (adjusted asset turnover) equal to C8 (original asset turnover rate) times 1.01.

     Record the EPS increase and then return F4 and E8 to their original values.

Equity ratio. These adjustments allow us to examine the EPS effect of various changes in the relationship of equity, debt, and assets.

The EPS effect of a 1% increase in dollar liabilities while dollar preferred equity and dollar common equity are unchanged can be found by simultaneously setting cells E9 (preferred equity ratio) and E10 (common equity ratio) equal to the following values.

     E9 = C9 ÷ {[1.01 * (1 - C9 - C10)] + C9 + C10}

     E10 = C10 ÷ {[1.01 * (1 - C9 -  C10)] + C9 + C10}

The EPS effect of a 1% increase in dollar common equity while the dollar amounts of preferred equity, the preferred equity charge, and dollar debt are unchanged is found by simultaneously adjusting the equity ratios and the book value.

     Set E9 (preferred equity ratio) equal to C9 ÷ [ 1 + (C10 * .01)].

     Set E10 (common equity ratio) equal to [C10 * 1.01] ÷ [1 + (C10 * .01)].

     Set E 11 (preferred charge to common equity) equal to C11 ÷ 1.01.

     Set E12 (book value) equal to C12  * 1.01.

The EPS effect of a 1% increase in dollar common equity replacing an equal dollar amount of debt is found by simultaneously adjusting the common equity ratio and the book value.

     Set E10 (common equity ratio) equal to C10 * 1.01.

     Set E11 (preferred charge to common equity) equal to C11 ÷ 1.01.

     Set E12 (book value) equal to C12 * 1.01.

The EPS effect of a 1% increase in assets through additional liabilities while the dollar amounts of preferred equity, common equity, and the preferred charge are unchanged is found by simultaneously adjusting the preferred and common equity ratios.

     Set E9 (preferred equity ratio) equal to C9 ÷ 1.01.

     Set E10 (common equity ratio) equal to C10 ÷ 1.01.

Preferred charge to common equity. The EPS effect of a 1% decrease in the preferred charge to common equity is found as follows.

     Set E11 equal to C11 * .99.

Book value.

To determine the EPS effect of a 1% increase in dollar assets when all else is unchanged, multiply the original book value times the appropriate improvement factor.

     Set cell E12 equal to C12 * 1.01.

To determine the EPS effect of a 1% decrease in the number of common shares outstanding, divide the original book value by the appropriate improvement factor.

     Set cell E12 equal to C12 ÷ .99.