Income Statement

• NOI = S*(1 - vc/s) - FC
• NIAT = (NOI - I)*(1-t)

• TA = D + E

• CFO = NIAT + Dep
• CFC = [NOI + Dep]/[I + DS/(1-t)]

• PM = NOI/S
• TAU = S/TA
• ROI = NOI/TA
• Note that ROI = PM * TAU

• ROE = NIAT/E
• i = I/D
• Note that ROE = [ROI + (D/E)*(ROI-i)]*(1-t)

• DOL = (NOI + FC)/NOI
• DFL = NOI/(NOI - I)

• p = exp (-x)
• where x = 0.711+0.707d*(1+0.416d)

• Income Stmt = matches costs to revenue in corresponding time periods.
• Balance sheet = Distribution of claims on assets.
• Cash flows = actual funds flowing to and from our checking account.
• PM [profit margin] = our ability to control costs = measured by the amount of operating income per dollar of sales.
• TAU [total asset utilization ratio] = our ability to use assets to generate sales = measured by the amount of sales generated per dollar of assets.
• ROI [return on assets] = bottom line of our operations that assesses whether it is a good business to be in = the amount of operating income generated per dollar of assets.
• i [little eye] = net cost of borrowed funds = measured as a percentage.
• ROE [return on equity] = the bottom line of the business enterprise that measures our ability to increase the wealth of the owners = measured as the amount of net income made available to our shareholders per dollar of their investment.
• DOL [degree of operating leverage] = the sensitivity of operating income to fluctuations in sales = the percentage change in NOI caused by a one percent change in sales = a measure of risk inherent in our operations = caused by fixed costs in our cost structure.
• DFL[degree of financial leverage] = the sensitivity of net income to fluctuations in operating income = the percentage change in NIAT caused by a one percent change in NOI = additional risk induced by the use of borrowed funds = caused by fixed financial charges due to our capital structure.
• FFL [favorable financial leverage] = when ROI is greater than i debt can be used to leverage (increase) ROE beyond ROI*(1-t).
• UFL [unfavorable financial leverage] = when ROI is less than i increased use of debt decreases ROE.
• DuPont analysis of operating decisions: ROI is partitioned into two multiplicative components - that which can be ascribed to our ability to control costs and that affected by our ability to use assets to generate sales. It is an analytical tool and not a computational tool.
• DuPont analysis of financial decisions: ROE is partitioned into two additive components - that which can be ascribed to operations and an additional component due to financial leverage. It is an analytical tool and not a computational tool.

Derivation of equations

• DOL = [dNOI/NOI]/[dS/S]
• = [dNOI/dS] * [S/NOI]
• = (1-vc/s)*S/NOI
• = (NOI+FC)/NOI

• DFL = [dNIAT/NIAT]/[dNOI/NOI]
• = [dNIAT/dNOI]*[NOI/NIAT]
• = (1-t)*NOI/NIAT
• = [(1-t)*NOI]/[(1-t)*(NOI-I)]
• = NOI/(NOI-I)

• ROE = NIAT/E
• = (1-t)*(NOI-I)/E
• = (1-t)*(ROI*TA - I)/E
• = (1-t)*(ROI*(D+E) - I)/E
• = (1-t)*(ROI*D + ROI*E - I)/E
• = (1-t)*(ROI*D + ROI*E - i*D)/E
• = (1-t)*(ROI*D/E + ROI*E/E - i*D/E)
• = (1-t)*[ROI + (D/E)*(ROI-i)]