Corporate Issuers formula sheet.

Where $t_c$ = corporate tax rate, $t_d$ = personal tax rate on dividends; assumes all after-tax profit is paid out and no tax credit.

Shows the total tax burden on corporate profit that reaches shareholders as dividends. Profit is taxed once at the company level, and what is left is taxed again in the owner's hands, which is why corporations face double taxation and pass-through forms do not.

Exam tip Do not just add the two rates: the dividend tax applies only to the $1 - t_c$ left after corporate tax (25% and 15% give 36.25%, not 40%).

Lesson: Corporate taxation and double taxation →All Organizational Forms, Corporate Issuer Features, and Ownership formulas

Where $r_d$ = pre-tax interest rate (cost) of the debt, $t$ = marginal corporate tax rate.

Interest is tax deductible, so the issuer's true cost of borrowing is below the rate it pays. This is the input for debt in WACC and one reason debt is cheaper than equity for the issuer.

Exam tip Use the current market yield on the company's debt as $r_d$ rather than an old coupon, and never apply the $(1 - t)$ adjustment to the cost of equity or preferred stock.

Lesson: Debt and equity: two different claims →All Investors and Other Stakeholders formulas

Where DOH = days of inventory on hand, DSO = days sales outstanding, DPO = days payable outstanding; all in days.

The number of days between paying suppliers and collecting cash from customers, so the time the company must finance its operations. A shorter cycle means less cash tied up in working capital and a stronger liquidity position.

Exam tip Payables days are subtracted: stretching payments to suppliers shortens the cycle, while slower collections or more inventory lengthen it.

Lesson: The operating cycle and the cash conversion cycle →All Working Capital and Liquidity formulas

Where DSO = days sales outstanding, DOH = days of inventory on hand, DPO = days payable outstanding, COGS = cost of goods sold.

Each measure divides a balance by one day's worth of its related flow, turning it into days. They are the building blocks of the cash conversion cycle and show how a change in credit, inventory or payment policy ties up or releases cash.

Exam tip Match the balance to its flow: receivables go with sales, inventory and payables go with COGS; dividing payables by sales is a classic distractor.

Lesson: The operating cycle and the cash conversion cycle →All Working Capital and Liquidity formulas

Where Discount = early-payment discount as a decimal; Net period = days until full payment is due; Discount period = days within which the discount applies.

The effective annual cost of skipping the supplier's discount and paying at the end of the net period. Compare it with the company's short-term borrowing rate: if it is higher, borrow and take the discount.

Exam tip The exponent uses only the extra days gained, net minus discount period (20 days for 2/10 net 30, giving about 44.6%), not the full 30 days.

Lesson: Shortening the cycle and the cost of trade credit →All Working Capital and Liquidity formulas

Where Numerator = the most liquid current assets; denominator = all current liabilities.

A stricter liquidity test than the current ratio because it leaves out inventory and other less liquid current assets. A higher value means short-term obligations can be met without relying on selling inventory.

Exam tip Inventory is excluded from the quick ratio; the cash ratio goes further and also drops receivables, so cash ratio $\le$ quick ratio $\le$ current ratio.

Lesson: Drags, pulls and liquidity ratios →All Working Capital and Liquidity formulas

Where $CF_t$ = expected after-tax incremental cash flow at time $t$ ($CF_0$ usually the negative outlay), $r$ = required return for the project's risk, $T$ = life.

The value a project adds for shareholders today. Accept independent projects with positive NPV; when projects are mutually exclusive, choose the highest positive NPV, since NPV is the preferred rule when it conflicts with IRR.

Exam tip Use incremental after-tax cash flows only: ignore sunk costs and financing costs (they are in $r$), but include opportunity costs and cannibalisation.

Lesson: The capital allocation process and NPV →All Capital Investments and Capital Allocation formulas

Where $CF_t$ = project cash flow at time $t$, $IRR$ = the discount rate that sets NPV to zero.

The project's own rate of return. Accept when the IRR exceeds the required return (hurdle rate). IRR and NPV agree on independent conventional projects but can rank mutually exclusive projects differently because of scale or timing.

Exam tip IRR assumes reinvestment at the IRR while NPV assumes reinvestment at $r$; unconventional cash flows (sign changes) can give multiple or no IRRs.

Lesson: IRR, and choosing between IRR and NPV →All Capital Investments and Capital Allocation formulas

Where Operating profit = profit before interest and taxes; average invested capital = average of opening and closing long-term liabilities plus equity.

Measures how well the company turns the capital supplied by all long-term investors into after-tax operating profit. ROIC above the cost of capital means value is being created; below it, value is being destroyed.

Exam tip Use after-tax operating profit (not net income) and average long-term capital; short-term liabilities are excluded from the denominator.

Lesson: Return on invested capital (ROIC) →All Capital Investments and Capital Allocation formulas

Where NPV (without options) = NPV of the base project; Option cost = what it costs to obtain the flexibility; Option value = value of that flexibility.

Real options (timing, abandonment, expansion, flexibility) give management the right, not the obligation, to change a project later. A project with a negative base NPV can still be worth doing if the option is worth more than it costs.

Exam tip Rearrange to back out the option value when you are given the NPV with and without the option and the option cost.

Lesson: Real options →All Capital Investments and Capital Allocation formulas

Where $w_d$, $w_e$ = weights of debt and equity (market or target), $r_d$ = pre-tax cost of debt, $t$ = marginal tax rate, $r_e$ = cost of equity.

The minimum return the company must earn on average-risk investments to satisfy all capital providers, and the discount rate for projects with the same risk as the firm. Add $w_p r_p$ when preferred stock is in the capital structure.

Exam tip Use market-value or target weights, not book values, and adjust only the cost of debt for tax.

Lesson: The cost of capital and WACC →All Capital Structure formulas

Where $r_e$ = cost of equity of the levered firm, $r_0$ = cost of capital of the all-equity firm, $r_d$ = cost of debt, $D/E$ = debt-to-equity ratio at market values.

In perfect markets without taxes, the cost of equity rises linearly with leverage because shareholders bear more financial risk. The benefit of cheaper debt is exactly offset, so WACC stays at $r_0$ and firm value is unchanged (Proposition I: $V_L = V_U$).

Exam tip Without taxes, WACC equals $r_0$ at every level of debt; only the split between debt and equity costs changes.

Lesson: Modigliani-Miller without taxes: capital structure irrelevance →All Capital Structure formulas

Where $V_L$, $V_U$ = value of the levered and unlevered firm, $t$ = marginal corporate tax rate, $D$ = value of (permanent) debt.

With corporate taxes, interest deductibility creates a tax shield worth $tD$, so firm value rises with debt. Taken alone, the model implies an all-debt capital structure, which is why financial distress costs are added in the trade-off theory.

Exam tip $tD$ is the present value of the tax shield on permanent debt; the annual saving is $t \times r_d \times D$.

Lesson: Modigliani-Miller with taxes, and the cost of financial distress →All Capital Structure formulas

Where $r_e$ = levered cost of equity, $r_0$ = unlevered cost of capital, $r_d$ = cost of debt, $t$ = tax rate, $D/E$ = debt-to-equity ratio.

The cost of equity still rises with leverage, but more slowly than without taxes because the slope is scaled by $(1 - t)$. As a result WACC falls as debt is added, consistent with firm value rising in Proposition I with taxes.

Exam tip The only difference from the no-tax version is the $(1 - t)$ factor on the slope; with taxes WACC declines with leverage instead of staying constant.

Lesson: Modigliani-Miller with taxes, and the cost of financial distress →All Capital Structure formulas

Where $tD$ = value of the debt tax shield, $PV$(costs of financial distress) = present value of expected direct and indirect distress costs.

Debt adds value through the tax shield but raises the expected cost of financial distress. The optimal capital structure is where the marginal tax benefit of debt equals the marginal expected distress cost, which is also where WACC is lowest and firm value is highest.

Exam tip Beyond the optimal debt level, extra debt lowers firm value and raises WACC; the optimum uses some debt, but not all debt.

Lesson: Optimal and target capital structures, pecking order and agency costs →All Capital Structure formulas

Where $F$ = fixed costs, $P$ = price per unit, $V$ = variable cost per unit, $P - V$ = contribution margin per unit.

The number of units at which revenue just covers fixed and variable costs. Business models with high fixed costs need a higher volume to break even but earn more per extra unit once past it.

Exam tip Divide fixed costs by the contribution margin per unit $P - V$, not by the price; volume above $Q_{BE}$ produces a profit.

Lesson: Value proposition, value chain and profitability →All Business Models formulas