MBA Formula Sheet Template (Finance, Accounting, Operations, Stats)

MBA Formula Sheet: [Programme, course or exam]

A one-document reference for the formulas of the MBA core: financial and managerial accounting, time value of money, capital budgeting, risk and the cost of capital, valuation, options, microeconomics and international finance, marketing metrics, operations and statistics. Every formula has an ID, KaTeX notation, a notation table, the matching Excel function or formula, a computed mini example and a note on the most common mistake. It is for admitted students preparing for the core, students revising for exams and graduates who want one place to look things up. Each formula was checked against two independent sources (the originating work or a standard textbook, plus a second textbook or official documentation), listed in the verification register in section 13. Source basis: the original papers named in each section (Sharpe 1964, Lintner 1965, Modigliani and Miller 1958 and 1963, Black and Scholes 1973, Merton 1973, Stoll 1969, Harris 1913, Arrow, Harris and Marschak 1951, Little 1961, Gupta, Lehmann and Stuart 2004 and others) and standard MBA textbooks named as further reading; all wording, notation choices and examples are original. Replace every [bracketed] value and every row marked Example. The companies are fictional: Northfield Outdoor Co., Corvane Robotics and Tallow Creek Medical Center.

Document control

Contents

1. Conventions and notation
2. Financial accounting and ratios
3. Managerial accounting and break-even
4. Time value of money
5. Capital budgeting
6. Risk, return and the cost of capital
7. Valuation
8. Options
9. Economics and international finance
10. Marketing metrics
11. Operations
12. Statistics and regression
13. Verification register
14. Choosing the right formula
15. Self-test

1. Conventions and notation

Throughout, $N(\cdot)$ is the standard normal cumulative distribution function (NORM.S.DIST(x, TRUE)) and $N^{-1}(\cdot)$ its inverse (NORM.S.INV(p)).

2. Financial accounting and ratios

F-01 Accounting equation. $\text{Assets} = \text{Liabilities} + \text{Equity}$. Every transaction keeps both sides equal (double entry, formalised by Pacioli in 1494).

F-02 DuPont decomposition of return on equity (developed in practice at the DuPont company in the early twentieth century):

F-03 Return on assets. $\text{ROA} = NI / A$. Some courses use $EBIT(1 - t)/A$ to remove the effect of financing; state which one you use.

F-04 Liquidity. $\text{Current ratio} = CA / CL$; $\text{Quick ratio} = (CA - \text{Inventory}) / CL$.

F-05 Working capital days and the cash conversion cycle.

F-06 Solvency. $\text{Interest coverage} = EBIT / \text{Interest expense}$; $\text{Debt-to-equity} = D / E$.

Mini example (Example, Northfield Outdoor Co., USD m). Sales 820, COGS 492, EBIT 82, interest 9, tax rate 25%, so pre-tax profit 73 and net income 54.75. Assets 640, equity 300, debt 180, current assets 210 (of which inventory 120), current liabilities 140, receivables 25, payables 60.

Read it: Northfield's ROE comes mostly from turnover and leverage, not margin; inventory days (89) dominate the cash cycle, which is typical for a seasonal outdoor retailer. As of October 2026, IFRS 18 (replacing IAS 1) applies to annual reporting periods beginning on or after 1 January 2027 and requires an operating profit subtotal in the statement of profit or loss; operating profit under IFRS 18 is not always equal to the EBIT your course uses, so check its definition (mba/mba-three-statements-card) and the standard on https://www.ifrs.org before you rely on it.

3. Managerial accounting and break-even

F-07 Contribution margin. $CM = P - V$ per unit; $CMR = (P - V)/P$.

F-08 Break-even and target profit.

F-09 Margin of safety and operating leverage.

Mini example (Example, Northfield tent line). $P = 250$, $V = 150$, $F = \text{USD }1{,}200{,}000$, planned volume 16,000 units.

A DOL of 4.0 means a 10% fall in volume cuts operating profit by about 40% at this volume.

4. Time value of money

F-10 Future and present value of a single sum. $FV = PV(1 + r)^n$; $PV = FV/(1 + r)^n$.

F-11 Effective annual rate. $EAR = (1 + \text{APR}/m)^m - 1$; with continuous compounding $EAR = e^{\text{APR}} - 1$ and $FV = PV\,e^{rT}$.

F-12 Ordinary annuity (equal payment $C$ at the end of each of $n$ periods):

F-13 Growing annuity (first payment $C_1$ at $t = 1$, growth $g$, $r \neq g$):

F-14 Perpetuity and growing perpetuity. $PV = C/r$; $PV = C_1/(r - g)$ for $r > g$.

F-15 Loan payment. $C = PV \cdot \dfrac{r}{1 - (1 + r)^{-n}}$.

Mini examples (Example).

5. Capital budgeting

F-16 Net present value. $NPV = \sum_{t=0}^{n} \dfrac{CF_t}{(1 + r)^t}$. Accept independent projects with $NPV > 0$.

F-17 Internal rate of return. The rate $IRR$ that solves $\sum_{t=0}^{n} CF_t/(1 + IRR)^t = 0$.

F-18 Payback period. The time until cumulative undiscounted cash flow turns non-negative; interpolate within the year: $\text{Payback} = (k - 1) + \dfrac{-\text{Cum}_{k-1}}{CF_k}$, where $k$ is the first year with non-negative cumulative cash flow.

F-19 Profitability index. $PI = PV(\text{future cash flows}) / |CF_0|$.

F-20 Equivalent annual annuity (to compare projects with different lives): $EAA = NPV \cdot \dfrac{r}{1 - (1 + r)^{-n}}$.

Mini example (Example, Corvane Robotics new picking cell, USD k). $CF_0 = -1{,}000$, then 250, 300, 350, 300, 200 in years 1 to 5, $r = 10\%$.

The NPV profile below shows NPV falling as the discount rate rises and crossing zero at the IRR (12.64%).

6. Risk, return and the cost of capital

F-21 Two-asset portfolio (Markowitz 1952):

F-22 Beta. $\beta_i = \text{Cov}(R_i, R_m)/\text{Var}(R_m)$.

F-23 Capital asset pricing model (Sharpe 1964, Lintner 1965):

F-24 Weighted average cost of capital (after-tax):

F-25 Unlevering and relevering beta (Hamada 1972, debt beta zero, constant debt): $\beta_U = \dfrac{\beta_L}{1 + (1 - t_c)D/E}$ and $\beta_L = \beta_U\left[1 + (1 - t_c)D/E\right]$.

F-26 Modigliani and Miller. Without taxes (1958): $V_L = V_U$ and $r_E = r_A + \dfrac{D}{E}(r_A - r_D)$. With corporate taxes (1963) and permanent debt: $V_L = V_U + t_c D$ and $r_E = r_U + \dfrac{D}{E}(1 - t_c)(r_U - r_D)$.

Mini examples (Example, Corvane Robotics).

7. Valuation

F-27 Free cash flow to the firm. $FCFF = EBIT(1 - t_c) + \text{D\&A} - \text{CapEx} - \Delta NWC$.

F-28 Enterprise value by DCF with a Gordon growth terminal value (Williams 1938, Gordon 1959):

F-29 Equity bridge. $\text{Equity value} = EV - \text{Net debt}$ (net debt = debt minus cash, plus other claims such as preferred stock and minority interests where present); value per share = equity value / diluted shares.

F-30 Dividend discount model (constant growth). $P_0 = \dfrac{D_1}{r_E - g}$.

Mini example (Example, Corvane Robotics, USD m). FCFF for years 1 to 5: 80, 95, 105, 115, 120; WACC 9%; $g$ = 3%; net debt 300; 50 million diluted shares.

8. Options

F-31 Payoffs at expiry. Call: $\max(S_T - K, 0)$. Put: $\max(K - S_T, 0)$.

F-32 Put-call parity (Stoll 1969; European options, no dividends):

F-33 Black-Scholes (Black and Scholes 1973, Merton 1973):

Mini example (Example). $S_0$ = 50, $K$ = 48, $r$ = 4%, $T$ = 0.5, $\sigma$ = 30%.

9. Economics and international finance

F-34 Price elasticity of demand (Marshall 1890). Point: $\varepsilon = \dfrac{dQ}{dP}\cdot\dfrac{P}{Q}$. Midpoint (arc):

F-35 Profit-maximising markup (Lerner 1934). With constant elasticity $\varepsilon < -1$:

F-36 Fisher relation (Fisher 1930). $(1 + i) = (1 + r_{\text{real}})(1 + \pi)$; approximately $i \approx r_{\text{real}} + \pi$.

F-37 Covered interest parity. With $S$ and $F$ quoted as domestic currency per unit of foreign currency:

Mini examples (Example).

10. Marketing metrics

F-38 Customer lifetime value (constant margin and retention, infinite horizon; Gupta, Lehmann and Stuart 2004 form, margins received at the end of each period the customer is retained):

If the first margin is received immediately at acquisition, $CLV = m\cdot\dfrac{1 + i}{1 + i - \rho}$.

F-39 Expected customer lifetime. $\dfrac{1}{1 - \rho}$ periods.

F-40 Customer value net of acquisition. $CLV - AC$; spend on acquisition only while this is positive.

Mini example (Example, Northfield loyalty members). $m$ = 120 a year, $\rho$ = 0.8, $i$ = 10%, $AC$ = 150.

11. Operations

F-41 Economic order quantity (Harris 1913):

F-42 Reorder point with safety stock (normal daily demand, fixed lead time): $ROP = \bar{d}L + z\,\sigma_d\sqrt{L}$, with $z = N^{-1}(\text{cycle service level})$.

F-43 Newsvendor critical ratio (Arrow, Harris and Marschak 1951):

F-44 Little's Law (Little 1961): $L = \lambda W$, for any stable system in the long run.

F-45 M/M/1 queue (Kendall 1953 notation; Poisson arrivals, exponential service, one server, $\rho < 1$):

Mini examples (Example).

Queue length explodes as utilisation approaches 1, which is why a "fully utilised" service desk is a long-wait desk:

12. Statistics and regression

F-46 Sample mean and standard deviation. $\bar{x} = \frac{1}{n}\sum x_i$; $s = \sqrt{\frac{1}{n - 1}\sum (x_i - \bar{x})^2}$.

F-47 Standard error and confidence interval for a mean. $SE = s/\sqrt{n}$; $\bar{x} \pm t_{0.975,\,n-1}\,SE$.

F-48 One-sample t-test (Student 1908): $t = \dfrac{\bar{x} - \mu_0}{s/\sqrt{n}}$, $df = n - 1$.

F-49 Simple linear regression by least squares (Legendre 1805, Gauss 1809):

F-50 Bayes' rule (Bayes 1763): $P(A \mid B) = \dfrac{P(B \mid A)P(A)}{P(B)}$.

Mini examples (Example).

The t-test does not reject $\mu_0$ = 50 at the 5% level; the interval shows the plausible range of the mean basket. The regression slope says each extra USD 1k of local advertising is associated with about USD 3.3k more sales in this sample of eight stores; it is an association, not a causal estimate, and the prediction at 30 lies outside the observed range of $x$ (an extrapolation).

13. Verification register

Each formula was compared with two independent sources: (1) the originating work or a standard corporate finance, operations or economics text, and (2) a second textbook or the official Microsoft Excel function documentation. Every mini example was recomputed in Python (numpy 2.5, numpy-financial 1.1, scipy 1.18) and the key Excel formulas evaluated with a spreadsheet engine; results matched to the decimals shown.

14. Choosing the right formula

Start from the decision the question asks you to support, not from the numbers given. A question that gives cash flows over several years is a time-value question even if it also mentions risk; a question about a single selling season with uncertain demand is a newsvendor question even if it mentions margins. The flow below routes the most common core-course question types to the formula IDs on this sheet.

15. Self-test

1. Excel returns 67.26 for =NPV(0.1,B2:B6)+B1 but your classmate's =NPV(0.1,B1:B6) returns 61.14. Which is right and why?
2. A bank quotes 9% APR compounded monthly. What is the effective annual rate?
3. Corvane's levered beta is 1.3 at $D/E$ = 1/3 with a 25% tax rate. What is its beta at $D/E$ = 0.5?
4. Why does the WACC multiply the cost of debt by $(1 - t_c)$ but not the cost of equity?
5. In the DCF example, what happens to enterprise value if $g$ rises from 3% to 4% (other inputs unchanged)? Give the new terminal value and EV.
6. A call and a put on the same stock both have $K$ = 48 and $T$ = 0.5; $S_0$ = 50 and $r$ = 4%. The call trades at 6.20 and the put at 2.79. Is put-call parity violated, and in which direction?
7. A retailer cuts price from 40 to 36 and units rise from 1,000 to 1,080. Compute the midpoint elasticity. Did revenue rise or fall?
8. With $m$ = 120, $\rho$ = 0.8 and $i$ = 10%, what retention rate would raise CLV (end-of-period convention) to 480?
9. The triage desk's arrival rate rises from 10 to 11 an hour with $\mu$ = 12. What is the new average wait in the queue in minutes?
10. In the newsvendor example, salvage value drops from 15 to 0. Does the optimal order rise or fall, and why?

My notes and next steps

Sources and further reading

• Arrow, K. J., Harris, T., and Marschak, J. (1951). Optimal inventory policy. Econometrica, 19(3), 250-272.
• Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, 53, 370-418.
• Black, F., and Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637-654.
• Fisher, I. (1930). The Theory of Interest. Macmillan.
• Gordon, M. J. (1959). Dividends, earnings, and stock prices. Review of Economics and Statistics, 41(2), 99-105.
• Gupta, S., Lehmann, D. R., and Stuart, J. A. (2004). Valuing customers. Journal of Marketing Research, 41(1), 7-18.
• Hamada, R. S. (1972). The effect of the firm's capital structure on the systematic risk of common stocks. Journal of Finance, 27(2), 435-452.
• Harris, F. W. (1913). How many parts to make at once. Factory, The Magazine of Management, 10(2), 135-136, 152.
• Kendall, D. G. (1953). Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain. Annals of Mathematical Statistics, 24(3), 338-354.
• Lerner, A. P. (1934). The concept of monopoly and the measurement of monopoly power. Review of Economic Studies, 1(3), 157-175.
• Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics, 47(1), 13-37.
• Little, J. D. C. (1961). A proof for the queuing formula: L = λW. Operations Research, 9(3), 383-387.
• Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7(1), 77-91.
• Marshall, A. (1890). Principles of Economics. Macmillan.
• Merton, R. C. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science, 4(1), 141-183.
• Modigliani, F., and Miller, M. H. (1958). The cost of capital, corporation finance and the theory of investment. American Economic Review, 48(3), 261-297.
• Modigliani, F., and Miller, M. H. (1963). Corporate income taxes and the cost of capital: a correction. American Economic Review, 53(3), 433-443.
• Sharpe, W. F. (1964). Capital asset prices: a theory of market equilibrium under conditions of risk. Journal of Finance, 19(3), 425-442.
• Stoll, H. R. (1969). The relationship between put and call option prices. Journal of Finance, 24(5), 801-824.
• Student (1908). The probable error of a mean. Biometrika, 6(1), 1-25.
• Williams, J. B. (1938). The Theory of Investment Value. Harvard University Press.
• Microsoft Support. NPV function, https://support.microsoft.com/en-us/excel/functions/npv-function, and Excel functions (by category), https://support.microsoft.com/en-us/excel/excel-functions-by-category (accessed 2026-10-28).
• NIST/SEMATECH e-Handbook of Statistical Methods, https://www.itl.nist.gov/div898/handbook/ (accessed 2026-10-28). Public domain.
• OpenStax (free; CC BY 4.0 or CC BY-NC-SA 4.0 by title): Principles of Accounting, Volumes 1 and 2; Principles of Economics; Introductory Statistics, https://openstax.org/.
• Further reading (by name only): Berk and DeMarzo, Corporate Finance; Brealey, Myers and Allen, Principles of Corporate Finance; Koller, Goedhart and Wessels, Valuation; Hull, Options, Futures, and Other Derivatives; Bodie, Kane and Marcus, Investments; Pindyck and Rubinfeld, Microeconomics; Cachon and Terwiesch, Matching Supply with Demand; Hillier and Lieberman, Introduction to Operations Research; Farris, Bendle, Pfeifer and Reibstein, Marketing Metrics.

Answer key

1. 67.26 is right. Excel's NPV discounts the first value in the range by one period, so including $CF_0$ inside the function discounts the investment a year too: $67.26/1.1 = 61.14$.
2. $(1 + 0.09/12)^{12} - 1 = 9.38\%$ (=EFFECT(0.09,12)).
3. $\beta_U = 1.3/1.25 = 1.04$; $\beta_L = 1.04 \times (1 + 0.75 \times 0.5) = 1.43$.
4. Interest is tax-deductible, so the firm's after-tax cost of debt is lower; dividends to shareholders are not deductible, so the cost of equity has no tax adjustment.
5. $TV_5 = 120 \times 1.04/0.05 = 2{,}496.00$; PV of TV $= 2{,}496/1.09^5 = 1{,}622.23$; EV $= 393.89 + 1{,}622.23 = 2{,}016.12$, an increase of about 16% from one point of growth.
6. Parity requires $C - P = 2.9505$; the market gives $6.20 - 2.79 = 3.41$. The call is rich relative to the put: sell the call, buy the put and the stock, borrow the present value of $K$ (before transaction costs).
7. $\%\Delta Q = 80/1040 = 7.69\%$, $\%\Delta P = -4/38 = -10.53\%$, elasticity $= -0.73$ (inelastic). Revenue fell from 40,000 to 38,880.
8. Solve $120\rho/(1.1 - \rho) = 480$: $120\rho = 528 - 480\rho$, so $\rho = 528/600 = 0.88$.
9. $\rho = 11/12 = 0.9167$, $L_q = 0.9167^2/0.0833 = 10.08$, $W_q = 10.08/11 = 0.9167$ h, about 55 minutes (up from 25).
10. It falls. $C_o$ rises to 35, so $CR = 45/80 = 0.5625$, $z = 0.157$ and $Q^* \approx 1{,}031.46$: each unsold unit now costs more, so the retailer orders less.

Revision history

Standard and licence note

Based on general financial mathematics, managerial economics, operations management and statistics as taught across MBA core courses, with attribution to the original works listed above; no single standard governs these formulas. The explanations, notation choices, worked examples and layout are original; no textbook text, published case or exam question is reproduced. The template is not affiliated with or endorsed by any business school, publisher or exam body. Check your own course materials for the notation and conventions they require. Template licence: MIT.