Pre-MBA Finance Primer Template

Pre-MBA Finance Primer: [Your name and start date]

A primer in the finance every MBA core course assumes: the time value of money, compounding and effective rates, annuities and perpetuities, net present value and internal rate of return, and the basics of risk and return (expected return, standard deviation, correlation, diversification, the Sharpe ratio and a first look at beta). It is for admitted and prospective MBA students, especially those without a finance or economics degree. Each idea is shown as a formula with a notation table, an Excel function and a computed example, followed by a half-solved example, an exercise, common mistakes and a self-test with an answer key. Source basis: Fisher (1930), Williams (1938), Markowitz (1952), Gordon (1959), Sharpe (1964, 1966) and Lintner (1965), plus Microsoft Excel function documentation, all explained in original words. The companies and figures are fictional (Corvane Robotics). Replace every [bracketed] value and every row marked Example when you reuse the worksheets. This is a learning aid, not investment or financial advice.

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Why finance starts with time and risk

Every valuation in an MBA, from a capital budgeting decision to a company's share price to the value of the degree itself, rests on two ideas. First, money has a time value: a dollar today can be invested and becomes more than a dollar later, so cash flows at different dates cannot be added directly. Second, risk has a price: investors demand a higher expected return for bearing risk they cannot diversify away. The first idea gives present value, NPV and IRR; the second gives the discount rate. The corporate finance core (mba/mba-corporate-finance-guide) builds on both within its first sessions, so a student who already computes present values fluently can focus on judgement: which cash flows, which rate, which risks.

Throughout, a timeline is the first tool. Draw time 0 (today), 1, 2 and so on, put each cash flow under its date with a sign (outflow negative, inflow positive), then choose the formula.

Single sums: future value and present value

Compounding moves a value forward in time; discounting moves it back.

The rule of 72 approximates the doubling time as 72 divided by the percentage rate: $72/7=10.29$ years, close to the exact 10.24. It is a sanity check, not a substitute for the formula.

Excel's argument order is FV(rate, nper, pmt, [pv], [type]) and PV(rate, nper, pmt, [fv], [type]). The pmt argument is 0 for single sums; type is 0 (end of period, the default) or 1 (beginning of period).

Compounding frequency and effective rates

A rate quoted as "12% compounded monthly" is an annual percentage rate (APR) of 12% split into twelve monthly rates of 1%. The effective annual rate (EAR) is the rate that, compounded once a year, gives the same result:

Excel: =EFFECT(12%,12) returns 12.6825%, and =NOMINAL(12.6825%,12) converts back to 12%. Always match the rate to the period of the cash flows: monthly payments need a monthly rate (6%/12) and a number of months.

Real and nominal rates. Fisher (1930) related the nominal rate $i$, the real rate $r$ and inflation $\pi$: $(1+i)=(1+r)(1+\pi)$. At a 7% nominal rate and 3% inflation, the real rate is $1.07/1.03-1=3.88\%$ (the shortcut $7\%-3\%=4\%$ is close only when rates are low). Discount nominal cash flows at nominal rates and real cash flows at real rates; mixing them is a classic valuation error.

Annuities: loans, savings and salaries

The present and future values of an ordinary annuity of $C$ per period are

and an annuity due is worth $(1+r)$ times the ordinary annuity, because each payment arrives one period earlier.

Loan amortisation. Each payment covers the interest on the opening balance and repays the rest of the principal.

=IPMT(6%/12,1,60,-30000) and =PPMT(6%/12,1,60,-30000) return the interest (150.00) and principal (429.98) of month

1. The interest share falls each month because the balance falls.

Growing annuities. If the first payment $C$ grows at rate $g$ each period for $n$ periods,

Example: an applicant expects the MBA to raise annual pay by 40,000 in the first year after graduation, growing 3% a year for 20 years, and discounts at 8%. The present value of the uplift, measured at the start of the first working year, is 490,001.66. In Excel, list the 20 amounts in a row (=40000*(1+3%)^(t-1)) and use =NPV(8%,range), which returns the same value. The decision itself (costs, forgone salary, risk) belongs in mba/mba-decision-roi.

Perpetuities

The growing-perpetuity formula is the basis of the dividend discount model associated with Williams (1938) and Gordon (1959), and of the terminal value in mba/mba-dcf-valuation-card.

The third line shows the delayed-perpetuity trick: the perpetuity formula values the stream one period before its first payment (at year 3), so discount that value back three years. In Excel: =5000/8%/(1+8%)^3.

NPV and IRR: Worked example A (fully solved)

Net present value adds the present values of all cash flows, including the initial outlay:

NPV rule. Accept independent projects with NPV above zero; among mutually exclusive projects, choose the highest NPV. A positive NPV means the project earns more than investors could earn elsewhere at the same risk, and the NPV is the value it adds today.

Situation (Example, fictional). Corvane Robotics is considering a pick-station upgrade for a customer site. It costs 1,200 (USD thousands) today and is expected to produce after-tax cash flows of 300, 400, 450, 400 and 300 in years 1 to 5. Corvane's cost of capital for projects of this risk is 10%.

With the year 0 flow in B2 and years 1 to 5 in C2:G2:

The discounted payback divides the remaining discounted shortfall after year 3 (258.60) by the year 4 discounted cash flow ($400/1.1^{4}=273.21$).

The NPV profile plots NPV against the discount rate. It crosses zero at the IRR.

Irregular dates. When cash flows do not fall at regular intervals, use XNPV and XIRR, which discount each flow by the actual number of days divided by 365 from the first date. Example: -500 on 15 January 2027, 150 on 30 September 2027, 220 on 30 June 2028 and 260 on 31 March 2029 (258, 532 and 806 days after the first date). With the amounts in B2:B5 and the dates in C2:C5, =XNPV(10%,B2:B5,C2:C5) returns 42.35 and =XIRR(B2:B5,C2:C5) returns 15.94%. Unlike NPV, XNPV discounts from the first date, so the first flow is not discounted.

Limits of IRR. IRR can mislead when (1) cash flow signs change more than once, so there may be several IRRs or none; (2) projects are mutually exclusive and differ in scale or timing, so the higher IRR can belong to the lower NPV (Exercise C); (3) the cost of capital changes over time, so there is no single hurdle to compare with. NPV has none of these problems, which is why the core course treats NPV as the decision rule and IRR as a communication aid. The deeper treatment is in mba/mba-npv-irr-card.

Worked example B (half solved): an equal-payment project

Situation (Example). Corvane can automate a test bench for 800 (USD thousands) today. Savings are 250 a year at the end of each of the next 4 years. The cost of capital is 9%.

Risk and return basics

Returns. The holding-period return of an asset bought at $P_0$, sold at $P_1$, with income $D$ received, is $R=(P_1-P_0+D)/P_0$.

Expected return and risk from scenarios. With probabilities $p_s$ for each scenario $s$,

Example (fictional funds, one-year horizon):

Excel, with probabilities in B2:B4 and stock returns in C2:C4: expected return =SUMPRODUCT(B2:B4,C2:C4) gives 8.75%; standard deviation =SQRT(SUMPRODUCT(B2:B4,(C2:C4-F2)^2)) with the expected return in F2 gives 15.96%. The covariance is $\sum_s p_s (R_{S,s}-E[R_S])(R_{B,s}-E[R_B]) = -0.00325$ and the correlation is $-0.00325/(0.1596 \times 0.0235) = -0.87$: the bond fund tends to do well when the stock fund does badly.

Portfolios (Markowitz 1952). For weights $w$ in the stock fund and $1-w$ in the bond fund,

The expected return is a weighted average; the risk is not, unless the correlation is exactly 1. With a correlation of -0.87 the mix is much less risky than either fund's weighted average risk.

The minimum-variance mix holds about 11.7% in the stock fund, with an expected return of 4.56% and a standard deviation of 1.03%: adding a small amount of the risky stock fund reduces risk below that of the bond fund alone.

Estimating from history. With six annual returns for a fictional share (22%, -3%, 15%, 11%, -14%, 18%) in B2:B7 and a market index (12%, -4%, 17%, 7%, -8%, 14%) in C2:C7:

The geometric mean (the compound annual growth rate actually earned) is below the arithmetic mean whenever returns vary; use the geometric mean to describe past growth and the arithmetic mean as an estimate of a single future year's expected return. Six observations are far too few for reliable estimates; the example shows the mechanics only. In older Excel versions enter the GEOMEAN formula as an array formula (Ctrl+Shift+Enter).

From total risk to market risk. Diversification removes the part of an asset's risk that is specific to it, so in equilibrium investors are rewarded only for the part that moves with the market, measured by beta. The capital asset pricing model (Sharpe 1964; Lintner 1965) states $E[R_i] = r_f + \beta_i\,(E[R_M]-r_f)$. With a risk-free rate of 4%, a beta of 1.2 and a market risk premium of 5%, the required return is $4\% + 1.2 \times 5\% = 10\%$. The Sharpe ratio (Sharpe 1966) measures excess return per unit of total risk. Both are developed in mba/mba-capm-wacc-card.

Exercise C (unsolved): two mutually exclusive projects

Situation (Example). Corvane must choose one of two warehouse layouts (USD thousands, cost of capital 10%):

1. Compute the NPV and IRR of each layout, with the Excel formulas.
2. Which layout has the higher IRR, and which the higher NPV?
3. Compute the cash flows of "A minus B", and their NPV and IRR. What does the incremental IRR tell you?
4. Which layout should Corvane choose, and why?

Common mistakes and misconceptions

1. Excel NPV on the whole range. =NPV(r, CF0:CFT) discounts the time-0 flow by one period. Use =NPV(r, CF1:CFT)+CF0.
2. Sign convention. PV, FV and PMT return negative values when the inputs are positive, because Excel treats one side as cash paid and the other as cash received. Enter the loan or deposit as negative to get a positive answer.
3. Rate and period mismatch. Monthly payments need a monthly rate and the number of months; an annual rate with 60 periods gives nonsense.
4. Comparing APRs with different compounding. Convert both to effective annual rates first.
5. Mixing nominal and real. Discount nominal cash flows at a nominal rate and real cash flows at a real rate.
6. Ranking mutually exclusive projects by IRR. Use NPV; IRR ignores scale.
7. Using a growing perpetuity with $g \ge r$. The formula only works when growth is below the discount rate.
8. Delayed perpetuity discounted one period too many or too few. $C/r$ values the stream one period before its first payment.
9. Treating payback as a value measure. Payback ignores the time value of money (simple payback) and all flows after the cut-off.
10. Adding standard deviations. Portfolio risk depends on correlation; only expected returns average linearly.
11. Confusing arithmetic and geometric means when describing past performance.

Self-test

1. What is 5,000 worth after 10 years at 5% a year, compounded annually?
2. What is the effective annual rate of 8% compounded quarterly?
3. What is the monthly payment on a 45,000 loan at 7% APR over 36 months, and the total interest paid?
4. What is the present value of 2,000 a year forever at 5%, first payment in one year? And if the payment grows 2% a year?
5. A colleague computes =NPV(10%,B2:G2) for the Corvane project with the year 0 outlay in B2 and gets 182.62. What is wrong, and what is the correct value?
6. Why can IRR and NPV rank two mutually exclusive projects differently?
7. A stock returns 20%, 8% or -10% with probabilities 0.3, 0.5 and 0.2. What is its expected return?
8. Two assets each have a standard deviation of 20% and a correlation of exactly 1. What is the standard deviation of a 50/50 portfolio? What if the correlation is below 1?
9. The nominal rate is 6% and inflation 2.5%. What is the real rate (exact Fisher relation)?
10. Why is the NPV rule preferred to payback?

My notes and next steps

Sources and further reading

• Fisher, I. (1930). The Theory of Interest. Macmillan.
• Williams, J. B. (1938). The Theory of Investment Value. Harvard University Press.
• Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7(1), 77-91.
• Gordon, M. J. (1959). Dividends, earnings, and stock prices. Review of Economics and Statistics, 41(2), 99-105.
• Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19(3), 425-442.
• 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.
• Sharpe, W. F. (1966). Mutual fund performance. Journal of Business, 39(1), 119-138.
• Microsoft Support. FV, PV, PMT, IPMT, PPMT, RATE, NPER, EFFECT, NOMINAL, NPV, IRR, MIRR, XNPV, XIRR, STDEV.S, COVARIANCE.S, CORREL and SLOPE functions, support.microsoft.com (accessed 2026-10-28).
• Open resource: OpenStax, Principles of Finance (CC BY-NC-SA 4.0), openstax.org.
• Further reading (by name only): Berk and DeMarzo, Corporate Finance; Brealey, Myers and Allen, Principles of Corporate Finance; Bodie, Kane and Marcus, Investments.

Answer key

Worked example B. (3) $NPV = 809.93 - 800 = 9.93$. (4) =NPV(9%,C2:F2)+B2 with the savings in C2:F2 and -800 in B2, result 9.93. (5) =IRR(B2:F2) returns 9.56%. (6) Accept: the NPV is positive (the IRR of 9.56% exceeds the 9% cost of capital), although the margin is thin, so test the savings estimate. (7) =PMT(9%,4,-800) returns 246.93: the project breaks even with savings of about 246.93 a year, only 1.2% below the forecast.

Exercise C. (1) Layout A: =NPV(10%,C2:E2)+B2 gives 108.94, =IRR(B2:E2) gives 17.21%. Layout B: NPV 46.73, IRR 18.09%. (2) B has the higher IRR; A has the higher NPV. (3) A minus B: -600, 340, 300, 140; NPV 62.21, IRR 16.67%. The extra 600 invested in A earns 16.67%, above the 10% cost of capital, so the extra investment is worth making. (4) Choose A: it adds 108.94 of value against 46.73 for B. B's higher IRR reflects its smaller scale, not more value.

Self-test.

1. =FV(5%,10,0,-5000) returns 8,144.47.
2. =EFFECT(8%,4) returns 8.2432%.
3. =PMT(7%/12,36,-45000) returns 1,389.47 a month; total interest $1{,}389.47 \times 36 - 45{,}000 = 5{,}020.90$ (computed on the unrounded payment).
4. $2{,}000/0.05 = 40{,}000$; growing at 2%, $2{,}000/(0.05-0.02) = 66{,}666.67$.
5. The range includes the year 0 outlay, so every flow is discounted one period too many; 182.62 is the true NPV divided by 1.10. Correct: =NPV(10%,C2:G2)+B2 = 200.88.
6. IRR is a rate, not an amount: it ignores scale and treats timing differently (the IRR ranking depends on where the NPV profiles cross, which happens above the cost of capital here). NPV measures the value added in currency at the cost of capital, which is what shareholders receive.
7. $0.3 \times 20\% + 0.5 \times 8\% + 0.2 \times (-10\%) = 8.00\%$; in Excel =SUMPRODUCT({0.3,0.5,0.2},{0.2,0.08,-0.1}).
8. With correlation 1, the portfolio standard deviation is the weighted average, 20%. With any correlation below 1 it is below 20%: that is diversification.
9. $1.06/1.025 - 1 = 3.41\%$.
10. NPV uses all cash flows, discounts them at the opportunity cost of capital and measures the value created; payback ignores the time value of money (in its simple form), ignores everything after the cut-off and has no objective cut-off.

Revision history

Standard and licence note

Based on the standard time-value-of-money, capital budgeting and portfolio results of Fisher (1930), Williams (1938), Markowitz (1952), Gordon (1959), Sharpe (1964, 1966) and Lintner (1965), and on the public Microsoft Excel function documentation, all explained in original wording with original examples. Every figure was computed independently in Python and checked with a spreadsheet-formula engine. Corvane Robotics, Northfield Outdoor Co. and all figures are fictional. Microsoft and Excel are trademarks of Microsoft Corporation, named only to identify the software; this template is not affiliated with or endorsed by Microsoft or by any business school, and it is a learning aid, not investment or financial advice. Template licence: MIT.