FNCE201: Finance 2A Course Notes (South African Universities)

Finance is the language of markets: it explains how money moves, how risk is priced, and how firms (and households) make decisions under uncertainty. FNCE201: Finance 2A typically builds on foundational accounting and corporate finance concepts, moving toward deeper analysis of investment valuation, risk and return, cost of capital, capital budgeting, and the financing of corporate activities. This study guide focuses on South African higher education contexts—Universities and TVET articulation pathways—by presenting the kinds of skills and methods students are assessed on in FNCE201-type modules.

Section 1: What FNCE201: Finance 2A Tests — Core Learning Outcomes, Financial Statements, and Corporate Decision Tools

The “shape” of FNCE201 assessments (what examiners usually test)

Across South African universities offering Finance-related modules (and in Finance 2A / 2nd-year corporate finance sequences), assessments tend to test whether you can:

Interpret financial statements and translate them into decision-relevant metrics.
Use time value of money (TVM) tools correctly (present value, future value, annuities).
Perform valuation and capital budgeting with appropriate discount rates.
Distinguish risk vs return, and apply risk measures to projects or portfolios.
Construct or interpret the cost of capital (e.g., WACC) and use it in investment decisions.
Understand basic financing choices (debt vs equity), and how these link to valuation.

FNCE201 is rarely “only theory.” Even when questions ask conceptual definitions, they often require:

The correct formula
Correct units (e.g., % vs decimals)
Correct assumptions (growth, compounding frequency, taxes)
A logical interpretation of results (e.g., accept/reject based on NPV).

Financial statements as the starting point: translating accounting into finance

A recurring assessment theme is converting accounting information into the numbers that matter for investment and financing.

Balance Sheet to “capital employed” logic

Key line items (names vary by institution) generally include:

Assets
- Current assets (cash, receivables, inventory)
- Non-current assets (property, plant & equipment, intangibles)
Liabilities
- Current liabilities
- Non-current liabilities (often interest-bearing debt)
Equity
- Share capital / ordinary shares
- Retained earnings

For corporate finance and valuation, a common construct is capital employed, roughly:

Capital employed ≈ Net operating assets
Often conceptually: (Assets used in operations) minus (Non-interest-bearing liabilities)

You don’t always compute it exactly, but exams may ask you to identify what counts as operating assets and what doesn’t.

Income Statement to “operating performance” metrics

Finance modules often separate:

Operating profit (EBIT) from
Interest expense and tax expense

Why? Because in valuation and WACC logic, discounts often relate to cash flows available to providers of capital (debt + equity), which link to unlevered operating performance.

A typical exam prompt:

You are given revenue, operating costs, depreciation, interest, tax.
You’re asked to compute:
- EBIT
- Tax on EBIT or on taxable income (depending on how the question is phrased)
- Net income
- Free cash flow

You should note that depreciation is non-cash, so it affects taxable income but not cash directly.

Cash Flow Statement: the exam uses it even if it’s not “in the syllabus”

Finance lecturers usually emphasize:

CFO (cash from operations)
CFI (cash from investing)
CFF (cash from financing)

Even if your class focuses on capital budgeting, cash flow logic is essential:

Capital budgeting uses incremental free cash flows, not accounting profit.

Core TVM toolkit (the “engine” behind valuation)

FNCE201-type problems frequently use the TVM formulas in multiple formats. You should be able to switch quickly between them.

Present value (PV) and future value (FV)

If a cash flow C is received in n periods with discount rate r:

PV = C / (1 + r)^n
FV = C(1 + r)^n

Annuities: equal payments

If you have annuity payments of PMT for n periods:

PV of ordinary annuity:
- PV = PMT × [1 − (1 + r)^−n] / r
PV of annuity due (payments one period earlier):
- PV(adjusted) = PV(ordinary annuity) × (1 + r)

Perpetuities (when n → infinity)

PV of perpetuity: PV = PMT / r
For growing perpetuity:
- PV = PMT1 / (r − g)
- Where PMT1 = PMT0(1 + g)

Exam tip: When growth models are used, always check that r > g, otherwise the present value diverges.

Incremental cash flows: the capital budgeting “language”

A common FNCE201 question: “Project X costs R… and yields cash flows … should the firm accept?” You will score if you treat cash flows correctly.

The exam expects you to compute incremental free cash flows:

Project operating cash flows
Less operating costs
Add back non-cash expenses (like depreciation)
Account for working capital changes
Include capex outflows and terminal values (sell-off, salvage, or continued value)
Apply taxes properly (especially on depreciation and disposal)

A structured method for free cash flow to firm (FCFF)-style logic

Even if a course uses a simplified approach, you should have a consistent template:

Unlevered operating profit (EBIT)
Taxes on EBIT:
- Tax = EBIT × tax rate
Add back depreciation:
- EBIT(1 − tax) + Depreciation
Subtract CAPEX
Subtract increase in Net Working Capital (NWC)
Add terminal cash flows at year N (e.g., salvage value minus taxes on disposal; recovery of NWC)

Working capital in exams (often where marks are lost)

Working capital changes can be:

An initial cash outflow (increase in NWC at t=0)
A recovery at the end (a release of NWC back into cash at terminal date)

If the question provides:

NWC at t=0 and NWC at t=1…t=n,
you compute changes:
ΔNWC_t = NWC_t − NWC_(t−1)

Then subtract cash outflows:

If ΔNWC is positive, subtract (use more cash now)
If ΔNWC is negative, add back (release cash)

Decision rules: NPV, IRR, and Payback (and what to say in written answers)

Net Present Value (NPV)

NPV = Σ [CF_t / (1 + WACC)^t] − Initial Investment

Interpretation:

If NPV > 0, accept
If NPV < 0, reject

Internal Rate of Return (IRR)

IRR is the rate k that makes:

NPV(k) = 0

Interpretation:

Accept if IRR > required return (e.g., WACC)

But examiners often warn you (sometimes implicitly) about IRR pitfalls:

Multiple IRRs when cash flows change sign more than once
IRR ranking problems with mutually exclusive projects and different scales/timelines

Payback period

Payback = time until cumulative cash flows become positive.

Useful for liquidity constraints
Not a good standalone metric because it ignores time value and cash flows after payback

Profitability Index (PI)

PI = PV of future cash flows / Initial investment
Accept if PI > 1

Written answers often require a brief justification: use NPV as the primary decision criterion.

Section 2: Risk, Return, and Valuation — The Capital Asset Pricing Model, Discount Rates, and Equity Valuation Logic

Why risk matters more in Finance 2A than in Finance 1A

In later-year finance modules, risk becomes central because it determines:

the discount rate for valuing cash flows
the required return demanded by investors
the suitability of projects given uncertainty

You typically move from describing risk to measuring and pricing it.

Returns and how to compute them correctly

Even if you think “returns are easy,” exam questions often include pitfalls:

Confusing nominal and real returns
Incorrect compounding periods
Mixing up arithmetic vs geometric averages

Simple return

If price changes from P0 to P1 and a dividend D is received:

R = (P1 − P0 + D) / P0

Arithmetic mean vs geometric mean

Arithmetic mean is the average of returns.
Geometric mean reflects compounding over time.

In exam modelling, the course may ask for:

average return over multiple years
estimated expected return using historical data

Unless stated, be careful: expected return is typically arithmetic average in CAPM contexts, but always follow the instruction.

Diversification and the meaning of “systematic” risk

A key conceptual point:

Total risk = systematic risk + unsystematic risk
Unsystematic risk can be diversified away in a large portfolio.
Systematic risk remains because it’s tied to market-wide factors.

So in CAPM:

Only systematic risk is priced.

CAPM: the standard link from risk to expected return

CAPM formula:

E(R_i) = R_f + β_i [E(R_m) − R_f]

Where:

R_f = risk-free rate
β_i = sensitivity of security i’s returns to market returns
E(R_m) = expected market return

Interpreting β

β = 1: moves with the market
β > 1: more volatile than the market (higher systematic risk)
β < 1: less volatile than the market
β < 0: moves inversely (rare for common stocks; could happen in certain hedged or defensive exposures)

Exam mechanics for calculating β

You might be given:

historical returns for a share and the market
and asked to estimate β.

Common approach:

β = Cov(R_i, R_m) / Var(R_m)

If your exam gives regression output:

identify β as the slope coefficient in:
- R_i = α + β R_m + error

Discount rates: using CAPM to value cash flows

In equity valuation:

You discount cash flows to equity at the cost of equity (often derived via CAPM).
In firm valuation (FCFF), you discount at WACC.

Cost of equity (Ke)

If using CAPM:

Ke = R_f + β × (E(R_m) − R_f)

Cost of debt (Kd)

Typically derived from:

interest expense / market value of debt or yield information
after-tax cost when used in WACC:
- Kd(after tax) = Kd × (1 − tax rate)

WACC: the weighted average of costs

WACC formula:

WACC = (E/V)Ke + (D/V)Kd(1 − tax) + (preferred/V)Kp

Where:

E = market value of equity
D = market value of debt
V = E + D + (preferred if applicable)

Important exam consistency: If a question provides book values instead of market values, use what the question allows. Some exams specify market weights; others allow book approximations.

Equity valuation approaches (what FNCE201 questions look like)

Common methods:

Dividend Discount Model (DDM): value based on future dividends
Residual Income Model (less common in early finance)
Free cash flow to equity (FCFE) discounting

Two-stage DDM (a favourite)

You may see:

High growth period for t = 1…N
Then stable growth thereafter
Valuation requires:
- PV of dividends during high growth
- PV of terminal price at t=N using stable growth formula

If dividends during stage 2 are modeled as growing at g2:

Terminal value at time N:
- P_N = D_(N+1) / (Ke − g2)

Then:

P0 = PV of D1…DN + P_N discounted

Check: Ke > g2 to be valid.

Example-style valuation logic (practical computational patterns)

A typical exam chain might be:

Compute cost of equity via CAPM
Use DDM assumptions (growth rates and dividend forecasts)
Compute intrinsic value
Compare with market price and interpret (undervalued/overvalued)

Make sure you keep the same Ke and growth assumptions throughout.

Risk premium and “risk-free” rates in South African settings

South African university finance courses often use the idea of:

R_f based on government bond yields (commonly referenced as relevant maturity)
Market risk premium estimated using historical excess returns or survey methods
β estimated from local or international datasets (depending on course tooling)

Even when your course does not explicitly require exact SA bond yields, exam questions may provide:

R_f value
market return assumption
or expected market return

Your job is to apply these numbers consistently.

Sensitivity analysis: what to say when assumptions change

Valuation is assumption-driven. Examiners reward students who:

compute a base case NPV or intrinsic value
then indicate how results move if:
- discount rate increases
- growth decreases
- cash flows are delayed
- inflation affects costs or dividends

A robust answer includes:

Directional effect reasoning:
- Higher discount rate → lower PV → lower value
- Lower growth → lower terminal value → lower PV
- Delayed cash flows → lower PV even if totals remain same

Section 3: Capital Budgeting and Project Appraisal — NPV under Uncertainty, Scenario/Incremental Analysis, and Working Capital Effects

Capital budgeting: the central “skill” of Finance 2A

Capital budgeting asks:

What projects should a firm invest in?
How do we compare mutually exclusive alternatives?
How do we handle risk and uncertainty?

A strong FNCE201 student:

sets up incremental cash flows correctly
discounts using the correct required return (often WACC or project-specific required return)
uses NPV/PI as primary decision tools

Step-by-step project appraisal method (repeatable exam workflow)

Use a repeatable sequence:

Identify cash flow timeline
- t=0 initial outflow (capex, initial working capital changes)
- years 1…N operating cash flows
- terminal year cash flows (salvage + NWC recovery)
Compute EBIT
- revenue minus cash operating costs (not depreciation yet)
- include depreciation as an accounting expense
Compute taxes
- tax = EBIT × tax rate (if taxes are computed on EBIT)
Compute after-tax operating cash flow
- CFO-like structure:
- EBIT(1 − tax) + Depreciation
Include capital expenditure
- subtract CAPEX each year it occurs
Include working capital changes
- subtract increase in NWC; add recovery
Discount at the required rate
- often WACC for FCFF projects
Compute NPV
- sum discounted cash flows
Decision
- Accept if NPV > 0
- Compare projects using NPVs

Mutual exclusivity and scaling problems (why “IRR only” can be misleading)

Exams sometimes give two projects:

Project A: larger NPV but lower IRR
Project B: smaller NPV but higher IRR

If they are mutually exclusive, the decision should generally follow NPV if the time horizon and cash flow structure are properly comparable.

Scale matters

A project with larger investment can produce a larger NPV even with lower IRR.
IRR focuses on percentage return, while NPV measures value created in currency terms.

Timing matters

If one project generates earlier cash flows:

its PV may be greater even if total cash flows are similar.

Incorporating financing effects: FCFF vs FCFE

A common confusion: you discount using WACC but include financing cash flows. This leads to double-counting.

FCFF (Free Cash Flow to Firm) assumes capital structure does not change.
- discount at WACC
- treat cash flows before financing flows (interest, principal repayments)
FCFE discounts cash flows to equity.
- needs to incorporate net borrowing / debt payments (depending on formulation)
- discount at cost of equity

Many FNCE201 questions simplify by asking for FCFF-style or by providing WACC and expecting it directly.

Working capital: numerical treatment and common exam traps

Consider a project requiring additional inventory and receivables:

NWC increases at the start → cash outflow
At the end:
those balances are recovered → cash inflow

Example trap: ignoring NWC recovery

Students often compute only operating cash flows and terminal salvage, forgetting that NWC tied up in operations releases at termination.

To handle correctly:

compute ΔNWC each year or at least:
- initial increase at t=0
- full recovery at terminal year

Depreciation and taxes: the key role of non-cash expenses

Because depreciation reduces taxable income:

Depreciation creates a tax shield.

A standard formula:

Tax shield from depreciation = Depreciation × tax rate

In the cash flow computation:

Add back depreciation (non-cash)
subtract tax on operating profit (which already accounts for depreciation)

This yields correct after-tax cash flows.

Scenario analysis and risk-based decision making

FNCE201 sometimes includes uncertainty:

demand can be high/medium/low
costs can vary
timing can slip

Two typical exam formats:

(A) Expected NPV using probabilities

You assign probabilities to scenarios and compute:

Expected NPV = Σ [Probability_s × NPV_s]

Decision rule:

Choose project with higher expected NPV, but sometimes exam expects you to note downside risk.

(B) Break-even discount rate or NPV sensitivity

You may be asked:

For what discount rate does NPV become zero?
This is a form of IRR-like break-even, but sometimes framed differently.

Depreciation schedules and tax shields (more detailed logic)

Some advanced FNCE201 questions include multiple depreciation years. If the problem provides:

depreciation expense each year
and tax rate

Then you compute year-by-year:

EBIT_t = EBIT_before_depreciation − Depreciation_t
Taxes_t = EBIT_t × tax rate
After-tax operating cash flow_t = (EBIT_t + Depreciation_t) − Taxes_t
- or equivalently EBIT_t(1 − tax) + Depreciation_t

Be careful: if the problem gives depreciation totals, make sure they match the timeline.

Terminal value: two common methods

Terminal value often appears in longer-horizon projects.

(1) Salvage value at end

If assets are sold for salvage value:

include salvage cash inflow
adjust for tax on sale:
- taxable gain/loss = Sale price − Book value
- tax on disposal = taxable gain × tax rate (loss reduces taxes or creates tax benefit)

(2) Growing perpetuity for continuing operations (less common in project appraisal, more in valuation)

If a project is expected to produce cash flows beyond year N, you may:

assume growth from N+1 onward
apply perpetuity or terminal value formulas

Again:

need discount rate > growth rate.

Section 4: Financing Decisions, Cost of Capital Practice, and Corporate Valuation Under Real-World Constraints (Including Taxes and Capital Structure)

Capital structure and the relevance of debt vs equity

In Finance 2A, debt/equity topics typically connect to:

the cost of capital
leverage and risk
valuation changes when financing structure shifts

Exams may ask you to:

compute WACC under a given capital structure
interpret changes in cost of capital when debt increases
explain trade-offs: tax benefits of debt vs financial distress costs

Cost of capital as a bridge between investment and financing

A project’s NPV depends on the discount rate.
The discount rate depends on:

financing mix
risk profile
investor required returns

WACC and the trade-off logic

Debt provides a tax shield because interest is tax-deductible.
However:

more debt increases default risk
default risk pushes the cost of debt up
equity investors demand higher returns when leverage increases

So WACC may initially decline with leverage (tax benefits) but later rise as risk dominates.

Practical WACC calculations: the “plug-and-chug” plus interpretation

A typical exam question gives:

market value of equity E
market value of debt D
cost of equity Ke
pre-tax cost of debt Kd
corporate tax rate t

Then:

WACC = (E/(E+D))Ke + (D/(E+D))Kd(1 − t)

Consistency check

Before finalizing:

confirm weights add to 1: E/(E+D) + D/(E+D) = 1
confirm you used pre-tax cost of debt and then multiplied by (1 − tax rate)
ensure Ke and Kd are in the same basis (both annual, both nominal vs real)

Debt cost of capital and taxes: interpreting “after-tax cost of debt”

Some students mistakenly apply taxes directly to interest cash flows without translating into cost of debt.

The standard approach:

Use Kd (pre-tax)
After-tax: Kd(1 − t)

If the question provides:

an effective interest rate net of taxes already,
then you should not apply (1 − t) again.

Follow the question wording strictly.

Preferred shares (if included)

If your module includes preferred dividends:

Kp = Dp / Pp (for constant dividend preferred shares)
WACC may include preferred equity:
- WACC = (E/V)Ke + (P/V)Kp + (D/V)Kd(1 − t)

Financing constraints and real-world adjustments

Many FNCE201 questions are stylized, but sometimes include:

constraints on borrowing
limits on equity issuance
or assumptions that the firm keeps target capital structure weights constant.

In such cases:

WACC remains stable across project timeline
or you may apply project-specific WACC if risk differs

If the question says “use WACC,” do so; don’t invent a different rate.

Valuation under leverage: equity vs firm value

A consistent valuation logic:

Firm value (enterprise value) is based on FCFF discounted at WACC.
Equity value is obtained by subtracting net debt:
- Equity Value = Firm Value − Net Debt
- Net Debt = Total Debt − Cash (if provided)

Exams might:

provide firm value and ask equity value
provide equity value and ask firm value

Example pattern: “project financed by a mix of debt and equity”

If a project is financed using the firm’s current capital structure:

discount at WACC
use unlevered cash flows

If a project changes leverage significantly, more advanced treatments would require:

adjusting WACC
or estimating project beta and deriving project cost of equity

Many second-year modules keep this simple; still, the written answer may expect you to recognize the distinction.

Taxes, risk, and the Modigliani–Miller intuition (often conceptual)

Even if derivations are not required, conceptual marks may appear.

Without taxes and with perfect markets: capital structure doesn’t affect value.
With corporate tax: debt provides tax shields → value increases.
In reality: bankruptcy costs, agency costs, and market frictions offset perfect tax-benefit story.

Examiners often award marks for:

listing trade-offs clearly
connecting to WACC directionally

Section 5: Exam-Ready Practice Framework — How to Solve FNCE201-Style Problems Fast and Accurately (with South African University Context Emphasis)

Building a personal “exam algorithm” for FNCE201

Finance exam success often comes from method, not only knowledge. Create your own checklist consistent with how FNCE201 questions are structured.

Pre-calculation checklist (60 seconds)

Before crunching numbers:

Identify whether question is about:
- PV/FV/annuity/perpetuity
- valuation (equity or firm)
- capital budgeting (NPV/IRR/WACC)
- cost of capital (Ke/Kd/WACC)
- risk/return (CAPM, β)
Confirm:
- discount rate basis (annual? nominal? real?)
- cash flow timing (end of year vs beginning)
- whether taxes are included in cash flows or in discounting
Check sign conventions:
- initial investments negative at t=0
- inflows positive

Calculation checklist (the “mark saver”)

Write formulas clearly.
Use consistent units (% vs decimal).
Round at the end (unless question expects specific rounding).
If using a calculator, record key intermediate results.

How to interpret NPV/IRR answers in writing

A common marker rubric:

correct computation = marks
correct interpretation = marks
correct method = marks even if final arithmetic has a slip

Interpretation statements you can reuse

NPV > 0: Project expected to increase firm value; accept if mutually exclusive constraints allow.
NPV < 0: Project expected to decrease firm value; reject.
IRR > required return: expected to earn returns above required; accept (with caution for mutually exclusive issues).
Payback: indicates liquidity; not sufficient alone for long-term value creation.

Common errors and how to avoid them (high-yield)

1) Mixing up cost of equity and WACC

Cost of equity (Ke) discounts equity cash flows.
WACC discounts firm-level free cash flows.
If you’re given WACC, it implies unlevered cash flows.

2) Forgetting working capital changes

NWC tied up consumes cash now.
NWC released at the end returns cash.

Always scan the question for:

“increase in working capital”
“ΔNWC”
“receivables/inventory/payables” linked to the project.

3) Treating depreciation as cash

Depreciation is non-cash. It affects taxes but not cash flow directly.

In free cash flow:

you typically add depreciation back after computing tax impact.

4) Discounting cash flows incorrectly

If cash flows occur at the end of each year, use ordinary annuity discounting.
If a cash flow occurs at the beginning, discount one period less.

A frequent trap:

applying an annuity formula when payments timing differs.

5) Using g ≥ r in growing perpetuity

Always check:

Ke > g for DDM growing perpetuity

If not, the valuation becomes invalid.

South African examination style: how to structure your working

While each South African institution has its own paper style, many finance exams reward:

clear stepwise working
neat labeling of columns by year (t=0, t=1, …)
tables for cash flow timelines

You should:

create a cash flow table even if not required
separate operating cash flows, capex, NWC, terminal value

A strong “presentation” often increases partial marks if final results are wrong.

End-to-end “model answer skeleton” you can follow

When faced with a capital budgeting question, structure your solution like:

Given:
- investment cost
- depreciation
- tax rate
- discount rate (WACC or project required return)
- cash flow forecasts
Timeline diagram:
- t=0 initial outflow
- t=1…N operations
- t=N terminal values
Compute:
- EBIT each year
- Taxes each year
- After-tax operating cash flow each year
- CAPEX cash flows each year
- ΔNWC each year
- Total free cash flow each year
Discount:
- discount factor each year: 1/(1+r)^t
- PV of each cash flow
NPV:
- sum PVs
- subtract initial if not already included
Decision and justification:
- accept/reject
- mention NPV criterion
- comment briefly on sensitivity if asked

How to practice: building a weekly study routine for FNCE201

A workable plan:

Day 1: TVM + quick practice sets (5–10 questions)
Day 2: CAPM + β estimation + cost of capital calculations
Day 3: WACC + WACC-weighted discounting problems
Day 4: capital budgeting (NPV) with working capital and tax shields
Day 5: mixed revision + timed past-paper drills

Aim to develop:

speed in arithmetic
accuracy in sign conventions
ability to explain decisions in one or two sentences

Mini-drills (conceptual) you should master

Use these as “mental flashcards.”

Drill A: What is the difference between EBIT and net income?

EBIT excludes interest and taxes.
Net income includes interest expense and taxes.

Drill B: Why is WACC used for firm cash flows?

Because WACC is the blended required return from both debt and equity holders, matching unlevered cash flows.

Drill C: When do you use cost of equity?

When discounting cash flows to equity (FCFE or equity dividends).

Drill D: What does β measure in CAPM?

Systematic risk: sensitivity to market movements.

Drill E: Why is NPV preferred?

NPV measures value created in currency terms and directly uses the time value of money.

Practical example categories to seek in past papers

Even without naming specific past papers, FNCE201 exams commonly include:

Bond/Share valuation using discount rates
CAPM cost of equity calculations
WACC and NPV project evaluation
Two-stage dividend growth valuation
Sensitivity analysis with changes in discount rates or growth
Working capital calculations
Tax shield calculations via depreciation
Mutually exclusive project selection

When you revise, ensure you can solve each category, not just recall formulas.

Institutional focus note (South Africa-specific learning pathways)

South African universities and TVET articulation pathways differ in prerequisites and tool usage, but the computational “core” is consistent: FNCE201-style content generally trains you to apply finance mathematics to decision-making in a corporate context. Whether you are studying at a university that offers a structured BCom pathway or through an articulation process from an institution offering business/financial studies, the exam skill set aligns around:

TVM fluency
risk-return logic
WACC and discounting
NPV/IRR decision-making with taxes and working capital

Practising with locally consistent examples (company-like cash flow statements, South African-style tax rate assumptions when provided, and bonds/yields when given) ensures you don’t lose marks due to assumption mismatch.

Section 6: Formula Sheets, Worked-Logic Templates, and High-Yield Practice Tables for FNCE201 (Finance 2A)

A compact “FNCE201 formula sheet” (only what you actually use in exams)

TVM

PV = C / (1 + r)^n
FV = C(1 + r)^n
PV ordinary annuity = PMT × [1 − (1 + r)^−n] / r
PV annuity due = PV ordinary × (1 + r)

Growing perpetuity / DDM stable stage

PV = D1 / (r − g)

CAPM

E(R_i) = R_f + β_i [E(R_m) − R_f]
β_i = Cov(R_i, R_m) / Var(R_m)

WACC

WACC = (E/V)Ke + (D/V)Kd(1 − T)

Capital budgeting

NPV = Σ [CF_t / (1 + r)^t]
Accept if NPV > 0

Worked-logic templates (copy into exam books)

Below are templates you can reproduce.

Template 1: Free cash flow for capital budgeting (FCFF-style)

For each year t:

EBIT_t = Revenue_t − Cash Costs_t − Depreciation_t
Tax_t = EBIT_t × T (if taxes computed on EBIT)
After-tax operating cash flow = EBIT_t(1 − T) + Depreciation_t
FCFF_t = After-tax operating cash flow − CAPEX_t − ΔNWC_t
Terminal:
- FCFF_N += Salvage after tax + Recovery of NWC

Then:

NPV = Σ [FCFF_t / (1 + WACC)^t]

Template 2: WACC calculation

Compute weights:
- wE = E/V, wD = D/V (and wP if needed)
Compute costs:
- Kd(after tax) = Kd(1 − T)
Combine:
- WACC = wEKe + wDKd(after tax) + wPKp

Template 3: Two-stage DDM

Forecast dividends D1…DN (stage 1)
Compute terminal price at time N:
- P_N = D_(N+1) / (Ke − g2)
Value at t=0:
- P0 = Σ [D_t / (1 + Ke)^t] + P_N / (1 + Ke)^N

Practice table: timeline cash flow layout (for speed)

When doing NPV, create a table like:

Year (t)	Cash Flow Type	Amount (ZAR)	PV Factor @ r	PV
0	Initial capex + ΔNWC	( )	1/(1+r)^0	( )
1	Operating FC		1/(1+r)^1
2	Operating FC		1/(1+r)^2
…	…		…
N	Terminal + operating FC		1/(1+r)^N
	Total NPV			NPV

Even if you can’t fill numbers yet, writing the structure makes you consistent.

Micro-case style scenarios (to build exam intuition)

These are the kinds of scenarios you often see: you practice setting up cash flows and applying the correct discount rate.

Scenario 1: Replacement decision with salvage and NWC

A firm considers replacing an old machine with a new one:

New capex at t=0
Old machine sold at t=0 (with possible tax on sale)
Depreciation differs across years
NWC change affects cash in early years
Terminal salvage at year N

What to practice:

If old machine sale is at t=0, include it at t=0.
Tax on sale uses:
- taxable gain/loss = Sale price − Book value (if the problem provides book value).
Include salvage at the end net of tax.

Scenario 2: Bond valuation with YTM vs coupon rate

If asked to price bonds:

you discount coupon payments and principal at YTM (required yield).
coupon rate is not the discount rate unless YTM equals coupon rate.

What to practice:

identify discount rate from the yield given
ensure coupon timing is correct (annual vs semiannual)

Scenario 3: Share valuation using CAPM and growth

Given:

risk-free rate R_f
market expected return E(R_m)
β
dividend forecast and growth rates

What to practice:

compute Ke via CAPM
ensure Ke > stable growth g
compute terminal price correctly in two-stage DDM

“Data consistency” exercises (avoid contradictions)

Many students lose marks by misusing inconsistent assumptions. Make these checks:

If tax rate is T, does the tax appear in cash flows or embedded in after-tax operating cash flow?
If the question gives WACC, do not also adjust cash flows for financing already.
If dividends are given in ZAR per share annually, do not discount as monthly.
If time is in years, do not use quarterly compounding unless given.

High-yield revision checklist (final week)

Before an exam:

rework at least 2 capital budgeting problems that include NWC + taxes
rework 2 valuation problems that include stable growth
rework 2 WACC problems using given capital structure weights
rework 2 CAPM problems using provided R_f, E(R_m), and β
rework 1 mixed question under time pressure

Section 7: Summary — The FNCE201 “Core Pack” You Must Master for High Marks

FNCE201: Finance 2A builds a coherent toolkit: TVM → risk-return (CAPM) → discount rates (cost of capital/WACC) → investment appraisal (NPV/IRR) → valuation logic (DDM/discounting). If you master the mechanics—especially incremental cash flow construction, correct tax handling, and consistent discount rate usage—you will consistently score high on both computational and conceptual questions.

The most exam-reliable habit is to work in a structured sequence: identify what the question asks (valuation vs project appraisal), set up cash flows on a timeline with correct signs, compute discount rates (Ke/WACC) using the provided inputs, then apply NPV (and interpret outcomes). With repeated practice using South African university-style problem patterns—where working capital and tax effects are common—you can confidently handle the full range of FNCE201 assessments.

If a lecturer marks you down, it is usually for one of the predictable reasons: discounting errors, working capital omissions, tax misapplication, or mixing cost of equity with WACC. Avoid those, and your answers become both accurate and “marker-friendly.”