Corporate Financial Decision Making

0 · How to Use Thisread first

FNCE20005 is graded 25% mid-sem test (1 hr, Wk 6) + 60% final exam + 5% homework quiz + 10% tutorials. A formula sheet is provided in the MST — so marks come from setting up & interpreting, not memorising. This sheet groups every formula with its decision rule + a worked number.

It is the second finance subject: TVM, bonds & CAPM are assumed background (Side 1); the taught, examinable core is the Australian-flavoured toolkit — imputation, payout, leases, capital structure, real options, M&A (Side 2).

0b · Exam Blueprintwhere marks live

MST (Wk 6, ~Lec 1–5): equity raising & rights, payout & imputation, leases, WACC & capital structure, advanced budgeting. Multi-part numerical with a formula sheet.

Final (60%, cumulative): adds real options, M&A valuation & economics, restructuring, distress, risk management. Expect one big DCF/valuation, one capital-structure/WACC, one payout/imputation, plus short theory.

• Show the formula → substitution → answer chain — method earns marks even if the number slips
• State your decision (accept/reject, lease/buy) explicitly
• Carry units & signs; label $ vs %
• Quote the decision rule threshold (NPV>0, IRR>k, PI>1) before you compute

The MST is short — practise the rights, imputation & WACC numericals to near-automatic; the final rewards clean valuation set-ups and tight theory.

0c · Master Toolkit Mapthe spine

Every valuation is one engine — discounted cash flow — pointed at a different object:

1. A bond → PV of coupons + face
2. A share → PV of dividends (Gordon)
3. A project → NPV of free cash flows
4. A firm → FCF ÷ WACC + terminal value
5. A target → firm value + synergies

Master the discount rate (CAPM for k_e, WACC for the firm) and the rest is bookkeeping.

Three recurring questions: what is it worth (valuation), should we invest (capital budgeting), how do we finance & pay out (structure, payout, imputation). The course is the bridge from "Principles" mechanics to real-firm decisions.

1 · Time Value of Moneybackground · on sheet

single sumFV = PV(1+r)^t   PV = FV/(1+r)^t

ordinary annuity (C for t yrs)PV = (C/r)·[1 − 1/(1+r)^t]
FV = (C/r)·[(1+r)^t − 1]

Annuity due (cash in advance, e.g. lease rentals): multiply the ordinary-annuity PV by (1+r), or place the first cash flow at t=0.

perpetuity / growing perp.PV = C/r   PV = C₁/(r−g)

growing annuityPV = (C₁/(r−g))·[1 − ((1+g)/(1+r))^t]

Rates: effective = (1 + i/m)^m − 1; after-tax = r(1−t_c). Compound more often ⇒ higher effective rate.

2 · Bond Pricing & YTMbackground

bond priceP = C·[1−(1+y)⁻ⁿ]/y + F/(1+y)ⁿ

YTM = the y that solves the price equation (iterate). Price moves inversely with yield.

Cost of debt k_d = today's market rate for that credit rating — not the coupon. For valuation, k_d is an expected return, not simply the promised YTM (which embeds default).

Trap: don't confuse coupon rate, current yield (C/P) and YTM; and don't plug YTM in as the cost-of-debt input in WACC when the question wants an expected return.

A bond trades at par when coupon = YTM, at a premium when coupon > YTM, at a discount when coupon < YTM. Longer maturity ⇒ more price sensitivity to yield.

3 · Share ValuationGordon · on sheet

general DDMP₀ = Σ E[D_t]/(1+k_e)^t

constant-growth (Gordon)P₀ = D₁/(k_e−g) = D₀(1+g)/(k_e−g)
⇒ k_e = D₁/P₀ + g

Ex: D₀=$2, g=4%, k_e=12% → P₀ = 2(1.04)/(0.12−0.04) = $26.00.

Traps: use D₁ not D₀; need k_e > g or the formula breaks; constant g is wrong for a high-growth firm — use a two-stage DDM (forecast then terminal Gordon) instead.

4 · Capital Budgeting RulesLec 5 · core

NPV — the dominant ruleNPV = Σ E[CF_t]/(1+k)^t − CF₀
accept if NPV > 0

IRR = the rate where NPV = 0; accept if IRR > k. Pitfalls: multiple/no IRR with sign changes, scale & timing, reinvestment assumption.

profitability indexPI = PV(inflows)/initial outlay → accept if > 1

Payback = years to recoup the outlay; discounted payback uses PV. Both ignore cash flows beyond the cutoff.

4b · NPV vs IRR Conflictexam favourite

For mutually exclusive projects, scale & timing differences can rank them oppositely. When they conflict, trust NPV (it measures $ value added; IRR is only a rate). Survey lore: US firms lean IRR, AU firms lean NPV.

The crossover rate = the IRR of the incremental cash-flow stream; below it, the bigger-NPV project wins. PI also helps rank under capital rationing when you can't take every +NPV project.

For a non-conventional stream (sign flips more than once) IRR can give multiple roots — fall back to NPV, or use the modified IRR (MIRR) which assumes reinvestment at k.

4c · Free Cash FlowLec 7 · on sheet

FCF to the firmFCF = EBIT(1−t_c) + Dep − ΔNWC
    − CapEx (+ after-tax asset sales)

Rules: use incremental after-tax CF; ignore sunk costs; include opportunity costs & ΔNWC.

depreciation tax shield= t_c × depreciation

Depreciation isn't a cash flow — only its tax shield is. ΔNWC reverses at project end (recover working capital).

terminal value (year T)TV_T = FCF_T(1+g)/(WACC−g)

TV is a growing perpetuity valued at year T — then discount it back T periods. It often dominates a DCF, so the long-run g assumption is where valuations are won or lost (keep g < WACC and below long-run GDP growth).

5 · Project-Risk ToolsLec 5

Sensitivity analysis · change one input (best/base/worst), hold the rest, read the NPV range. The widest range = the most sensitive variable (often selling price).

Scenario analysis · move several linked inputs together (e.g. a recession case) — captures interrelations sensitivity misses.

Break-even · solve the input value that sets NPV = 0 (e.g. price can fall 2.8%, volume 19.9%).

Monte Carlo · assign distributions to inputs, draw thousands of NPVs → P(NPV<0) & a 95% band. (Excel demo: optional, not examinable.)

Decision trees · sequential choices under probability; solve by roll-back (solve the most distant decision first, work back to today). The branch values capture the option to abandon, expand or continue.

Each tool answers a different question: sensitivity → which input matters; break-even → how far it can move; scenario → combined downside; simulation → the whole NPV distribution.

6 · Risk & Returnbackground

expected return / varianceE[R] = Σ p_iR_i
σ² = Σ p_i(R_i − E[R])²

Portfolio return = weighted average of asset returns. For two assets:

2-asset varianceσ²_p = w_A²σ_A² + w_B²σ_B²
    + 2w_Aw_Bρσ_Aσ_B

Diversification cuts only unsystematic (firm-specific) risk; systematic (market) risk remains.

6b · Two Kinds of Riskknow the split

This is why "diversification" is a dubious takeover motive — shareholders can diversify themselves cheaply, so a firm merging to diversify creates no value for them.

Correlation ρ drives the gain: the lower ρ, the more variance falls for a given expected return. Adding assets removes idiosyncratic risk until only market risk (the systematic floor) remains — about 20–30 stocks captures most of it.

7 · CAPM & the SMLon sheet · core

Beta β = sensitivity of a stock to the market (a covariance measure) — the slope of stock returns regressed on market returns. β=1 moves with the market; β>1 amplifies it.

CAPM — cost of equityk_e = R_f + β_e·[E(R_M) − R_f]

Ex: R_f=2.75%, β=1.25, MRP=5.76% → k_e = 2.75 + 1.25×5.76 = 9.95%.

The security market line (SML) plots E[R] against β; its slope = the market risk premium [E(R_M)−R_f]. Assets above the SML are underpriced (buy); below = overpriced.

Traps: use β (systematic risk), not total σ; never use a stale/levered β for a project of different risk (see Side 2 §13).

Reading the SML is a classic exam move: a stock plotting above the line offers more return than its β warrants (buy); below the line it's overpriced (sell). In equilibrium all assets sit on the SML. Don't confuse the SML (return vs β) with the CML (return vs total σ).

7b · Estimating the InputsCAPM in practice

• R_f — government bond yield (match the horizon)
• MRP — long-run historical equity premium (~6%)
• β — regression slope; lever/unlever for gearing changes
• k_e always > k_d — equity is the riskier, residual claim

Two routes to k_e: CAPM or the Gordon-growth DCF (k_e = D₁/P₀ + g) — quote both if a question gives the data. The CAPM rewards only β; total risk σ is irrelevant to a diversified investor.

8 · Raising EquityLec 1

Equity = permanent capital, full voting rights, residual + subordinated claim, the riskiest claim. Ladder: private equity (angel, VC) → IPO → SEOs (placement, rights, DRP). The primary market (firm ↔ investor) funds the firm; the secondary (investor ↔ investor) does not.

IPO pricing: fixed price (AU traditional), book-building (US), Dutch auction (Google 2004).

IPO underpricing= (1st-day close − offer)/offer

Ex: Alibaba ($93.89−$68)/$68 = 38.1% — "money left on the table." Why: winner's curse (info asymmetry), market-feedback, IB conflicts, litigation insurance, signalling. Long-run IPOs tend to underperform (clientele, impresario, window-of-opportunity hypotheses).

8b · Rights Issueson sheet · MST

A 1-for-N issue at subscription price S, cum-rights price M:

theoretical ex-rights priceX = (N·M + S)/(N + 1)

value of a rightR = X − S = N(M − S)/(N + 1)

Ex (1-for-5, M=$3.50, S=$2.50):
X = (5×3.50 + 2.50)/6 = $3.33;
R = 3.33 − 2.50 = $0.83.

Renounceable rights: exercise OR sell the right leaves wealth unchanged; doing nothing dilutes you & loses wealth. Non-renounceable rights can't be sold.

Placement ≤15% of capital / 12 mo without approval (ASX LR 7.1; temporarily 25% in COVID); at a discount ⇒ wealth transfer to new holders & voting dilution. DRP = "a very small rights issue."

9 · Worked · Mini-NPVthe full shape

Project: outlay $100k; EBIT $40k/yr for 3 yrs; dep $20k/yr (3 yrs); t_c=30%; k=10%; no ΔNWC.

annual FCF= 40(1−.3) + 20 = 28 + 20 = $48k

NPV= 48·[1−1.10⁻³]/0.10 − 100
= 48×2.4869 − 100 = +$19.4k

NPV > 0 ⇒ accept. Depreciation enters only via the +$6k/yr tax shield, already inside the EBIT(1−t)+Dep line.

IRR check: the rate that sets this NPV to 0 is ≈24%; since 24% > k=10%, IRR agrees — accept. If a question added ΔNWC of $5k at t=0, you'd subtract it now and recover it at t=3. PI here = 119.4/100 = 1.19 (>1) — all three rules agree.

Side-1 Formula Beltmemory hooks

PV_ann=(C/r)[1−(1+r)^−t]
Perp=C/r  GrowPerp=C₁/(r−g)
P₀=D₁/(k_e−g)
NPV=ΣCF_t/(1+k)^t−CF₀
FCF=EBIT(1−t_c)+Dep−ΔNWC−CapEx
TV=FCF_T(1+g)/(WACC−g)
k_e=R_f+β[E(R_M)−R_f]
X=(NM+S)/(N+1)
R=N(M−S)/(N+1)

Discipline: rate ↔ risk; sign & timing of each CF; always discount the TV back; D₁ not D₀; effective vs nominal rates.

10 · WACCLec 4 · on sheet

WACC (market-value, target weights)WACC = k_d(1−t_e)(D/V) + k_e(E/V)
V = D + E

Interpretation: the minimum return on existing-risk assets that preserves security value — the hurdle rate for same-risk projects.

k_d = risk-free + default spread (by credit rating, or a synthetic rating from interest coverage = EBIT/interest). k_e = CAPM or Gordon DCF.

Divisional pitfall: one firm-wide WACC over-funds high-risk divisions and starves low-risk ones — use a pure-play comparable's WACC matched to the project's risk.

11 · Dividend ImputationLec 2/4 · signature

The AU system since 1987 — franking credits pass corporate tax to resident holders, undoing double taxation.

grossed-up dividendDiv_gross = Div_cash/(1 − t_c)

franking credit= t_c × Div_gross

Ex: $70 cash, t_c=30% → gross = 70/0.7 = $100; credit = 0.30×100 = $30. The holder is taxed on $100, then offsets the $30.

effective tax ratet_e = t_c(1 − λ)

λ = fraction of corp tax reclaimed; λ=0 classical, λ=1 full imputation. Ex: 0.30(1−0.60) = 0.12.

11b · Payout PolicyLec 2

Measures: yield = DPS/price; payout = DPS/EPS.

drop-off ratio (with taxes)(P_cum−P_ex)/Div = (1−t_d)/(1−t_cg)

Perfect market ⇒ drop = dividend (ratio 1). MM irrelevance: payout doesn't change value; investors make homemade dividends. It breaks via signalling (dividends are sticky), agency/free-cash discipline, taxes, issue costs.

If div & gains are taxed equally, drop = dividend; div taxed higher ⇒ drop < dividend; div taxed lower ⇒ drop > dividend.

Buybacks: lift EPS, signal undervaluation, add flexibility; no ex-div drop. Post-2023 AU: no tax edge to off-market. Trap: gross up by dividing by (1−t_c); don't apply franking to non-resident holders.

12 · WACC · Workedtie it together

Given: D/V=40%, E/V=60%, k_d=7%, k_e=18%, t_c=30%, λ=0.6 → t_e=0.12.

WACC= 7%(1−.12)(.40) + 18%(.60)
= 7×.88×.40 + 10.8
= 2.46 + 10.8 = 13.3%

Had you wrongly used t_c=30%: 7×.70×.40 = 1.96 ⇒ WACC 12.76% — so imputation raises the after-tax cost of debt, because less of the tax shield is "real."

13 · Capital StructureLec 4 · core

Cost-of-capital approach: firm value = Σ CF_t/(1+WACC)^t; value is maximised where WACC is minimised — a U-shape with an interior optimum.

levered beta · on sheetβ_L = β_u·[1 + (1−t_e)·D/E]

β_u (asset β) = business risk only; β_L adds financial risk. Unlever a comparable, re-lever to your gearing → k_e at each debt level.

13b · The Theories in Wordsexam theory

MM (no tax): perfect markets ⇒ structure irrelevant (pie theory — slicing the pie doesn't change its size).

MM (+ tax): perpetual debt ⇒ PV(tax shield) = t_e·D. Imputation neutralises this (λ=1 ⇒ t_eD=0), implying lower optimal AU leverage.

Trade-off: balance the tax shield against PV(expected distress) = P(distress)×cost — it has a target.

Pecking order (Myers–Majluf): asymmetric info ⇒ no target; finance from internal equity → debt → hybrids → external equity last; leverage = cumulative external need. Explains the negative price reaction to equity issues and why firms are reluctant to issue equity.

Distress costs: direct (legal — small) + indirect (lost customers/suppliers, reputation, management distraction — larger). Shareholders bear the expected cost via dearer debt.

Non-tax drivers: tangible/general-use assets → more debt capacity; debt disciplines empire-builders (Jensen's free-cash-flow problem); R&D-heavy/young firms carry less debt.

Trap: don't treat MM no-tax & with-tax interchangeably; trade-off has a target, pecking-order doesn't.

14 · Debt & LeasesLec 3

Debt vs equity: temporary, prior + fixed claim, no votes, interest is tax-deductible, least risky to the investor; policed by covenants (negative/positive).

Operating lease = short, cancellable (lease-vs-buy). Finance lease = long, non-cancellable, effectively a loan (lease-vs-borrow-to-buy).

finance lease NPV (lessee)+ asset cost − PV(rentals)
+ PV(t_c·rentals) − PV(t_c·dep)
− PV(residual & tax on sale)

discount rateafter-tax cost of borrowing = k_d(1−t_c)

Ex: k_d=15%, t_c=34% → 15(1−.34)=9.9%. NPV<0 ⇒ borrow-to-buy, reject the lease.

Frictionless: NPV_lessor = −NPV_lessee, so leases exist only via frictions — tax-rate differences, different costs of capital (k_lessor<k_lessee), transaction costs; off-balance-sheet is a dubious reason (IFRS 16 now capitalises). Operating-lease value = finance-lease NPV + PV(option to cancel).

Hybrids: convertible notes (debt + option to convert if the share price exceeds conversion value); preference shares (cumulative, non-voting; reset/step-up variants).

Trap: get the sign of each of the six cash flows right (you avoid the asset cost, so it's +); don't discount at the project's required return.

15 · Real OptionsLec 6

Real option = the right (not duty) to wait, expand, abandon or switch as news arrives. Static NPV is now-or-never, so it undervalues flexible projects.

option value= NPV_{with option} − NPV_{without option}

Equity = a call on firm value, strike = face of debt: Max(0, V−D).

Ex (option to delay): static NPV = $100−$95 = $5; waiting a year, [0.5×Max(150−100,0)+0.5×0]/1.15 = $21.74; option value = 21.74−5 = $16.74 = max fee worth paying to wait.

Black–Scholes is shown but not examinable — know the five inputs (V, X, σ, T, r) and that real options aren't exact-priced (long maturity, firm-specific, untraded).

16 · M&A ValuationLec 7

Three approaches:

1 · intrinsic / DCFFirm V = Σ E[FCF_t]/(1+WACC)^t + PV(TV)
Equity = Firm V − net debt

2 · relative / multiplesP_target = (P/E)_industry × Earnings_target

3 · contingent claim (real-option) — for distressed, resource, biotech, high-growth firms.

APV= V(all-equity) + PV(interest tax shields)
shield/yr = D·t_c·k_d

Traps: discount FCF-to-firm at WACC, not k_e; subtract net debt for equity value; discount the TV back; don't use YTM as k_d.

16b · M&A EconomicsLec 8 · on sheet

synergy gainGain = V_AT − (V_A + V_T)

cash bid NPV= Gain − (cash paid − V_T)

scrip bid NPV= Gain − (b·V_AT − V_T)

b = the fraction of the combined firm owned by the target's old holders. Ex: synergy $3m, $6 cash on a $5 share ⇒ NPV = 3 − 2 = $1m; max price (NPV=0) = $6.50. Cash vs scrip differs in who bears pre-close market risk (collars cap both sides).

Stylised facts: targets gain ~+16%, acquirers ~−0.7% (announcement CARs). Sensible motives: synergy, market power, replacing weak management, tax. Dubious: diversification, empire-building, hubris.

16c · EPS Bootstrappinga trap

A high-P/E firm buying a low-P/E firm mechanically lifts EPS with no value created. The combined P/E must be re-estimated as the earnings-weighted average:

combined P/E= (P/E_A·E_A + P/E_T·E_T)/E_A+T

The "magic" earnings bump disappears once you re-price correctly.

16d · AU Thresholdsbright lines

5% substantial-holder notice · 20% = must launch a bid · 50.1% control · 75% special resolutions · 90% compulsory acquisition. A creeping bid = +3%/6 mo past 20%.

17 · RestructuringLec 9

Diversification discount (Berger & Ofek): multi-segment firms trade ~12.7–15.2% below single-segment comparables ⇒ breaking up can unlock value.

LBO/MBO: small equity + large outside debt buys (and takes private) a mature, low-risk, stable-cash-flow firm. Value via (1) financial engineering — debt discipline + interest tax shield + leverage amplifying equity returns; (2) governance — high management equity + active PE monitoring. Exits: secondary IPO, trade sale, on-sell to another PE fund. Needs predictable cash flows; high risk if they wobble.

Why restructure: three families — business (expansion via M&A/JV, or contraction), financial (LBO, debt-for-equity swaps), organisational. Contraction often creates value by reversing the diversification discount.

18 · Corporate DistressLec 10

Distress ⊃ insolvency: financial distress spans events up to insolvency (e.g. a covenant breach); insolvency = can't pay debts as they fall due; in AU "bankruptcy" = personal insolvency.

Two insolvency tests: stock/balance-sheet (assets < debt) and flow/cash-flow (can't meet payments). Near distress, equity = a call on V ⇒ two distortions:

• Asset substitution — pick a risky, even −NPV, project to shift value from debt to equity
• Debt overhang — reject a +NPV project because the gains flow to creditors

Resolution: reorganisation as a going concern (AU Voluntary Administration; the administrator proposes a Deed of Company Arrangement — reject ⇒ liquidation) vs liquidation (sell assets for salvage). APR: liquidation costs → secured → employee entitlements → unsecured → shareholders (often violated in practice).

18b · Altman Z-Scoreon sheet

Z= 3.3(EBIT/TA) + 1.0(Sales/TA)
+ 1.2(NWC/TA) + 1.4(RE/TA)
+ 0.6(MV equity/BV debt)

Z < 1.81 high insolvency risk; Z > 2.99 low (a grey zone between). Note it is MV equity over BV debt. Ex: US Composite scored Z = 5.214 ⇒ safe.

Traps: mixing stock vs flow insolvency; getting the coefficients/ratios wrong; both distortions arise because equity is a call — limited downside, unlimited upside.

19 · Risk ManagementLec 11

MM benchmark: in perfect markets, hedging is irrelevant — investors hedge themselves. So hedging adds value only via frictions.

Six reasons it can add value:

1. Convex taxes — stabilising income lowers expected tax
2. Cuts bankruptcy/distress costs
3. Avoids underinvestment (low CF ↔ good projects)
4. Managerial self-interest (undiversified)
5. Cleaner earnings signal
6. More debt capacity → more tax shields

Tools: derivatives (hedge net exposure, minimally — it's costly) + natural hedges (produce where you sell; borrow in the revenue currency).

Sources of risk: market (interest/FX/commodity — derivatives), commercial/operational (not derivative-hedgeable), external-event (insurable). Trap: MM makes hedging the benchmark, not "always irrelevant"; hedge net, not each gross exposure.

20 · Top Exam Trapslose-no-marks

• t_e ≠ t_c under imputation; gross up by ÷(1−t_c)
• NPV vs IRR conflict → trust NPV
• MM no-tax vs with-tax are different conclusions
• Discount a lease at k_d(1−t_c), not the project rate
• FCF-to-firm uses WACC; FCFE uses k_e
• Subtract net debt for equity value; discount the TV back
• Abandon = put; b = post-merger ownership fraction
• Sunk costs out; opportunity costs & ΔNWC in

Side-2 Formula Beltmemory hooks

WACC=k_d(1−t_e)(D/V)+k_e(E/V)
t_e=t_c(1−λ)
Div_gross=Div_cash/(1−t_c)
Frank=t_c·Div_gross
β_L=β_u[1+(1−t_e)D/E]
V_L=V_U+t_eD (−PV distress)
RO=NPV_w/−NPV_w/o (abandon=put)
Cash NPV=Gain−(cash−V_T)
Scrip NPV=Gain−(b·V_AT−V_T)
Z=3.3(EBIT/TA)+1.0(S/TA)
 +1.2(NWC/TA)+1.4(RE/TA)+0.6(MVE/BVD)

Exam Disciplinefinal word

Read each question for which rate the cash flow needs. Write the formula first, substitute second, state the decision last. Budget time by marks; bank the easy short-theory parts early, and keep partial working visible so method marks survive an arithmetic slip.