3/2/26, 4:23 AM Exam Cheat Sheet — Corp Finance — Dang Spring 2026
📊 CORPORATE FINANCE EXAM CHEAT SHEET — DANG SPRING 2026 PAGE — FORMULA MASTER SHEET
TIME VALUE OF MONEY BOND PRICING STATE PRICES & NO-ARBITRAGE
PV — CONSTANT RATE BOND PRICE CORE SYSTEM
ₜ
PV = Σ CF / (1+r)ᵗ P = Σ c/(1+r)ᵗ + F/(1+r)ᵀ Xᵀ · q = p
c=coupon · F=face · r=r_f+spread · X=payoff matrix · q=state prices ·
PV — VARIABLE RATES
T=maturity p=asset prices
PV = CF₁/(1+r₀₁) + Solve → if ALL qᵢ > 0: No Arbitrage
PRIMARY MARKET RULE
CF₂/[(1+r₀₁)(1+r₁₂)] + ... · if any qᵢ ≤ 0: Arbitrage
Coupon rate = Market rate →
NPV ASSET PRICE UNDER NA
NPV = Σ (Rev − ₜ
P = 100
p = x · q = Σ x · q ₛ ₛ
ₜ
Cost )/(1+r)ᵗ − I₀
ZCB YIELD FROM PRICE
ₜ ₜ
p = 1/(1+y )ᵀ → y = ₜ RISK-FREE RATE
YIELD OF INVESTMENT
ₜ
(1/p )^(1/T) − 1
Σqᵢ = 1/(1+r_f) → r_f =
1/(Σqᵢ) − 1
y = (FinalValue /
Rating Spread Rating Spread
Investment)^(1/T) − 1 CALL / PUT PAYOFFS
YTM — SOLVE FOR Y
AAA 0.20% BBB 2.30%
ₛ
Call: max(S − E, 0) Put:
ₜ
P = Σ CF / (1+y)ᵗ [use
AA 0.50% BB+ 2.70% ₛ
max(E − S , 0)
calculator] A+ 0.80% BB 3.40%
PUT-CALL PARITY (R=0)
A 1.20% B+ 3.70%
C + E = S + P → C − P = S −
A− 1.60% B / B− 4..40% E
ALWAYS FALSE: "Higher rates raise COUPON TO PRICE AT PAR
bond prices" — NEVER TRUE
(100 + C) · q₁ = 100 →
solve for C
ALWAYS FALSE: "NA implies flat yield
curve" — NEVER TRUE
CAPM — 8 STEPS (EXECUTE IN ORDER) CAPITAL STRUCTURE & OPTIMAL DEBT
# Formula Compute MM NO TAX
1 r_{i,s} = (CF_s − I) / I Project return per state V_L = V_U [capital structure irrelevant]
2 ₛ
E[rᵢ] = Σ π · r_{i,s} Expected project return MM + TAX
3 ₘ ₘ
r_{m,s} = (x_{m,s} − P ) / P Market return per state V_L = V_U + τD [tax shield = τ · D · r per
4 ₘ ₛ
E[r ] = Σ π · r_{m,s} Expected market return period]
5 ₛ ₘ
Cov = Σ π (r_{i,s}−E[rᵢ])(r_{m,s}−E[r ]) Covariance FULL VALUE (TAX + BANKRUPTCY)
6 Var = Σ πₛ(r_{m,s}−E[rₘ])² Market variance V = [X(1−τ) + τDr − (D/E[X])² · BC] / (1+r)
7 β = Cov / Var Beta OPTIMAL DEBT D*
8 ₘ
μ_CAPM = r_f + β(E[r ] − r_f) Required return D* = τ · r · E[X]² / (2 · BC)
FOC: marginal tax benefit = marginal expected bankruptcy
INVEST if E[rᵢ] > μ_CAPM · NPV = E[X]/(1+μ_CAPM) − I cost
ₛ ₛ
E[X] = Σ π · CF | Entrepreneur min price = NPV
REVERSE-SOLVE FOR TAX RATE Τ
ALWAYS FALSE: "Invest in project with higher expected return" —
τ = 2 · BC · D* / (r · E[X]²)
must compare EACH project to ITS OWN μ_CAPM
WILLINGNESS TO PAY FOR TAX ADVICE
WTP = (τ_new − τ_old) · D · r / (1+r)
PORTFOLIO VARIANCE — 2 ASSETS
σ²_PF = a₁²σ₁² + 2a₁a₂σ₁₂ + a₂²σ₂²
MIN VARIANCE WEIGHT
a*₁ 08:59:18
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GMT σ₁₂) / (σ₁² − 2σ₁₂ + σ₂²)
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, 3/2/26, 4:23 AM Exam Cheat Sheet — Corp Finance — Dang Spring 2026
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📊 CORPORATE FINANCE EXAM CHEAT SHEET — DANG SPRING 2026 PAGE — FORMULA MASTER SHEET
TIME VALUE OF MONEY BOND PRICING STATE PRICES & NO-ARBITRAGE
PV — CONSTANT RATE BOND PRICE CORE SYSTEM
ₜ
PV = Σ CF / (1+r)ᵗ P = Σ c/(1+r)ᵗ + F/(1+r)ᵀ Xᵀ · q = p
c=coupon · F=face · r=r_f+spread · X=payoff matrix · q=state prices ·
PV — VARIABLE RATES
T=maturity p=asset prices
PV = CF₁/(1+r₀₁) + Solve → if ALL qᵢ > 0: No Arbitrage
PRIMARY MARKET RULE
CF₂/[(1+r₀₁)(1+r₁₂)] + ... · if any qᵢ ≤ 0: Arbitrage
Coupon rate = Market rate →
NPV ASSET PRICE UNDER NA
NPV = Σ (Rev − ₜ
P = 100
p = x · q = Σ x · q ₛ ₛ
ₜ
Cost )/(1+r)ᵗ − I₀
ZCB YIELD FROM PRICE
ₜ ₜ
p = 1/(1+y )ᵀ → y = ₜ RISK-FREE RATE
YIELD OF INVESTMENT
ₜ
(1/p )^(1/T) − 1
Σqᵢ = 1/(1+r_f) → r_f =
1/(Σqᵢ) − 1
y = (FinalValue /
Rating Spread Rating Spread
Investment)^(1/T) − 1 CALL / PUT PAYOFFS
YTM — SOLVE FOR Y
AAA 0.20% BBB 2.30%
ₛ
Call: max(S − E, 0) Put:
ₜ
P = Σ CF / (1+y)ᵗ [use
AA 0.50% BB+ 2.70% ₛ
max(E − S , 0)
calculator] A+ 0.80% BB 3.40%
PUT-CALL PARITY (R=0)
A 1.20% B+ 3.70%
C + E = S + P → C − P = S −
A− 1.60% B / B− 4..40% E
ALWAYS FALSE: "Higher rates raise COUPON TO PRICE AT PAR
bond prices" — NEVER TRUE
(100 + C) · q₁ = 100 →
solve for C
ALWAYS FALSE: "NA implies flat yield
curve" — NEVER TRUE
CAPM — 8 STEPS (EXECUTE IN ORDER) CAPITAL STRUCTURE & OPTIMAL DEBT
# Formula Compute MM NO TAX
1 r_{i,s} = (CF_s − I) / I Project return per state V_L = V_U [capital structure irrelevant]
2 ₛ
E[rᵢ] = Σ π · r_{i,s} Expected project return MM + TAX
3 ₘ ₘ
r_{m,s} = (x_{m,s} − P ) / P Market return per state V_L = V_U + τD [tax shield = τ · D · r per
4 ₘ ₛ
E[r ] = Σ π · r_{m,s} Expected market return period]
5 ₛ ₘ
Cov = Σ π (r_{i,s}−E[rᵢ])(r_{m,s}−E[r ]) Covariance FULL VALUE (TAX + BANKRUPTCY)
6 Var = Σ πₛ(r_{m,s}−E[rₘ])² Market variance V = [X(1−τ) + τDr − (D/E[X])² · BC] / (1+r)
7 β = Cov / Var Beta OPTIMAL DEBT D*
8 ₘ
μ_CAPM = r_f + β(E[r ] − r_f) Required return D* = τ · r · E[X]² / (2 · BC)
FOC: marginal tax benefit = marginal expected bankruptcy
INVEST if E[rᵢ] > μ_CAPM · NPV = E[X]/(1+μ_CAPM) − I cost
ₛ ₛ
E[X] = Σ π · CF | Entrepreneur min price = NPV
REVERSE-SOLVE FOR TAX RATE Τ
ALWAYS FALSE: "Invest in project with higher expected return" —
τ = 2 · BC · D* / (r · E[X]²)
must compare EACH project to ITS OWN μ_CAPM
WILLINGNESS TO PAY FOR TAX ADVICE
WTP = (τ_new − τ_old) · D · r / (1+r)
PORTFOLIO VARIANCE — 2 ASSETS
σ²_PF = a₁²σ₁² + 2a₁a₂σ₁₂ + a₂²σ₂²
MIN VARIANCE WEIGHT
a*₁ 08:59:18
This study source was downloaded by 100000900703063 from CourseHero.com on 03-05-2026 = (σ₂² − -06:00
GMT σ₁₂) / (σ₁² − 2σ₁₂ + σ₂²)
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https://www.coursehero.com/file/254327115/Exam-Cheat-Sheet-Corp-Finance-Dang-Spring-2026pdf/
, 3/2/26, 4:23 AM Exam Cheat Sheet — Corp Finance — Dang Spring 2026
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