Vol. I — Time Value of Money & Quantitative Methods
Master the formula,and the exam is just arithmetic. Every question here is generated fresh from the formula itself — and every wrong answer on offer is a real mistake with a name. Learn why each formula works, then prove it under the clock.
Time Value of Money 10 entries F V = P V ( 1 + r ) n FV = PV(1 + r)^n F V = P V ( 1 + r ) n best 0 Drill P V = F V ( 1 + r ) n PV = \frac{FV}{(1 + r)^n} P V = ( 1 + r ) n F V best 0 Drill E A R = ( 1 + r m ) m − 1 EAR = \left(1 + \frac{r}{m}\right)^{m} - 1 E A R = ( 1 + m r ) m − 1 best 0 Drill F V = P V ⋅ e r t FV = PV \cdot e^{r t} F V = P V ⋅ e r t best 0 Drill F V = P M T × ( 1 + r ) n − 1 r FV = PMT \times \frac{(1+r)^n - 1}{r} F V = P M T × r ( 1 + r ) n − 1 best 0 Drill P V = P M T × 1 − ( 1 + r ) − n r PV = PMT \times \frac{1 - (1+r)^{-n}}{r} P V = P M T × r 1 − ( 1 + r ) − n best 0 Drill F V d u e = P M T × ( 1 + r ) n − 1 r × ( 1 + r ) FV_{due} = PMT \times \frac{(1+r)^n - 1}{r} \times (1+r) F V d u e = P M T × r ( 1 + r ) n − 1 × ( 1 + r ) best 0 Drill P V = P M T r PV = \frac{PMT}{r} P V = r P M T best 0 Drill P V = P M T 1 r − g PV = \frac{PMT_1}{r - g} P V = r − g P M T 1 best 0 Drill N P V = − C F 0 + ∑ t = 1 n C F t ( 1 + r ) t NPV = -CF_0 + \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t} N P V = − C F 0 + ∑ t = 1 n ( 1 + r ) t C F t best 0 Drill
Quantitative Methods 14 entries H P R = P 1 − P 0 + D P 0 HPR = \frac{P_1 - P_0 + D}{P_0} H P R = P 0 P 1 − P 0 + D best 0 Drill R ˉ = 1 n ∑ i = 1 n R i \bar{R} = \frac{1}{n}\sum_{i=1}^{n} R_i R ˉ = n 1 ∑ i = 1 n R i best 0 Drill R G = [ ∏ i = 1 n ( 1 + R i ) ] 1 / n − 1 R_G = \left[\prod_{i=1}^{n}(1+R_i)\right]^{1/n} - 1 R G = [ ∏ i = 1 n ( 1 + R i ) ] 1/ n − 1 best 0 Drill R ˉ w = ∑ i = 1 n w i R i , ∑ w i = 1 \bar{R}_w = \sum_{i=1}^{n} w_i R_i, \qquad \sum w_i = 1 R ˉ w = ∑ i = 1 n w i R i , ∑ w i = 1 best 0 Drill s = ∑ i = 1 n ( R i − R ˉ ) 2 n − 1 s = \sqrt{\frac{\sum_{i=1}^{n}(R_i - \bar{R})^2}{n-1}} s = n − 1 ∑ i = 1 n ( R i − R ˉ ) 2 best 0 Drill C V = s X ˉ CV = \frac{s}{\bar{X}} C V = X ˉ s best 0 Drill S = R p − R f σ p S = \frac{R_p - R_f}{\sigma_p} S = σ p R p − R f best 0 Drill S F = R p − R L σ p SF = \frac{R_p - R_L}{\sigma_p} S F = σ p R p − R L best 0 Drill ρ A B = C o v A B σ A σ B \rho_{AB} = \frac{Cov_{AB}}{\sigma_A \sigma_B} ρ A B = σ A σ B C o v A B best 0 Drill E ( X ) = ∑ i = 1 n p i X i E(X) = \sum_{i=1}^{n} p_i X_i E ( X ) = ∑ i = 1 n p i X i best 0 Drill P ( B ) = P ( B ∣ A ) P ( A ) + P ( B ∣ A c ) P ( A c ) P(B) = P(B\mid A)\,P(A) + P(B\mid A^{c})\,P(A^{c}) P ( B ) = P ( B ∣ A ) P ( A ) + P ( B ∣ A c ) P ( A c ) best 0 Drill P ( A ∣ B ) = P ( B ∣ A ) P ( A ) P ( B ) P(A\mid B) = \frac{P(B \mid A)\,P(A)}{P(B)} P ( A ∣ B ) = P ( B ) P ( B ∣ A ) P ( A ) best 0 Drill n C r = ( n r ) = n ! ( n − r ) ! r ! {}_{n}C_{r} = \binom{n}{r} = \frac{n!}{(n-r)!\,r!} n C r = ( r n ) = ( n − r )! r ! n ! best 0 Drill n P r = n ! ( n − r ) ! {}_{n}P_{r} = \frac{n!}{(n-r)!} n P r = ( n − r )! n ! best 0 Drill
Economics 3 entries E d = % Δ Q % Δ P = Δ Q / Q ˉ Δ P / P ˉ E_d = \frac{\%\Delta Q}{\%\Delta P} = \frac{\Delta Q / \bar{Q}}{\Delta P / \bar{P}} E d = %Δ P %Δ Q = Δ P / P ˉ Δ Q / Q ˉ best 0 Drill ( 1 + i ) = ( 1 + r ) ( 1 + π e ) (1 + i) = (1 + r)(1 + \pi^e) ( 1 + i ) = ( 1 + r ) ( 1 + π e ) best 0 Drill M V = P Y MV = PY M V = P Y best 0 Drill
Financial Statement Analysis 7 entries Current = C A C L Quick = C A − Inventory C L \text{Current} = \frac{CA}{CL} \qquad \text{Quick} = \frac{CA - \text{Inventory}}{CL} Current = C L C A Quick = C L C A − Inventory best 0 Drill Net margin = Net income Revenue \text{Net margin} = \frac{\text{Net income}}{\text{Revenue}} Net margin = Revenue Net income best 0 Drill R O E = Net income Average shareholders’ equity ROE = \frac{\text{Net income}}{\text{Average shareholders' equity}} R O E = Average shareholders’ equity Net income best 0 Drill R O E = N I R e v ⏟ margin × R e v A s s e t s ⏟ turnover × A s s e t s E q u i t y ⏟ leverage ROE = \underbrace{\frac{NI}{Rev}}_{\text{margin}} \times \underbrace{\frac{Rev}{Assets}}_{\text{turnover}} \times \underbrace{\frac{Assets}{Equity}}_{\text{leverage}} R O E = margin R e v N I × turnover A sse t s R e v × leverage E q u i t y A sse t s best 0 Drill C C C = D O H + D S O − D P O CCC = DOH + DSO - DPO C C C = D O H + D S O − D P O best 0 Drill g = b × R O E , b = 1 − payout ratio g = b \times ROE, \qquad b = 1 - \text{payout ratio} g = b × R O E , b = 1 − payout ratio best 0 Drill E P S = N I − D p r e f weighted-average common shares EPS = \frac{NI - D_{pref}}{\text{weighted-average common shares}} E P S = weighted-average common shares N I − D p r e f best 0 Drill
Corporate Issuers 5 entries r d a f t e r = r d ( 1 − t ) r_d^{after} = r_d(1 - t) r d a f t er = r d ( 1 − t ) best 0 Drill r p = D p P p r_p = \frac{D_p}{P_p} r p = P p D p best 0 Drill r e = D 1 P 0 + g r_e = \frac{D_1}{P_0} + g r e = P 0 D 1 + g best 0 Drill W A C C = w d r d ( 1 − t ) + w e r e WACC = w_d\,r_d(1-t) + w_e\,r_e W A C C = w d r d ( 1 − t ) + w e r e best 0 Drill D O L = S − V C S − V C − F = contribution operating income DOL = \frac{S - VC}{S - VC - F} = \frac{\text{contribution}}{\text{operating income}} D O L = S − V C − F S − V C = operating income contribution best 0 Drill
Equity Investments 3 entries E V = Market cap + Debt − Cash EV = \text{Market cap} + \text{Debt} - \text{Cash} E V = Market cap + Debt − Cash best 0 Drill P c a l l = P 0 1 − I M 1 − M M P_{call} = P_0\,\frac{1 - IM}{1 - MM} P c a l l = P 0 1 − M M 1 − I M best 0 Drill P 0 E 1 = p r − g \frac{P_0}{E_1} = \frac{p}{r - g} E 1 P 0 = r − g p best 0 Drill
Fixed Income 8 entries C Y = annual coupon price CY = \frac{\text{annual coupon}}{\text{price}} C Y = price annual coupon best 0 Drill P = C × 1 − ( 1 + y ) − n y + F ( 1 + y ) n P = C \times \frac{1-(1+y)^{-n}}{y} + \frac{F}{(1+y)^{n}} P = C × y 1 − ( 1 + y ) − n + ( 1 + y ) n F best 0 Drill P = F ( 1 + z n ) n P = \frac{F}{(1+z_n)^n} P = ( 1 + z n ) n F best 0 Drill M a c D u r = ∑ t = 1 n t ⋅ C F t ( 1 + y ) t P MacDur = \frac{\sum_{t=1}^{n} t \cdot \frac{CF_t}{(1+y)^t}}{P} M a cD u r = P ∑ t = 1 n t ⋅ ( 1 + y ) t C F t best 0 Drill M o d D u r = M a c D u r 1 + y ModDur = \frac{MacDur}{1+y} M o d D u r = 1 + y M a cD u r best 0 Drill M o n e y D u r = M o d D u r × P , P V B P = M o n e y D u r × 0.0001 MoneyDur = ModDur \times P, \qquad PVBP = MoneyDur \times 0.0001 M o n ey D u r = M o d D u r × P , P V B P = M o n ey D u r × 0.0001 best 0 Drill Δ P P ≈ − M o d D u r ⋅ Δ y + 1 2 ⋅ C o n v ⋅ ( Δ y ) 2 \frac{\Delta P}{P} \approx -ModDur \cdot \Delta y + \tfrac{1}{2} \cdot Conv \cdot (\Delta y)^2 P Δ P ≈ − M o d D u r ⋅ Δ y + 2 1 ⋅ C o n v ⋅ ( Δ y ) 2 best 0 Drill ( 1 + z 2 ) 2 = ( 1 + z 1 ) ( 1 + f 1 , 1 ) (1+z_2)^2 = (1+z_1)(1+f_{1,1}) ( 1 + z 2 ) 2 = ( 1 + z 1 ) ( 1 + f 1 , 1 ) best 0 Drill
Derivatives 3 entries F 0 = S 0 ( 1 + r ) T F_0 = S_0 (1 + r)^T F 0 = S 0 ( 1 + r ) T best 0 Drill S 0 + p 0 = c 0 + X ( 1 + r ) T S_0 + p_0 = c_0 + \frac{X}{(1+r)^T} S 0 + p 0 = c 0 + ( 1 + r ) T X best 0 Drill c 0 = π c u + ( 1 − π ) c d 1 + r , π = ( 1 + r ) − d u − d c_0 = \frac{\pi c_u + (1-\pi) c_d}{1+r}, \qquad \pi = \frac{(1+r) - d}{u - d} c 0 = 1 + r π c u + ( 1 − π ) c d , π = u − d ( 1 + r ) − d best 0 Drill
Alternative Investments 2 entries V = N O I cap rate V = \frac{NOI}{\text{cap rate}} V = cap rate N O I best 0 Drill fees = m ⋅ A 1 + i ⋅ max ( A 1 − A 0 − m A 1 , 0 ) \text{fees} = m \cdot A_1 + i \cdot \max(A_1 - A_0 - m A_1,\, 0) fees = m ⋅ A 1 + i ⋅ max ( A 1 − A 0 − m A 1 , 0 ) best 0 Drill
Portfolio Management 5 entries σ p = w A 2 σ A 2 + w B 2 σ B 2 + 2 w A w B ρ A B σ A σ B \sigma_p = \sqrt{w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2 w_A w_B \rho_{AB}\sigma_A\sigma_B} σ p = w A 2 σ A 2 + w B 2 σ B 2 + 2 w A w B ρ A B σ A σ B best 0 Drill β i = C o v ( R i , R m ) σ m 2 = ρ i m σ i σ m \beta_i = \frac{Cov(R_i, R_m)}{\sigma_m^2} = \rho_{im}\,\frac{\sigma_i}{\sigma_m} β i = σ m 2 C o v ( R i , R m ) = ρ im σ m σ i best 0 Drill E ( R i ) = R f + β i [ E ( R m ) − R f ] E(R_i) = R_f + \beta_i\,[E(R_m) - R_f] E ( R i ) = R f + β i [ E ( R m ) − R f ] best 0 Drill α p = R p − [ R f + β p ( R m − R f ) ] \alpha_p = R_p - \left[R_f + \beta_p(R_m - R_f)\right] α p = R p − [ R f + β p ( R m − R f ) ] best 0 Drill T = R p − R f β p T = \frac{R_p - R_f}{\beta_p} T = β p R p − R f best 0 Drill