Valuation M&A Portfolio Mutual Funds Risk Mgmt Corp. Val. FOREX International Finance Derivatives

AFM Formula Sheet

CA Final · Advanced Financial Management · Compiled by Harsh C

Valuation of Securities

65 formulas
#NameFormulaRemark
1Valuation of Bond
Int(1+Kd)1+Int(1+Kd)2+ … +Redemption Value(1+Kd)n
1. While Determining the issue price make sure to take the "as to yield %" ie (Company's POV)2. Interest is not paid per annum - Discount and Coupon Raten , Time × n3. Transaction cost should be added with PVCO4. If β is given in question then market price shall be Intrinsic value × β
2Time Value
FV = PV × (1+r)n
PV = FV(1+r)n
3Current Yield
Annual InterestMarket Price×100
4Realized Yield
FV = PV × (1+r)n
5Yield to Maturity (Approx.)
YTM = Int + RV − MPNRV + MP2
Interpolation: L + V₀ − V₁V₀ − V₂ × (H − L)1. Wordings in Question - "Prevailing Interest on the similar Type"2. Equivalent bond % given and asked to show the spread - which means YTM% - % of equivalent bond = Spread.3. Tax Rate given in Question - Interest(1−t), Capital Gain(1−t)
6Forward Rates
(1+YTM)2 = (1+f₁)(1+f₂)
7Macaulay's Duration
Σ t × PV of CFΣ PV of all CF
t = year in which CF is received
Note: if Interest rate fall, Price will increase, buy long duration bonds vice versa.Increase in DF will reduce MD.1. Duration shall be given in question and asked to calculate Market price - just follow the stepsYTM not equal to coupon rate, so take the coupon rate as "x" and solve it.
8Modified Duration (Volatility)
Macaulay's Duration1 + YTM (Existing)
Modified Duration × Δ int. rates (+/−) → Price (−/+)
Change in price for 1% change in YTM.1. In case increase/decrease in rate is given based on Modified duration (volatility) the revised price shall be find, also it can be cross verified by applying PVCI calculation with revised rate (approx. match)
9Convexity
C = V₊ + V₋ − 2V₀2V₀ × (ΔYTM)²
Convexity Effect = C × (ΔYTM)² × 100
Corrects non-linear price change from modified duration.
10Valuation of Preference Shares
Redeemable:PD₁(1+Kp)1+PD₂(1+Kp)2+…+RVn(1+Kp)n
Irredeemable:DividendKp [g=0%]
11Gordon's Growth Model
P₀ = D₁Ke − g
12CAPM → Ke
Ke = Rf + (Rm−Rf) × β
(Rm−Rf) = Market Risk Premium
13Gordon's Formula → Ke
Ke = D₁P₀ × 100 + g
D₀ = "Company's Last Dividend Paid"D₀ = "Company's just declared a dividend"D₁ = "Company Pays Dividend"1. Investor's expected x% of return and Marginal tax is y% then Cost of Equity is x(1−y)2. Whenever inflation premium given in question make sure to include that in RM and RF
14Earning Yield → Ke
Ke = EPSMPS × 100
∴ Ke = 1P/E Ratio × 100
MPS = EPS × P/E
15Dividend Yield → Ke
Ke = D₁P₀ × 100
16FCFE
+PAT (after Int. & Pref. Dividend)
+Depreciation
−/+Increase / Decrease in WC
−/+Increase / Decrease in FA
−Borrowings / Pref. Shares Repaid
+Borrowings Taken / Pref. Shares Issued
Value of Equity = FCFEKe − g
If Debt Ratio (D) given → multiply all items incl. depreciation by (1 − D).
FA purchase can be debt-funded; adjust debt component separately.If FCFE given is CURRENT (FCFE₀):
   P₀ = FCFE₀ × (1+g)Ke − gIf FCFE given is NEXT YEAR (FCFE₁):
   P₀ = FCFE₁Ke − g
17FCFF
+PAT + Int.(1−T) or EBIT(1−T)
+Depreciation + Pref. Dividend
−/+Increase / Decrease in WC
−/+Increase / Decrease in FA
Value of Firm = FCFFWACC − g
Firm-level CF → borrowings NOT separately considered.
18Earnings Growth Model
P₀ = E₁Ke − g
19P/E Multiple Approach
P₀ = EPS × Implied P/E
Implied P/E = 1Ke × 100
ICAI assumes ROE = Ke
20Yield Method (VPS)
VPS = Actual Yield %Normal Yield % × Paid-up Value per Share
Actual Yield % = Actual Yield (₹)Paid-up ESC  |  Normal Yield % = Normal Rate ± Risk Adj.
If method not given, use (PAT − Pref. Dividend) as actual yield.In Question the ratio will be given and asked to find the value per share in this case need to find the adjust normal Yield %Steps:1. Find the Yield in Rs. Either instruction to find will be given or take PAT − Pref. Dividend.2. Convert that into x%  →  Yield % = Yield (₹)Equity Share Capital × 1003. Make the Adjustment in Normal Yield % based on the ratio and instruction given in the question.4. Finally apply the Yield formula → VPS = Actual Yield %Normal Yield % × Paid-up ValuePAT − Pref. Dividend = what is AVAILABLE for equity

Out of that:
  Some is PAID as Dividend  →  goes into Yield formula
  Rest is RETAINED  →  goes to Reserves
21Walter's Model
P₀ = D + (E−D) × rKeKe
r > Ke → 0% payout  |  r < Ke → 100%  |  r = Ke → Indifferent
22Run Test
μ = 2N₁N₂N₁+N₂ + 1
σ = √2N₁N₂ x (2N₁N₂−N₁−N₂)(N₁+N₂)²×(N₁+N₂−1)
N₁ = positive signs  |  N₂ = negative signs
Also read from book for full steps.Upper Limit: μ + t × σ
Lower Limit: μ − t × σ
23Auto Correlation
X̄ = ΣXN  ,  Ȳ = ΣYN
Covariance = Σ(x−X̄)(y−Ȳ)N
Correlation = Covarianceσx×σy
Divide data into X & Y series. Also read from book.
24Technical Analysis
EMA = 2n + 1
Date(1) NIFTY(2) EMAprev(3) = (1) − (2)(4) = (3) × EMANew EMA = (2) + (4)
………………
25Post-Issue MP per Share
Post-issue Market CapitalisationPost-issue Number of Shares
26Sustainable Growth Rate
g = r × b
b = 1 − Dividend Payout Ratio  |  r = ROE = PAT / Eq. SHF
27Valuation of Right Shares
Ex-right = (Cum-right Price × Shares Held) + (Issue Price × Shares Allotted)Shares Held + Shares Allotted
Value of Right = Ex-right Price − Right Issue Price
28Valuation of Buyback
Assume Net Profit & P/E remain same pre & post buyback (unless stated).
When Post Market Capitalisation is given:
Post Market Cap = (Old No. of Shares − Buyback No. of Shares) × Post MPS
Example:
180 L = (10 L − (24 L / x)) × 1.1x
Solve "x" → you get the Buyback Price
Q: Calculate the Interest amount, loan taken and Premium on buyback for Buyback of shares.1. Calculate PAT using EPS and No. of shares Post Buyback and Pre Buyback, then back-calculate to EBT. Compare Pre and Post — the difference is the Interest amount.2. Back-calculate with rate of interest to get the Loan amount.3. Divide the Loan amount by No. of shares bought back → Buyback Price. The difference between Post MPS and Buyback Price = Premium.
29Warrant
Intrinsic Value = (MP of ES − Exercise Price) × Exercise Ratio
Warrant Premium = MP of Warrant − Intrinsic Value
30Conversion Value
MPS of Equity × Conversion Ratio
31Straight Value
PV of future coupons + PV of Redemption Value
32Theoretical Value
Higher of { Conversion Value , Straight Value }
33Conversion Premium
MP of Convertible Bond − Conversion Value
34Downside Risk / Premium over Straight Value
MP of Bond − Straight Value
35Conversion Parity Price
Market Price of BondConversion Ratio
36Income Differential
Annual Int. per Bond − (Annual Dividend per Share × Conversion Ratio)
37Premium Payback Period
Conversion Premium per BondFavourable Income Differential
38Bond Equivalent Yield
BEY = F−PP × 100 × 365Days
Effective Rate = ( 1 + BEYM )M − 1
M = no. of compounding periods per year
39Repo
1st Transaction (Loan)
+Clean Price + Accrued Interest = Dirty Price
−Margin = Proceeds
2nd Transaction (Repayment)
+Proceeds + Interest on Repo = Repayment
Clean = Ex-Int.  |  Dirty = Cum-Int.
40Asset Turnover Ratio
SalesTotal Assets
41Operating Margin
EBITSales × 100
Note: EBIT = Operating Income
42Coverage Ratio
PAT + Fixed InterestFixed Interest + Fixed Pref. Dividend
43Capital Gearing Ratio
Debentures + PSCESC + Reserves (Equity SHF)
44Return on Equity
PATEquity Share Capital + Reserves
Ratios
45Return on Capital Employed
EBITEquity Share Capital + Reserves + Debt (Borrowings)
Ratios
46Book Value per Share
Equity Share Capital + Reserves − Preference Share CapitalNumber of Equity Shares
Ratios
47Earnings Per Share
PAT − Preference DividendNumber of Equity Shares
Ratios
48Asset Turnover
SalesTotal Assets
Ratios
49Operating Margin
EBITSales
Ratios
50Dividend Payout Ratio
Dividend PaidPAT
Ratios
51Capital Gearing Ratio (Detailed)
Debentures + Preference Share CapitalEquity Share Capital + Reserves
Ratios
52Coverage Ratio (Detailed)
PAT + Fixed InterestFixed Interest + Preference Dividend
Fixed Interest can also be added back net of tax
Ratios
53Total Assets
Debt + Equity
Basics
54Ratio (Cross Multiplication)
When values given as x : y → cross multiply to find unknown
Sales : (STL + Payables) 4 : 3 720 : ? ? = 720 × 3 ÷ 4 = ₹ 540
Basics
55Immunised Portfolio
WA·DA + WB·DB + WC·DC
W = Weights  |  D = Duration (calc. as per Macaulay's Duration)
The Immunised portfolio should be equal to the "outflow scheduled in x Years"
56Fund Rebalancing
Step 1 — PV of Benefits
A = (rold − rnew) × FV × (1 − t) × PVIFA(r, n)
B = (New Flotationn − Old Amort) × t × PVIFA(r, n)
C = Unamortised Old Flotation × t
Step 2 — Cash Outflows
D = Call Premium × (1 − t)
E = New Flotation Cost  [Gross, no tax]
F = Net Overlapping Interest × (1 − t)
   Net Overlapping Interest = Interest on Old Bond − Income earned on reinvested new proceeds
Step 3 — NPV
NPV = (A + B + C) − (D + E + F)
r = rnew × (1 − t)  |  n = Life of New Bond
Make sure to take the discounting factor as "After tax cost of debt"
57Multi Stage Dividend Growth Model
Variable Growth Rate — g changes each year
Step 1 — Calculate Dividends
D₁ = D₀ × (1 + g₁)
D₂ = D₁ × (1 + g₂)
Dₙ = Dₙ₋₁ × (1 + gₙ)
Step 2 — PV of Each Dividend
PV(Dₜ) = Dₜ(1 + Ke)ᵗ → Sum all = A
Step 3 — Terminal Value
TV = Dₙ × (1 + gstable)Ke − gstable
B = TV(1 + Ke)ⁿ
TV computed at end of last year of variable g
Step 4 — Intrinsic Value
P₀ = A + B
Note: There are adjustment related to the Terminal value related to change in Cost of Equity, Growth, and Dividend payout ratio.Question wordings = "He expects the market price of this share to be Rs. X" this means the TV is given in question
58Change in MPS
Change in MPS due to Bonus Share, Stock Split & Reverse Stock Split
Revised Price = P₀ × No. of Shares (Before)No. of Shares (After)
59Market Capitalization
MPS × No. of Shares
60Efficient Market Hypothesis
EMH — Expected Share Price After New Issue
Semi-Strong Form: Price reflects all public info
New P₀ = New Total Market ValueTotal Shares
Step 1 — Old Market Value
Old MV = Existing Shares × Current Price
Step 2 — Adjustments
ALWAYS ADD: A = Gross Proceeds of New Issue  |  B = NPV of New Project
ALWAYS DEDUCT: C = Flotation Cost (Gross Proceeds × Flotation %)
IF BOND REDEEMED EARLY → ±D = PV of future outflows − Redemption cost now
IF SURPLUS INVESTED → +E = PV of Surplus Investment Income
Step 3 — New MV & Price
New MV = Old MV + A + B − C ± D + E
New P₀ = New MVOld Shares + New Shares
Weak Form→ Correlation ≈ 0 (near zero — past prices cannot predict future)Semi-Strong Form→ Correlation = 0 (exactly zero for all public info)Strong Form→ Correlation = 0 (zero for all info — public + private)Semi - Strong Market:CREATES value→ ADD to Old MVDESTROYS value→ DEDUCT from Old MVNew cash raised (gross)→ ALWAYS ADD (it sits in firm)Flotation→ ALWAYS DEDUCT (wasted cost)
61Efficient Market Hypothesis (Weak Form Test)
Steps to test Weak Form:
1. Trade data list is given
2. Lag of n days → create series X and Y (n items apart)
3. X̄ = ΣXN  |  Ȳ = ΣYN
4. σx, σy, COVxy
5. r = COVxyσx · σy
6. If r ≈ 0 → Weak Form holds
62External Fund Requirement
ASSETS SIDE
Inventory, Receivables, Cash → Scale with sales  |  Fixed Assets → Don't scale
LIABILITIES SIDE
Payables, Provisions → Scale  |  Share Capital, Reserves, LTL, STL → Don't scale*
*Unless specific ratio or info given
EFR = Scaled Assets − Scaled Liabilities − Retained Earnings
p = PATSales  |  r = 1 − Dividend Payout Ratio  |  Retained Earnings = p × S₁ × r
63EBITDA – PAT
 EBITDA
−Depreciation
 EBIT
−Interest
 EBT
−Tax
 EAT (PAT)
If in question EBIT is given that means it is after Depreciation (don't subtract the depreciation again)
64DuPont Analysis
ROE = Net ProfitSales × SalesTotal Assets × Total AssetsEquity
Note: Total Assets = Equity + Debt
65Cost of Capital (KO)
WACC = WE × Ke + WD × Kd
If Tax is given then Post-Tax cost of Debt shall be taken

Merger & Acquisition

10 formulas
#NameFormulaRemark
1Post-Merger EPS
Pre PAT(A) + Pre PAT(T) + SynergiesPre Shares(A) + Pre Shares(T) × Exchange Ratio
2Exchange Ratios
Favourable to Target = Target (T) factorAcquirer (A) factor
Adverse to Acquirer = Acquirer (A) factorTarget (T) factor
3Book Value per Share
Eq. Share Capital + ReservesNo. of Shares or Total Assets − LiabilitiesNo. of Shares
4Return on Equity (ROE)
PATEquity Shareholders' Fund × 100
5Capital Adequacy Ratio (CAR)
Share Capital + Reserves & SurplusRisk Weighted Assets × 100
6Gross NPA %
Gross NPA (₹)Advances × 100
7Equal Annual Installment (EAI)
Value of DebtPVAF (Int. Rate, N)
N = no. of years for which debt is taken
Covers Principal + Interest.
8Post-Merger MPS (Different Growth Rates)
Step 1: Ke = D₁P₀ + g (existing)
Step 2: P₀ = D₁Ke − g (revised)
Use Market Cap for post-merger price, not PAT.
9Calculation of Premium
Cash: Cash Paid (Total) − Pre-Merger Mkt. Cap (T)
Swap: (Shares Issued × Post MPS) − Pre-Merger Mkt. Cap (T)
10Economic Value Added (EVA)
EVA = NOPAT − (Capital Employed × WACC)
Capital Employed = ESC + PSC + Reserves + Debt − Fictitious Assets
MVA → use Market Weights
EVA Dividend = EVA (Calculated)Equity Shares
Note: NOPAT = PAT + Interest(1−t)  or  EBIT(1−t)
Unrecognised assets → treat as equity.Q: "Company has 6L equity shares outstanding. How much dividend can the company pay before the value of the entity starts declining?" → Use EVA Dividend formula.

Portfolio Management

17 formulas
#NameFormulaRemark
1Single Security Return
Single Year = P₁−P₀+DP₀ × 100
Multi Year (Simple) = Pₙ−P₀+DP₀ × 100 × 1N
Compound: Pₙ = P₀(1+r)n
Use Ex-dividend or Ex-bonus price for P₁ & P₀.
2Single Security Risk (σ)
σ = √Σ(x−x̄)²√N
If probability: σ = √Σp(x−x̄)²
3Portfolio Return
Rxy = WxRx + WyRy
Weights = Amount invested at beginning of year
4Portfolio Risk – Markowitz
σxy = √( Wx²σx² + Wy²σy² + 2·Wx·Wy·σx·σy·rxy )
(a+b)²=a²+b²+2ab
5Covariance
COVxy = Σ(x−x̄)(y−ȳ)N or Σp(x−x̄)(y−ȳ)
COVxy = βx·βy·σm² (method 3)
COVxy = ΣXY − NX̄ȲN (method 4)
6Correlation Coefficient (r)
rxy = COVxyσx·σy
COVxy = rxy·σx·σy
7Minimum Variance Portfolio
Wx = σy² − COVxyσx² + σy² − 2·COVxy
Wy = 1 − Wx
8Beta (β)
β = rsm·σsσm = COVsmσm² = ΣXM−NX̄M̄ΣM²−NM̄²
2 obs.: β = ΔReturn of SecurityΔReturn of Market
9Portfolio Beta
βxy = Wx·βx + Wy·βy
10Characteristic Line
X = α + β·M
α = X̄ − β·M̄
11Capital Market Line (CML)
Ke = Rf + Rm−Rfσm × σs
(Rm−Rf)/σm = Market Risk Reward Tradeoff Ratio
12Systematic & Unsystematic Risk
Systematic Risk = rsm²·σs²
Unsystematic Risk = Total Risk − Systematic Risk
13Portfolio Risk – Sharpe Index
σxy = √( βxy²·σm² + Wx²·Ex² + Wy²·Ey² )
14Performance Measures
Sharpe = Rx−Rfσx
Treynor = Rx−Rfβx
Jensen's α = Rx − Ke
15Arbitrage Pricing Theory (APT)
Ke = Rf + λf₁·βf₁ + λf₂·βf₂ + …
λ = Actual − Expected
16Sharpe Optimal Portfolio
i)
Treynor = Rx−Rfβx → rank descending
ii)
Cx = σm² × Σ (Rx−Rf)·βxEx²1 + σm² × Σ βx²Ex² (cumulative)
iii)
Zx = βxEx² × ( Rx−Rfβx − C* )
Ex² = Unsystematic Risk  |  C* = final cut-off point
17Private Company Valuation
βA = βE × ED(1−T)+E [Proxy Co.]
βE = βA × D(1−T)+EE [Valuation Co.]
βA = Asset + Debt Beta.
Key Points – Portfolio Management
  • Always take weights in decimal, standard deviation in %.
  • r² = Coefficient of Determination.

Mutual Funds

6 formulas
#NameFormulaRemark
1Net Asset Value (NAV)
NAV = Net Assets (Fair Value)No. of Units
+MV of all Investments + Cash/Bank
+Receivables (Dividend / Interest)
−Liabilities = Net Assets
2Investor's Return (Annualized)
Rmf = NAV₁−NAV₀+DNAV₀ × 100 × 12N
3Dividend Re-investment Plan (DRIP)
Return = Total NAV₁ − Total NAV₀Total NAV₀ × 100 × 12N
New Units = Total DividendNAV at dividend distribution date
4Dividend Equalisation (D.E.)
DE p.u. = Income earned during periodExisting units during period
Added irrespective of issue/redemption. Entry/exit load on Opening NAV (excl. D.E.).
5Constant Ratio StrategyMaintain a constant debt-equity ratio throughout the investment horizon.
6CPPI
i)Find maximum possible fall
ii)Floor Value = Original Portfolio Value − Max. Fall
iii)Cushion = Portfolio Value − Floor Value
iv)Allocation to Equity = Cushion × Multiplier (default = 1)
Floor stays constant. Recalculate at each rebalancing date.
Key Points – Mutual Funds
  • Entry Load (Front-end) → Added to Opening NAV
  • Exit Load (Back-end) → Deducted from Redemption NAV

Risk Management

1 formula
#NameFormulaRemark
1Value at Risk (VAR)
VAR = Daily σ(₹) × Z value × √Days
VAR = Portfolio σ × Portfolio Value (₹)
Z values:
99% confidence → 2.33
95% confidence → 1.65
90% confidence → 1.29

Corporate Valuation and Allied

3 formulas
#NameFormulaRemark
1Net Assets Method (NAV)
Total Assets − Total Liabilities − Pref. Share CapitalNo. of Equity Shares
Fictitious assets should be ignored
Have to consider MV
2Enterprise Value / Firm Value (Multiple Approach)
EV = Equity Value + Debt Value
= PAT × P/E ratio
= EBIT × EV/EBIT ratio
3Earning Capitalisation Approach
Equity Value = PAT + DepreciationKe
Firm Value = PAT + Depreciation + Interest (= EBITDA, without tax)Ko

Foreign Exchange (FOREX)

26 formulas
#NameFormulaRemark
1Hedge Efficiency
Gain on futuresLoss on spot × 100
2Real Appreciation / Depreciation (Currency)
Implied fwd rate − Actual fwd rateActual fwd rate × 100
Without inflation effect.
3Real Return
1 + rnominal = (1 + rreal)(1 + rinflation)
Based on Sensex return
Return over and above Indian inflation.
4Return for Indian Investor from US Bond
Ke = (1 + rBond)(1 + r$) − 1
Risk free return → $
5Direct Quote
Units of home currencyUnits of foreign currency
e.g. ₹50/$ → Non base / Base currency
6Indirect Quote
1Direct Quote
7Spread
Ask Rate − Bid Rate
8Inflation Rate Parity
FS = (1 + inon base)n(1 + ibase)n
Annual compounding assumed. If <1 yr: use M/12 or Days/365
9Interest Rate Parity Theory
FS = (1 + rNB)(1 + rB)
NB = Non base  |  B = Base. Annual compounding assumed.
10Forward Premium / Discount
On Base Currency:
F − SS × 100 × 12M
On Non-Base Currency:
S − FF × 100 × 12M
11Swap Points
Ascending → Add (from right side)
Descending → Deduct (from right side)
If swap points in % or currency, ignore right-side rule.
12Covered Interest Arbitrage
Implied fwd < Actual fwd → Base Overvalued → Sell base fwd, Buy base spot, Borrow non-base
Implied fwd > Actual fwd → Base Undervalued → Buy base fwd, Sell base spot, Borrow base
Shortcut: Overvalued → borrow non-base. Undervalued → borrow base.
13Money Market Hedging
Importer: Foreign Liability → Hedge: Asset (Foreign) → Borrow Local
Exporter: Foreign Asset → Hedge: Liability (Foreign) → Borrow Foreign
14Leading & Lagging
Leading → Add interest cost
Lagging → Deduct interest
Use borrowing cost of capital of home currency
If both rates given → use borrowing rate (unless surplus funds → deposit rate).
15Currency FuturesRead thoroughly from the book
16Cancellation of Forward Contract
Take reverse (off-setting) contract
Before due date: At fwd rate of balance unexpired period
On due date: At spot rate of cancellation date
Not futures (those are tradable).
17Extension of Forward Contract
i)Cancel as above
ii)Take fresh fwd for new extended period
18Early Delivery of Forward Contract (FEDAI)
a.Settle original fwd at agreed rate
b.Bank: Importer → Spot buy  |  Exporter → Spot sell
c.New forward to reverse offset: Importer → Fwd sell  |  Exporter → Fwd buy
d.Swap cost → (Diff. b&c) × Contract Value
e.Interest → (Diff. a&b) × rate × D/365
Total charges = Swap cost ± Interest
Positive → Transfer to customer. Negative → Recovered from customer.
19Late / Automatic Cancellation (Rule 6 of FEDAI)
a. Exchange diff = Agreed fwd vs Spot actual cancellation
Importer → Spot sell  |  Exporter → Spot buy
b. Swap loss = Spot (30/11) vs Fwd earliest
Importer → Fwd buy  |  Exporter → Fwd sell
c. Interest = Spot (30/11) vs Off-setting rate
All formulas for $1; multiply by contract size for total.
20Issue Price per GDR
Issue price per share × No. of shares per GDR × Exchange rate
21Transaction Exposure
When transaction is unhedged:
Gain/(Loss) = Spot rate − Actual fwd rate
22Translation Exposure
Notional gain/loss from translating financial statements of foreign branch or subsidiary
23Operating Exposure
= Transaction exposure ± Gain/Loss due to change in demand
Gain/Loss = Profit per unit × Change in qty demanded
Change in qty = % change in price for customer × Elasticity
24Daily Balance (Margins)
Initial Margin = μ + 3σ
μ = Daily Absolute Change
σ = Standard Deviation
25Money Market Cover
Logic: Create a NATURAL HEDGE using deposits & borrowings — Do everything TODAY → eliminate future uncertainty
FOR PAYABLE (need to pay FC later)
1.FC Deposit = FC Payable ÷ (1 + FC deposit rate × n/12) — Use DEPOSIT rate of FOREIGN country
2.Buy that FC at SPOT today: Home Currency needed = FC Deposit ÷ Spot BID rate — Selling Home Currency → Bank Buys Home Currency → BID rate
3.Borrow home currency today to fund Step 2: Home Currency borrowed = same as Step 2
4.Repay home borrowing on due date: Repayment = Home borrowed × (1 + Home borrow rate × n/12) — Use BORROWING rate of HOME country — This repayment = your FINAL COST
FOR RECEIVABLE (will receive FC later)
1.FC Borrowed = FC Receivable ÷ (1 + FC borrow rate × n/12) — Use BORROWING rate of FOREIGN country
2.Convert FC to home currency at spot today: Home Currency = FC Borrowed × Spot BID rate — Selling FC → Bank buys FC → BID rate
3.Deposit home currency today — Same amount as Step 2
4.Collect deposit on due date: Receipt = Home deposit × (1 + Home deposit rate × n/12) — Use DEPOSIT rate of HOME country — This receipt = your FINAL RECEIPT
Memory Aid:   PAYABLE → Deposit FC | Borrow Home  |  RECEIVABLE → Borrow FC | Deposit Home  |  Always OPPOSITE actions in each currency
26Currency Options
STEP 1 — CHECK INVOICE vs BASE CURRENCY
Base Currency = currency quoted FIRST in futures.  Invoice = Base? YES → use invoice amount directly.  NO → convert Invoice to Base using OPENING FUTURES PRICE (only to find number of contracts — nothing else).
Example: Invoice = EUR 2,00,000 | Futures = Rs./$ → Base = $ | EUR ≠ $ → Convert: 2,00,000 × 1.10 (Opening Futures EUR/$) = $2,20,000 ← use this for contracts only
STEP 2 — IDENTIFY HEDGE STRATEGY
Look at ORIGINAL INVOICE transaction only.
PAYABLE → you will PAY FC in future → fear = FC will APPRECIATE → BUY futures ✔
RECEIVABLE → you will RECEIVE FC in future → fear = FC will DEPRECIATE → SELL futures ✔
STEP 3 — NUMBER OF CONTRACTS
Contracts = Invoice Amount (in Base $)Contract Size ($)  (always round to whole number)
STEP 4 — OPEN THE HEDGE
State clearly: "BUY / SELL [N] contracts at [Opening FUTURES Price Rs./$]"
STEP 5 — PREMIUM (Options only)
Premium in invoice currency → convert to home currency at OPENING SPOT rate
Premium (Rs.) = Contracts × Contract Size × Premium per unit ÷ Opening SPOT (Rs./$)
Premium PAID on Day 1 → Opening SPOT. Always a COST → deduct from receipt or add to payment.
STEP 6 — FIND UNHEDGED AMOUNT
Hedged ($) = Contracts × Contract Size  |  Hedged (Invoice) = Hedged $ ÷ Opening Futures Rate  |  Unhedged = Original Invoice − Hedged Invoice → transact at CLOSING SPOT rate
STEP 7 — GAIN / LOSS ON FUTURES
BUY position: Gain = (Closing Rs./$ − Opening Rs./$) × Contracts × Contract Size
SELL position: Gain = (Opening Rs./$ − Closing Rs./$) × Contracts × Contract Size
Always on Rs./$ futures price — never on converted cross rate.
STEP 8 — ACTUAL PAYMENT / RECEIPT
At CLOSING SPOT on due date: PAYABLE → Payment = Invoice × Closing SPOT ASK (Rs./$)  |  RECEIVABLE → Receipt = Invoice × Closing SPOT BID (Rs./$)
If cross currency: Rs./Invoice = Rs./$ × $/Invoice currency (at closing spot rates)
STEP 9 — INTEREST ON MARGIN (Futures only)
Interest = Margin × Rate × Days/365  |  Margin blocked = Contracts × Margin per contract
Always a COST: PAYABLE → Add to effective cost  |  RECEIVABLE → Deduct from effective receipt
STEP 10 — EFFECTIVE COST / RECEIPT
PAYABLE RECEIVABLE Actual Payment (Step 8) Actual Receipt (Step 8) Less: Futures Gain (Step 7) Add: Futures Gain (Step 7) Add: Premium (Step 5)* Less: Premium (Step 5)* Add: Interest (Step 9)† Less: Interest (Step 9)† ──────────────────────────── ───────────────────────────── = Effective Cost = Effective Receipt * Options only † Futures only
Decision: PAYABLE → Lowest cost = Best ✔  |  RECEIVABLE → Highest receipt = Best ✔
Key Points – FOREX
  • Bid/Ask selection: Purchase ₹ & base ₹ → Ask rate. Purchase ₹ & base £ → Bid rate.
  • Options – same currency: Importer → Buy Call  |  Exporter → Sell Put
  • Options – different currency: Importer → Buy Put  |  Exporter → Sell Call
  • Call option viable: Sx > Ex  |  Put option viable: Sx < Ex

International Financial Statement

5 formulas
#NameFormulaRemark
1Net Present Value (NPV)
NPV = PVCI − PVCO
Positive → Accept  |  Negative → Reject
2Evaluation of Project
Home Approach:
i)Convert foreign CF using forward rates (if not given, use IRP/Inflation Parity)
ii)Discount using home currency discount rate
Foreign Currency Approach:
i)Discount at foreign discount rate
ii)NPV in foreign currency → convert at today's spot rate
3Calculation of Foreign Discount Rate
(1 + K) = (1 + Rf)(1 + Re)
i)Calculate risk premium using home cost & risk-free rate
ii)Apply same risk premium + foreign risk-free rate
Rf differs by country. Risk premium (Re) stays same unless stated.
4Nominal & Real Cash Flows
Nominal → with inflation  |  Real → without inflation
Nominal CFs discounted at nominal rate  |  Real CFs at real rate
5Adjusted NPV
Modify NPV by discounting different CFs with the rate consistent with that specific CF

Derivatives Analysis and Valuation

14 formulas
#NameFormulaRemark
1Theoretical Future Price
Non-dividend paying stock:
Annual: F = S(1+r)N (if <1yr: F = S(1+r×M/12))
Other compounding: F = S(1+r/m)N×m
Continuous: F = S·erN  e=2.71828, N=years
Dividend paying stock:
F = S(1+r×M/12) − D(1+r×t/12) t = months in contract after dividend
At end: F = S(1+r×M/12)−D  |  At beginning: F = (S−D)(1+r×M/12)
Futures don't provide dividend compensation ∴ deducted.
2Index Future HedgingRefer immediately from book
3Index Futures with Dividend
F = S(1 + (r−d)×M/12)
Continuous: F = S·e(r−d)n  |  d = dividend yield % p.a.
In index, dividend % applied on spot price, assumed uniform p.a.
4Commodity Theoretical Future Price
= Spot price + Cost of carry + Storage cost − Convenience yield
(Time value should be adjusted)
5Hedge Ratio (β) for Commodities
β = rsm × σsσF
rsm = correlation  |  S = Spot  |  F = Futures
No. of contracts = Portfolio × βFutures contract size
6Margin (Applicable in Futures)
Initial margin = μ of daily absolute change + 3σ of those absolute changes (₹)
Maintenance margin = 70–80% of initial margin.
7Payoff
Gross gain earned by holder on exercise (without premium)
Call → Sx − Xp  |  Put → Xp − Sx
Holder → + or Nil  |  Writer → − or Nil
Nil when not exercised.
8Net Payoff
Holder: Payoff − Upfront premium
Writer: Payoff + Upfront premium
Can be positive, negative or nil.
9Theoretical Option Value
C₀ = S₀ − PV of Xp
P₀ = PV of Xp − S₀
Answer cannot be negative — treat as nil if negative.
10Binomial Option Value
a) Replicating Portfolio Approach
b) Risk-Less Hedge
c) Risk Neutral Probabilities: S₀ = [S₁(p) + S₂(1−p)] / (1+r×M/12)
Multi-stage American option: compare each C₀ with (Spot−Xp), take higher
Very important — read from book immediately.
11Black & Scholes Model
C₀ = S₀ × N(D₁) − Xpert × N(D₂)
D₁ = IN(S₀/Xp) + (r + σ²/2)tσ√t
D₂ = D₁ − σ√t
IN[S₀/X₀] = log₁₀(S₀/Xp) / log₁₀e  |  log₁₀e = 0.4343
If dividend: S₀ = S₀ − D/ert
Refer all steps from book.
12Option Greeks
Delta: Change in premium per ₹1 increase in spot → Call: +ve  |  Put: −ve
Gamma: Change in delta per ₹1 increase in spot → Both: +ve
Vega: Change in premium per 1% increase in volatility → Both: +ve
Theta: Change in premium per 1 day less to expiry → Both: −ve
Rho: Change in premium per 1% increase in interest rate
13Call Put Parity Theory
P₀ + S₀ = C₀ + PV of Xp
P₀ = Put premium  |  C₀ = Call premium  |  Xp = Exercise price
14Black & Scholes (Continuous Compounding)
C₀ = S₀ × N(D₁) − Xpert × N(D₂)
D₁ = IN[S₀/X₀] + [r + σ²/2] × tσ√t
D₂ = D₁ − σ√t
e = 2.71828  |  t = months/12
Key Points – Derivatives
  • Exercise price = Strike price. European → exercised only at expiry. American → any time.
  • Straddle: Buy 1 call + Buy 1 put (same ex-price & expiry)
  • Strip: Buy 1 call + Buy 2 puts  |  Strap: Buy 2 calls + Buy 1 put (same ex-price & expiry)
  • Strangle: Buy 1 call + Buy 1 put (different ex-prices or expiry)
  • Butterfly: Long 2 extreme exercise prices + Short 2 calls at middle exercise price
  • Basis = Spot − Future → Negative = Contango  |  Positive = Backwardation
  • 1 MT = 1000 Kgs

AFM Formula Sheet · CA Final · Compiled by Harsh C