Option Valuation - CA Final SFM

Binomial Model

Formula	Remarks
VOC = P x Cu + (1 – P) x Cd                            R	Where, R = 1 + Rf Cu = Call Upside Gain Cd =  Call Downside Gain Pu = Put Upside Gain Pd =  Put Downside Gain d = ds  (expected downside price divided by spot price)        s u = us  (expected upside price divided by spot price)        s
VOC = P x Pu + (1 – P) x Pd                            R
P = R – d        U – d
Value of American Option  =  Max of Discounted Value or Intrinsic Value

Put Call Parity Theory (PCPT)

Spot Price + Value of Put = Value of Call + Present Value of Exercise/Strike Price

PCPT is the relationship between European Call and Put Option on the same stock, the maturity period and EP is same.

The PCPT equation is made to prevent arbitrage profit. If LHS ≠ RHS, then there would arise arbitrage profit.

LHS Þ SP + VOP    (Protective Put – S⁺, P⁺)

RHS Þ VOC + PV of EP   (Fiduciary Call – C⁺, ZCB⁺)

Risk Neutral Valuation

The Price of an option is independent of the risk preference of Investor Called risk-neutral valuation.

Black Scholes Model

Formula	Remarks
European Call Option = SP x N (d1) – PV of EP x N (d2)	Where, Ln = Natural Log SP = Spot Price EP = Exercise Price R= Rate of Interest T = time
d1 = ln (SP) + (r + .5 σ2) x t               EP………………..                         σ√t
d2 = d1 -  σ√t
Assumption of Block Scholes Model European options are considered. No Transaction Costs. Short Term interest rates are known and constant. Stocks don’t pay dividend. Stock Price Movement is similar to random walk. Stock returns are normally distributed over a period of time. Variance of return is constant over the life of an option.

    

When Probability distribution or probable market price is given for market price of share on expiration then value of option will be calculated as follows: -

Value of Option = (AMP –EP) x Probability + (AMP – EP) x Probability + ……………….. (.i.e. we should check individually)

Future/(1 + R_f) = Spot Price + PV of Storage – PV of Convince Yield

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Valuation in Merger & Acquisitions - CA Final SFM

Analysis of Format of P&L

Particulars	Amount
Sales Less: - Operating Cost (Excluding Depreciation)	XXX (XXX)
EBITDA	XXX
Less: - Depreciation & Amortization	(XXX)
EBIT	XXX
Less: - Interest Cost (Non – Operating Expenses) Add: - Non – Operating Income	(XXX) XXX
PBT	XXX
Less: - Tax	(XXX)
PAT	XXX
Less : - Preference Dividend	(XXX)
Profit for Equity Shareholders	XXX

Abnormal item should be ignored for the purpose of valuation.

Income/Expenses: -

Operating: - Related to Business

Non – Operating: -

Normal: - Projection is Possible

Abnormal: - Projection is not possible

EBITDA is treated as proxy cash flow since it is not impacted by depreciation & amortization.

Enterprise Value  

Enterprise Value (EV) stands for theoretical takeover price of a co.

EV = Market Capitalization + Net Debt

Net Debt = Total Debt – Cash & Cash Equivalent

EV = Market Capitalization + Debt – Cash & Cash Equivalent

EBITDA Multiple = EV/EBITDA

Sales Multiple = EV/Sales

EBIT Multiple = EV/EBIT

Value of Firm/Enterprise

Based on Capitalization Method/Earning Capitalization Method

Value of Firm/Enterprise = [Future Maintainable Profit]/[Capitalization Rate]

For Calculating Future Maintainable profit only operating income and expenditure should be considered. If any new income from business operation is anticipated or any reduction in Business Income or any operating Expenses is anticipated then such anticipated items should be considered while calculating FMP.

Value of Firm Based on Dividend Discount Model

Value of Firm = D₁/(K_e – g)

Value of Firm Based on Earning Growth Model (EGM)

Value of Firm = E₁/(K_e – g)

Value of Firm Based on Chop – Shop Method

Step I: - Identify the firm’s various business segments and calculate the average capitalization ratios for firms in those industries.

Step II: - Calculate a theoretical market value based upon each average capitalization Ratios.

Theoretical Market Value = (Sales/Assets/Income) x Capitalization Rate

Step III: - Average the Theoretical Market Values to determine the “Chop –Shop” Value of the Firm.

Value of Firm Based on Free Cash flow Approach

Free Cash Flow to Firm (FCFF): - It is the free cash flow left after meeting operating and capital expenditure needs.

Free Cash Flow to Equity (FCFE): - It is the free cash flow left after meeting operating and capital expenditure needs and debt obligations (Principal and Interest).

Steps for Free Cash Flow Valuation

Step I: - Determine free cash flows

Free Cash Flows to Firm (FCFF) = No PAT + Depreciation & Amortization – (Capital Expenditure + Working Capital Investment)

Step II: - Estimate a suitable Discount Rate for Acquisition.

For FCFF Discount Rate would be WACC.

For FCFE Discount Rate would be cost of Equity.

Step III: - Calculate Present Value of Cash Flows.

Value of Company = PV of Cash Flows during the forecast period + PV of Terminal Value

Terminal Value = Sum of realisable of various Assets based on capital employed.

Terminal Value Based on Earning Multiple

Terminal Value = Last Year Profit x P/E Multiple

Terminal Value Based on Free Cash Flows (Growing Perpetuity)

Terminal Value = [(Last Year Cash Flow) x (1+ g)]/(K_e – g)

Terminal Value Based on Free Cash Flow (Stable Perpetuity)

Terminal Value = (Free Cash Flow)/Discount Rate 

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Mergers, Acquisitions & Restructuring - CA Final SFM

Acquisition: - An acquisition is when both the acquiring and acquired companies are still left standing as separate entities at the end of the transaction.

Merger: - A merger results in the legal dissolution of one of the companies.

Consolidation: - A consolidation dissolves both the parties and creates a new one into which the previous entities are merged.

Types of Merger

Horizontal Merger: - The two companies which have merged are in the same the Industries.

Vertical Merger: - This happens when two companies that have ‘buyer – seller’ relationship (or potential buyer – seller relationship) come together.

Conglomerate Merger: - Such merger involves firms engaged in unrelated type of business operation.

Congeneric Merger: - In these mergers, the acquired and the target companies are related through basic technologies, production process or market.

Reverse Merger: - Such merger involves acquisition of a public (Shell Company) by a private company.

Reasons for Mergers and Acquisitions

Synergistic operating economic: - synergy may be defined as

V_(AB) > V_(A) + V_(B)

The difference between the combined value and the stand value of target and Acquire is attributable to synergy.

Net gain is the value of synergy – premium paid

Premium Paid = Price paid over the market value + other costs of integration.

Diversification: - In case of merger between two unrelated companies would lead to reduction in business risk.

Taxation: - The provision of set off and carry forward of losses as per Income Tax Act may be another strong reason for merger and acquisition.

Growth: - The Acquiring Company avoids delays such attached with purchasing of building, site, and setting up of the plant and hiring personal etc.

Consolidation of Production Capacities and increasing market power: - Due to reduced competition marketing power increases and also the production capacities are increased by combined of two or more plants.

Exchange/Swap Ratio

If Deals is based on EPS then,

Swap Ratio = (EPS of Target) / (EPS of Acquirer)

If Deals is based on MPS then,

Swap Ratio = (MPS of Target) / (MPS of Target)

If Deal is based on Book Value per Share (BVPS) then,

Swap Ratio = (BVPS of Target) / (BVPS of Acquirer)

Note: -

If Deal is based on EPS then there would be no Gain/Loss to shareholders of both companies in earning them. It means if Deal happens in any other ration other than EPS then one party would gain and another party will lose in term. The above concept is applicable only when there 100% stocks deal. Both parties can gain in terms of market value terms.

Minimum and Maximum Exchange Ratio

Minimum Exchange Ratio is the minimum Expectation of Target to get amount or share so that there would be no loss to target in terms of EPS or MPS.

Maximum Exchange Ratio is the ability of acquirer to pay to target company that amount which would do not results to lose in the value of EPS or MPS term.

S. No.	Formula
1.	Maximum Exchange Ratio in Terms of EPS	EPSold =	Earning of Acquirer + Earning of Target + Synergy Gain No. of Share Outstanding of Acquirer + (No. of Share Outstanding of Target X ER)
2.	Maximum Exchange Ratio in Terms of MPS	MPSold =	Market Value of Acquirer + Market Value of Target + Synergy  Gain No. of Share Outstanding of Acquirer + (No. of Share Outstanding of Target X ER)
3.	Minimum Exchange Ratio in Terms of EPS	EPSold =	(Earning of Acquirer + Earning of Target + Synergy Gain)  x ER No. of Share Outstanding of Acquirer + (No. of Share Outstanding of Target X ER)
4.	Minimum Exchange Ratio in Terms of MPS	MPSold =	(Market Value of Acquirer + Market Value of Target + Synergy  Gain)  x ER No. of Share Outstanding of Acquirer + (No. of Share Outstanding of Target X ER)

Free Float Capital

Shares Held by Public is known as free float shares.

Free Float Market Capitalization = Free Float Shares X Share Price

Non – Free Float Capital

Shares held by promoter are known as non- free float shares.

Non- free Float Market Capitalization = Share Held by Promoters X Share Price

Total Market Capitalization = Free Float Market Capitalization + Non Free Float Market Capitalization

Accretion – Dilution Analysis

If Post Acquisition EPS increase we call deal is Accretive.

If Post Acquisition EPS decrease we call deal is dilutive.

If a high P/E Ratio Acquires a low P/E Ratio by issue of shares then Deal would be Accretive (increase in EPS) for Acquirer and dilutive (decrease in EPS) for target.

Value of Acquisition = Post Acquisition – Pre Acquisition Value of Merged Entity

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Leasing Decision - CA Final SFM

 Parties to Lease Agreement: -

There are two parties under any lease agreement:-

Lessor: - Owner of the asset is known as Lessor.

Lessee: - The party who uses the asset is known as Lessee.

Calculation of Equated Annual Install

When question specifies that loan is payable in Equal Installment then EAI should be calculated.

EAI = (Principle Amount)/PVAF_{(Interest  Rate, No. of Years)}

Note: - Discount Rate or Interest for Calculation of EAI = Interest Rate on Loan amount without taking any effect of Tax on it.

Tax Shield on Expenses done at zero period will be taken during first year (Leasing Topic Only).

Present Value Factor of Annuity when Inflow/Outflow is at beginning of Year then

PVAF_(r,n) = PVAF_{[r, (n-1)]} + 1

Calculation of Lease Rent

When a leasing company desires a certain percentage on gross value of assets then,

Lease Rent = (Cost of Assets)/Annuity factor at rate desire of leasing co.

When Value of Machine and other Expenses given then,

Lease Rent = [PV of Cash Out Flow – PV of Inflow (Tax Shield on Depreciation/Expenses)]/Annuity Factor at Interest Rate

Salvage Value is deducted only when question specifies the method of depreciation as SLM.

Steps to Take Decision Whether Buy or at Assets on Lease by Lessee Point of view

Step I: - Calculate PV of Cash Outflow if Assets by Funding from Loan.

Step II: - Calculate PV of Cash Outflow if Assets is taken on Lease.

Step III: - Comparing PV Cash Outflow in both cases.

Step IV: - Decision: - Option which has lower Cash Outflow should be chosen.

Note: - Any Expenses which is common in both cases then those expenses is irrelevant for decision making.

Steps to take Decision whether Assets should be leased out or not by Lessor Point of view

Step I: - Calculate PV of Cash Inflow (After Tax Lease Rent).

Step II: - Calculate PV of Cash Outflow (Initial Cash Outflow and Recurring Expenses)

Step III: - Calculate NPV (PV of Cash Inflow – PV of Cash Outflow).

Step IV: - Decision: - If NPV is positive then Assets should be leased out otherwise not.

Step to decision for which option to choose for Sale and Buy Back Case     

Step I: - Calculate NPV at each option.

Step II: - Compare NPV at each options.

Step III: - Decision: - Option which has Highest NPV should be chosen.

Discount Rate to be used: –

For Lessee: - K_d(1 – Tax Rate)

For Lessor: - Weighted Average Cost of Capital.

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Foreign Exchange Basic Concept - CA Final SFM

 Currency Symbols and Currency Codes

S. No.	Symbol	Code
1.	£	GBP
2.	€	EUR
3.	$	USD
4.	₹	INR
5.	¥	JPY
6.	£ > € > $ > ₹ > ¥

Quotations

1$ = ₹ 60       (Left Hand Side Currency should be treated as Commodity)

Direct Quote

1 Unit of Foreign Currency (FC) = How Many Home Currency (HC)

Indirect Quote

1 Unit of HC = How Many units of FC

1$ = ₹ 60 – 61      (Where 60 is Bid Rate and 61 is Ask Rate)

Ask Rate > Bid Rate

How to Read Quotation

Academic Style

₹/$ = How many Rupee per dollar

Practical Style (ACI – Association CAhambisle International)

₹/$ = How many dollar per Rupee  

How to Identify in Exam

If Rupee Relationship is given then rest of relation shall be read with same style.

Otherwise check for Market Parity

             £ > € > $ > ₹ > ¥

If Market parity is not possible then use Academic style.

Spread

The Difference of Ask Rate and Bid Rate is profit to bank and is known as Spread.

S. No.	Formula
1.	Spread = Or	Ask – Bid Rate Bid Rate
2.	Spread =	Ask – Bid Rate Ask Rate

Exchange Rate

An Exchange Rate between two currencies is the rate at which one currency will exchanged for another.

Spot Exchange Rate

Spot Exchange Rate refers to the current exchange rate.

Forward Exchange Rate

Forward Exchange Rate refers to an exchange rate that is quoted and traded today but for delivery and payment on a specific future period.

In simple words, it is the agreed rate between the buyer and seller of currency to buy and sell the currency at specified rate on specified rates date.

Premium

Premium means increase in the rate of one currency in comparison to price currency.

Example: - 1$ = ₹ 60, after certain period 1$ = ₹ 65, then dollar is said to be at premium.

In above example,

Dollar is at premium.

Purchasing Power of dollar is increases.

Dollar becomes costly.

Dollar has become stronger.

Dollar is appreciating.

Discount

Discount means decrease in the rate of one currency in comparison to price currency.

 Example: - 1$ = ₹ 60 (1₹ = 1/60) and after certain period 1$ = ₹65 ( 1₹ = 1/65), then ₹ is said to be at discount.

In above example,

₹ is at Discount

Purchasing Power of ₹ decreases.

₹ becomes cheaper

₹ is depreciating.

S. No.	Formula
1.	Premium =	FR – SR x100 SR
2.	Discount =	FR – SR x 100 SR
	Premium ≠ Discount (Siegel’s Paradox)

Gain & Loss to Exporter & Importer

S. No.	Particular	Gain	Loss
1.	Exporter	When FC is at Premium When HC is at Discount	When FC is at Discount When HC is at Premium
2.	Importer	When FC is at Discount When HC is at Premium	When FC is at Premium When HC is at Discount

Cross Currency

S. No.	Given Quotation	Required Quotation	Solution
1.	1 $ = ₹ 60 -65   (₹/$) 1£ = $ 1.50 – 1.60  ($/£)	(₹/£)	Bid Rate(₹/$) = (₹/$)Bid Rate x ($/£) = 60 x 1.50 = ₹ 90 Similar Calculation of Ask Rate
2.	1 $ = ₹ 45.85 – 45.90 (₹/$) 1£ = $ 1.7840 – 1.7850 ($/£) 1£ = SGD 3.1575 – 3.1590 (SGD/£)	(₹/SGD)	Bid Rate(₹/SGD) = (₹/$) x ($/£) x (£/SGD) = 45.85 x 1.7840 x 1/3.1590 1 SGD = ₹ 25.9487

Covering Position means to buy what we sell earlier.

Exchange Margin

Margin is charged by bank to exchanger (buyer/seller of currency) on sale or purchase of currency.

Impact of Margin on Exchange Rates

Merchant Rate for Buyer = Inter Bank Rate + Exchange Margin

Merchant Rate for Seller = Inter Bank Rate – Exchange Rate

Swap Points/Forward Points

I. If forward points are given in low – high form i.e. Ascending order then –

LHS Currency (Commodity Currency) would at premium.

Forward Rate = SR + Forward Points 

II. If Forward points are given in High – Low form i.e. Descending order then –

LHS Currency (Commodity Currency) would at discount.

Forward Rate = SR – Forward Points

Modification in Forward Contract

In Case of a forward contract, the time and amount of foreign exchange to be delivered are predetermined and customer is bound by this agreement. If customer may not fulfill their contract as per agreement, in such case forward contract can be altered or modified in following ways: -

Cancellation

Request for Extension

Fulfill of contract before due date

Partial Honor of Contract

In Case of modification original contract will be settled as usual and new contract will executed at new terms. In case of cancellation on or before due date customer will be entitled for profit/loss as case may be but in case cancellation of contract after due date (either by customer or automatically by bank) he will liable for losses only and no entitlement for profit.

Types of Accounts

Nostro: - Our Account with You.

Vostro: - Your Account with Us.

Loro: - Their Account with them.

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