Equity Valuation

Constant Growth Model (Gordon Growth Model)

The Constant Growth Model, also known as the Gordon Growth Model (GGM), is
a method used to value a stock by assuming that dividends will grow at a constant rate
indefinitely. It is primarily used for companies with stable growth rates and dividend policies.
Definition
The model calculates the intrinsic value of a stock based on its expected future dividends,
which grow at a constant rate, and the required rate of return by investors.

Meaning
This model simplifies stock valuation by focusing on dividend growth and assumes a
perpetual growth rate. It is widely used for mature companies that consistently pay dividends,
such as utility firms or blue-chip companies.

Characteristics
1. Constant Growth Rate: Assumes dividends grow at a fixed annual rate, ggg.
2. Stable Dividends: Best suited for firms with a predictable and consistent dividend
payout.
3. Perpetuity: Assumes the growth continues indefinitely.
4. Discount Rate: Requires the cost of equity or required rate of return (rrr) to be greater
than the growth rate (r>gr > gr>g) for the model to be valid.
5. Simplified Assumptions: Ignores external factors like market fluctuations or
temporary changes in dividend policy.
Formula
The intrinsic value of a stock is calculated using the formula:

1. Applicability: Only suitable for companies with predictable and stable dividend growth.
 2. Limitation: Fails for high-growth firms where g>rg > rg>r.
3. Sensitivity: Small changes in rrr or ggg significantly affect the calculated value.

Two-Stage Growth Model

Definition
The Two-Stage Growth Model is a stock valuation method that assumes two distinct phases of
dividend growth:
1. High-Growth Phase: Dividends grow at a high but non-constant rate over a finite period.
2. Stable-Growth Phase: Dividends grow at a constant, sustainable rate indefinitely after
the high-growth phase.
This model is useful for companies experiencing rapid growth that will eventually stabilize.
Characteristics
1. Two Phases of Growth: Initial period of high growth followed by perpetual stable growth.
2. Transition Phase: Explicitly accounts for the transition between high growth and stability.
3. Higher Complexity: Requires estimates for the high-growth period and stable-growth
phase.
4. Discounted Cash Flow: Dividends during both phases are discounted back to the present
value.

Three-Stage Growth Model

Definition

The Three-Stage Growth Model expands on the Two-Stage Growth Model by incorporating three
distinct growth phases:

1. Initial High-Growth Phase: Rapid dividend growth over a short period.

2. Transitional Growth Phase: Slowing growth rate as the company matures.
3. Stable Growth Phase: Dividends grow at a constant rate indefinitely.

This model is ideal for companies transitioning through significant lifecycle stages.

Characteristics
1. Three Phases of Growth: Accounts for rapid growth, gradual slowdown, and stable
growth.
2. Detailed Transition: Provides a more realistic valuation for companies in different
stages of growth.
3. Complex Calculations: Requires accurate estimation of growth rates and durations for
each phase.
 Aspect Two-Stage Growth Model Three-Stage Growth Model
Phases of Growth High and Stable High, Transition, and Stable
Complexity Moderate High
Applicability Companies with two growth Companies with more lifecycle
phases stages

Valuation Through Price-Earnings (P/E) Ratio

The Price-Earnings (P/E) ratio is a popular valuation metric used to assess the intrinsic value
of a stock based on its earnings. It measures the relationship between a company's market
price per share and its earnings per share (EPS).

Considerations When Using P/E Ratio for Valuation

1. Earnings Quality:
Ensure earnings are consistent and free from one-time or non-recurring items.
2. Industry Relevance:
Use the P/E ratio of a comparable industry or peer group for accurate valuation.
3. Growth Adjustments:
Adjust P/E ratio if the company’s growth rate differs significantly from the industry
average.
4. Market Sentiment:
P/E ratios can be influenced by broader market trends or investor optimism/pessimism.
5. Negative Earnings:
The P/E ratio is not meaningful for companies with negative EPS. Alternative methods,
such as Price-to-Sales or Price-to-Book ratios, should be used.
Key Advantages of P/E-Based Valuation
 Simplicity: Easy to understand and calculate.
 Comparability: Enables direct comparison with industry peers.
 Growth Insight: Indicates market expectations of growth when combined with PEG
(Price/Earnings-to-Growth) ratio.
Limitations
 Earnings Volatility: Can be misleading if earnings fluctuate frequently.
 Not Suitable for Loss-Making Firms: Cannot be used if EPS is negative.
 Market Overvaluation: High P/E ratios may indicate overvalued stocks.
Balance Sheet Valuation
Definition: Balance sheet valuation estimates a company's intrinsic value based on its assets,
liabilities, and equity as recorded in its balance sheet. It provides a snapshot of the company's
financial position, focusing on its net worth or book value.
Key Components
1. Assets: Resources owned by the company (e.g., cash, inventory, fixed assets).
2. Liabilities: Obligations owed by the company (e.g., loans, accounts payable).
3. Equity: The residual interest after liabilities are subtracted from assets.
Formula: Equity (Net Worth) =Assets−Liabilities
Steps in Balance Sheet Valuation
1. Calculate Book Value of Equity:
Subtract total liabilities from total assets as per the balance sheet.
2. Adjust for Market Values:
a. Revalue tangible assets to reflect their current market value.
b. Include intangible assets like goodwill or patents if relevant.
c. Adjust liabilities for current repayment terms or interest rates.
3. Determine Intrinsic Value Per Share:
Divide the adjusted equity value by the number of shares outstanding:
Intrinsic Value per Share= Adjusted Equity Value/Outstanding Shares
Applications
 Asset-Heavy Companies: Effective for industries like real estate, manufacturing, or
banking.
 Liquidation Scenarios: Useful for estimating a company’s worth if liquidated.
 Stable Companies: Ideal for firms with consistent tangible asset valuations.

Advantages
 Tangible Focus: Emphasizes concrete, book-recorded values.
 Simple to Calculate: Based on readily available financial data.
 Reliable for Asset-Based Companies: Accurately reflects the worth of asset-heavy
businesses.

Limitations
 Ignores Intangibles: Often underestimates value for companies with significant
intangible assets.
 Historical Costs: Uses outdated asset values unless adjusted.
 Not Reflective of Market Conditions: Does not account for growth potential or
market sentiment.

Valuation of Investment in Debt Securities

Introduction
Debt Market is a financial market where investors enter into buying and selling of debt
securities. Such debt securities mostly involve Bonds, Debentures, T-Bills, Commercial
Papers and Certificate of Deposits.
Indian Debt Market has been witnessing growth over past 2 decades as more and more
investors are dazzled with the peculiar characteristics of the debt securities. Indian Debt
Market is broadly classified in two categories viz. G-Sec Market and Bond Market. G-Sec
Market refers to the securities issued by Central and State Governments.
Type of Debt Instruments
Debt Instruments can be classified as:
a) Money Market Instruments
b) Government Securities
c) Corporate Bonds / Debentures
Money Market Instruments
Typical Money Market Instruments have a maturity of less than 1 year. Some of the
important money market instruments in India are Treasury Bills, Certificate of Deposits and
Commercial Papers.
The treasury bills are the securities issued by the Government with varied maturities like 91
days, 182 days and 364 days. T-Bills are virtually risk-free. Investors feel T-Bills attractive
because these are actively traded in the secondary market and these can be readily transacted
being in bearer form.
A Certificate of Deposit is a negotiable receipt of funds deposited with a bank. Bearer form
of CD is more popular due to its acceptance in the secondary market. Similar to the T-Bills,
CDs are usually issued at a discount and redeemed at par.
Commercial Papers are issued by financially sound and highly rated companies with a
maturity period of minimum 7 days and maximum 365 days. Similar to the T-Bills and CDs,
CPs are usually issued at discount and redeemed at par. Therefore, the implicit rate is the
function of the size of the discount and maturity period involved. However, CPs being issued
by private firms, are considered to be riskier as compared to T-Bills and CDs.

Government Securities
The Central Government sells Government Securities which are essentially medium to long-
term bonds issued by the Reserve Bank of India on behalf of the Central Government. State
Governments also sell similar bonds to the investors. Apart from the Government, many
Public Sector Undertakings issue similar securities with varying coupon rates and
periodicities.
Corporate Bonds / Debentures
Bonds and Debentures are regularly issued by PSUs, Banks and Public Companies and
Private Companies. Such bonds / debentures are of different nature and characterised by
different terms and conditions attached to such bonds / debentures. Debentures are often
coupled with convertibility features either compulsorily or optionally by embedding put / call
option.
Valuation of Debt Securities
Provisions of the ICAI Valuation Standards
ICAI Valuation Standard 303 – Financial Instruments speaks about valuation approaches,
methods and techniques for valuation of financial instruments. The standard defines financial
instrument as any contract that gives rise to a financial asset of one entity and a financial
liability or equity instrument of another entity. Equity instruments, derivatives, debt
instruments, fixed income and structured products, compound instruments, etc. are certain
examples of financial instruments.
When it comes to valuation of a Debt Instrument, important considerations are use of the debt
instrument, purpose of valuation, characteristics of the instrument and availability of
information. As per the provisions of ICAI Valuation Standard 102 – Valuation Bases,
valuers need to select appropriate valuation bases relevant in the context of the instrument
being valued. Furthermore, appropriate approaches and methods need to be applied as per the
provisions of ICAI Valuation Standard 103 – Valuation Approaches and Methods.
In most of the circumstances, Present Value method under the Income Approach is the most
appropriate. While applying the Present Value method, one needs to consider the following
factors:
· Contractual Cash Flows arising out of the Debt Instrument
· The timing when the entity expects realisation of the cash flows
· The basis of calculation of cash flows viz. interest / coupon rate, underlying index etc.
· Contractual restrictions like lock-in period, put / call option, extension, conversion etc.
In the case of a debt instrument having embedded call / put option, one needs to bifurcate the
instrument into debt and equity and calculate the value of the option by applying Black-
Scholes-Merton model. For the sake of simplicity, we shall consider pure-debt instruments
without having any embedded options for the purpose of understanding valuation of debt
instrument in this article.

Valuation of Debt Instrument using Present Value technique

Valuing a debt instrument using Present Value method includes consideration of following
points from the perspective of the market participants as on the valuation date:
· Estimation of the cash flows arising out of such Debt Instrument viz. periodic interest /
coupon and redemption proceeds and premium if any
· Estimation of timing and possible variations including inherent uncertainty in realisation
of the cash flows
· Estimation of the Discount Rate on the basis of Risk-Free Rate and Appropriate Risk
Premium
· Calculation of Present Value of the Estimated Cash Flows
Estimation of cash flows usually depends upon the terms of the agreement of the debt
security being valued. One needs to ascertain the possibility of variations and accordingly
map the periodical cash flows in the DCF model.
The most important part is to ascertain the discount rate. When it comes to valuation of listed
debt securities, the price reflected on the stock exchange is assumed to be the fair value.
Accordingly, yield to maturity (YTM) is calculated using the formula:
Where,
YTM = Yield To Maturity
C = Annual Coupon
F = Face Value of the Bond
P = Price of the Bond
Under normal circumstances, YTM is assumed to be the discount rate. As such, while valuing
an unlisted debt instrument, it become important to identify similar bonds / debentures being
traded in the open market and calculation of YTM of such bonds. By making suitable
adjustment on account of risks associated with the company whose bonds / debentures are
being valued, suitable discount rate can be arrived at.
Another approach is to add appropriate risk premium to the risk-free rate and arrive at
suitable discount rate. Doing so, one needs to understand major risks associated with the
company / the instrument being valued. Some typical risks associated could be:
Credit Default Risk
Credit Default Risk refers to the risk that the company may not pay interest and / or principal
on time.
It is normally measured by way of credit rating assigned to the debt instrument by an
independent credit rating agency like CRISIL, ICRA, CARE etc. Other things kept constant,
bonds / debentures carrying a higher credit default risk would trade at a higher yield to
maturity. Based on the Credit Rating, appropriate mark-up can be added to the risk-free rate.
While assessing the credit risk, rating agencies take into account factors like counterparty
risk, capital leveraging, hierarchy of the security, collateral available, history of default etc.
Liquidity Risk
All debt instruments may not be as liquid as government securities. Unless the instrument is
listed on any stock exchange, there is a lack of marketability which adds to the liquidity risk
associated with the instrument. There is a standard practice of adding a lump-sum percentage
to the discount rate on account of liquidity risk. The more scientific practice could be
understanding the effect of similar debt instruments and having observable inputs from the
secondary market.
Interest Rate Risk
Another risk associated with the debt securities is Interest Rate Risk. As we know, bond
prices and yields are inversely related. As such, in a perfect market, securities are priced in
such a fashion that fair expected returns are offered to the investor. For example, a bond with
10% return and 10% YTM would trade at par. If the Market Rate of Return increases, the
YTM would eventually increase, bringing down the effective price of the bond. Similarly,
reduction in Market Rate of Return would result into lowering of YTM and increase in the
effective price of the bond.
Valuation of Debt Securities of Private Firms
A peculiar challenge may arise while valuing debt securities of private firm / small
companies where instrument specific credit rating is not available. Under such circumstances,
valuer may need to create a Synthetic Rating Model by assessing the Credit Default Risk
associated.
In simple words, valuer may need to step into the shoes of a credit rating agency and consider
the impact of counterparty risk, capital leveraging, hierarchy of the security, collateral
available, history of default etc. on the financial position of the company. Valuer also needs
to
ascertain the risk associated with the company based on the interest coverage ratio and / or
debt service coverage ratio in order to assign weightage in the synthetic rating model.

What Is Bond Valuation?

Bond valuation is a method to calculate the present value of the expected future returns,
earnings, or cash flow from a bond investment. An investor who invests in a debt instrument
such as a bond uses the valuation method to determine whether the cost of the bond is worth
the returns over time.

Bond valuations assist an investor in deciding whether the future yields from the
bond investment are suitable for their portfolio. Thus, an investor determines the value of a
bond through its trading prices, interest rate, and par or face value. While the bond's interest
rates and par value remain the same, changes occur in the bond prices and investors' returns
over time.
Key Takeaways
 Bond Valuation is the method of calculating and estimating the present value of future
interest payments to estimate total bond yields at maturity.
 The valuation considers the market interest rate or discounted cash flow rate to value
the bond yields accurately for an investor.
 The calculation estimates the interest payments (quarterly, semi-annually, or
annually) based on the details mentioned in a bond indenture or agreement. Then adds
these annuities to the face value of the bond or principal amount for valuation.
 The par value and interest payments are pre-determined while the investor calculates
the return rate.
 Bond Valuation Explained
The bond valuation enables an investor to estimate the present value of their future
earnings from interest payments and adds it to the bond's par value or the principal amount.
A bond is a debt instrument, meaning the bond issuer borrows from an investor or lender. In
exchange, the bond issuer ensures a fixed interest rate for the period the investor holds the
bond. Thus, the interest provides a steady income for the bondholder till the maturity date of
the bond. Hence, upon maturity, the borrower repays the bondholder per the face value, less
than the face or more than the face value.
On the other hand, a zero-coupon bond will not pay any coupon payments or timely interest to
the investor or bondholder. Rather, in the case of a zero coupon bond, the bond price is
lowered, or the bond issuer issues the bond at a discounted rate to its face value. Thus, at
maturity, the investor receives a guaranteed full amount or par value of the bond. As a result,
the difference amount between the purchase price of the bond and the par value at maturity
becomes the interest earned by the investor.
Factors
Stock and bond valuation is affected by numerous factors, including changes in the rates of
interest, possibilities of inflation, economic conditions, etc. Let us have a look at some of the
factors that affect the bond prices:
 Interest rates: When the interest rates change, it affects the discount rate of the bonds
issued. In this scenario, the bond prices fall when the interest rates rise and vice-versa.
 Inflation: The expected inflation influences the market in a huge way. The same
happens to the bond market. The high expectations of inflation lead to increased rates
of interest, thereby lowering the bond prices. However, when the expectations of
inflation are low, it’s an opposite scenario, i.e., lower interest rates and higher bond
prices.
 Economic conditions: Whether it is the Gross Domestic Product (GDP) or market or
customer sentiments, an economy is highly affected. When the economy is towards
progress and growth, the interest rates are high and bond prices are low. On the
contrary, if the economy is weak, the interest rate is low, and the price of the bond is
high.
 Credit rating: The change in the credit rating affects the risk factor associated with
an investment. When there is an increase in the credit rating, the credit spread lessens,
thereby increasing the price of the bond, while a decrease in the credit rating means a
wider credit spread and lower bond price.
 Market Liquidity: A liquid bond market will mean lower volatility in bond value,
while an illiquid market will lead to higher volatility in the prices of the bonds.
  Financial state of the issuer: It is one of the most important factors to be taken into
consideration. The issuer is the one who requires fulfilling their bond obligations.
Hence, their financial status must be assessed. For the issuer of the bond with a well-
performing business and fewer debt obligations, the bond price is higher than the
issuers with high debt obligations and poorly-performing business.
Methods
The types of bond valuation include traditional, relative, and option-adjusted spread methods.
Tradition Method
This is the conventional means that involves two means of evaluating and pricing bonds. These
are discounted cash flow and yield-to-maturity methods. The former is the method used to
calculate the present value of the future cash flows from a bond. This helps investors in
learning about the returns they can expect from an investment they are considering.
In yield-to-maturity, the investors can calculate the returns that they can expect if the bond is
held until maturity. In the process, the current price of the bond is considered along with face
value, coupon rate, and maturity period. As a result, investors get a chance to compare bonds
and decide where to invest.
Relative Method
As the name suggests, this involves evaluating and pricing a bond with respect to or in relation to
other bonds in the market. One such method is credit spread analysis where one bond is
compared against a benchmark bond in the market. The credit spread calculated helps
investors know about the additional risk associated with the bond being analyzed with respect
to that benchmark bond.
The relative method assesses a bond in relation to another bond, which is a benchmark in the
market, with similar traits and maturity.
Option-Adjusted Spread (OAS) Method
This type of bond valuation, as the name implies, offers investors an opportunity to adjust their
chance of redemption of the bond before maturity. The investors can use callable and puttable
bonds and buy and sell the same as and when they realize the potential for profits associated
with the bond they hold in the market.
Risks
Undoubtedly, evaluating and pricing the bonds is an important aspect of the bond market, but this
valuation also has some limitations, which one must know of. Let us have a look at them
below:
 The calculations of returns and risks are based on assumptions. In short, the valuation
is subjective.
 The changes in the market conditions affect the analysis, thereby influencing the bond
valuation.

Bond Returns and Risk:

Return: The gain or loss on an investment, expressed as a percentage of the initial
investment.
Types of Bond Returns:
1. Coupon Payments (Interest Income):
Bonds pay periodic interest, known as coupon payments, based on the bond’s coupon rate
and face value.
Formula:
Coupon Payment = Face Value × Coupon Rate
Coupon Payment=Face Value × Coupon Rate
For example, a bond with a face value of Rs. 1,000 and a 5% coupon rate pays Rs. 50
annually.
Coupon income is a major component of bond returns, especially for long-term investors
2. Capital Gains or Losses:
If a bondholder sells the bond before maturity, the selling price may differ from the purchase
price due to market conditions.
Capital Gain occurs when the bond is sold for more than its purchase price.
Capital Loss occurs when the bond is sold for less than its purchase price.
Formula:
Capital Gain/Loss = Selling Price − Purchase Price
Capital Gain/Loss=Selling Price−Purchase Price
Capital gains/losses depend on factors like interest rate changes, credit risk, and market
demand.
3. Yield to Maturity (YTM):
Represents the total return an investor can expect if the bond is held until maturity,
accounting for:
Coupon payments.
The difference between purchase price and face value.
YTM is expressed as an annualized percentage and considers the time value of money.
It assumes that all coupon payments are reinvested at the same rate.
4. Yield to Call (YTC):
Applicable to callable bonds, where the issuer has the option to redeem the bond before its
maturity date.
YTC calculates the return if the bond is called early, factoring in:
Coupon payments until the call date.
The call price (usually higher than the face value).
Formula is similar to YTM but adjusts for the call date and call price instead of maturity.
5. Current Yield:
Measures the return based on the bond’s current market price rather than its face value.
Formula Current Yield= Annual Coupon Payment/Current Market Price x 100
Current yield provides a snapshot of the bond’s income return relative to its market price, but
it does not account for capital gains/losses.
6. Reinvestment Return:
Bond investors often reinvest coupon payments to generate additional returns.
The reinvestment return depends on the prevailing interest rates and the frequency of coupon
payments.
Higher reinvestment returns can significantly boost total bond returns, especially for long-
term bonds.
7. Total Return:

The sum of all income streams from a bond, including:

Coupon payments.
Capital gains or losses.
Reinvestment income.
Formula:
Total Return = Total Income (Coupon + Reinvestment + Capital Gains)
Purchase Price × 100
Total return gives a comprehensive view of the bond’s overall profitability.

Real Return:
Reflects the bond’s return adjusted for inflation, showing the actual increase in
purchasing power.
Formula: Real Return = Nominal Return − Inflation Rate
Real Return=Nominal Return−Inflation Rate
Inflation erodes the value of fixed payments, so real return is a critical measure for
assessing bonds in inflationary environments.
Risk: The uncertainty of achieving expected returns, including the possibility of financial
loss.
Types of Risks Related to Bonds:
1. Interest Rate Risk:
o Definition: The risk that changes in market interest rates will affect
bond prices.
o Mechanism: Bond prices and interest rates have an inverse relationship.
When interest rates rise, existing bond prices fall, as newer bonds offer
higher yields.
o Impact: Long-term bonds and low-coupon bonds are more sensitive to
interest rate changes.
o Measurement: Duration and convexity are used to measure interest rate risk.
2. Credit Risk (Default Risk):
o Definition: The risk that the bond issuer may fail to make scheduled coupon
payments or repay the principal.
o Factors Influencing Credit Risk:
 Financial health of the issuer.
 Credit ratings assigned by agencies (e.g., Moody’s, S&P).
o High-Risk Bonds: Junk bonds (rated below investment grade) carry higher
credit risk but offer higher yields.

3. Inflation Risk:
o Definition: The risk that inflation reduces the purchasing power of the bond’s
fixed payments.
o Impact: Real returns on bonds decline as inflation increases, especially for
bonds with fixed coupon rates.
o Protection: Inflation-indexed bonds (e.g., TIPS in the U.S.) adjust payments
based on inflation.
4. Reinvestment Risk:

o Definition: The risk that coupon payments or principal repayments

are reinvested at lower interest rates than the original bond’s yield.
o Impact: Affects investors in a declining interest rate environment, particularly
for high-coupon or callable bonds.
5. Liquidity Risk:
o Definition: The risk that the bondholder cannot sell the bond quickly or at a
fair market price.
o Factors Influencing Liquidity:
 Market demand for the bond.
 Size of the bond issue.
 Presence of secondary markets.
o Impact: Smaller or lesser-known issuers’ bonds often face higher liquidity
risk.

6. Call Risk:
o Definition: The risk that the issuer may redeem the bond before
maturity, usually when interest rates decline.
o Impact:
 Investors lose out on future coupon payments.
 Forced reinvestment at lower interest rates.
o Common in: Callable bonds, where issuers repay debt early to refinance
at lower costs.
7. Currency Risk:
o Definition: For bonds issued in a foreign currency, fluctuations in exchange
rates can impact returns.
o Impact: If the home currency appreciates, the bondholder’s returns decrease
when converted back to the home currency.
8. Event Risk:
o Definition: The risk of unexpected events (e.g., mergers, acquisitions,
regulatory changes, natural disasters) affecting the issuer’s ability to
make payments.
o Impact: Sudden credit rating downgrades or financial instability.
9. Sovereign Risk:
o Definition: Specific to government bonds, it is the risk that a government may
default on its debt.
o Impact: Common in bonds issued by emerging or economically
unstable countries.
10. Market Risk:
o Definition: Broader risk arising from macroeconomic factors that affect bond
prices, such as economic growth, political stability, or global market trends.
Bond Pricing Theorems:
Definition
Bond pricing theorems are principles that explain the relationship between a bond's
price, its yield to maturity (YTM), and changes in market interest rates. They provide a
foundation for understanding the behavior of bonds in response to economic and market
changes.
Key Terms
1. Bond Price: The current market value of a bond, determined by discounting its future
cash flows (coupons and principal) at the market interest rate.
2. Yield to Maturity (YTM): The rate of return anticipated on a bond if held until
maturity.
3. Coupon Rate: The fixed annual interest payment expressed as a percentage of the
bond's face value.
4. Maturity: The time remaining until the bondholder receives the principal repayment.
5. Duration: A measure of the weighted average time until cash flows are received;
used to assess interest rate sensitivity.

Theorems and Their Meaning

1. Inverse Relationship Between Bond Prices and Yields
 Theorem: Bond prices and yields move inversely.
 Meaning: When market interest rates rise, the present value of future cash
flows decreases, leading to a drop in bond prices. Conversely, when rates fall,
bond prices increase.
 Example: If the interest rate increases from 5% to 6%, the price of a bond
paying 5% will decrease to remain competitive.

2. Price Sensitivity Varies by Maturity

 Theorem: Longer-term bonds are more sensitive to interest rate changes than
shorter-term bonds.
 Meaning: The farther the cash flows, the greater the impact of changes in
discount rates. This makes long-term bonds riskier in volatile rate
environments.
 Example: A 30-year bond will experience a larger price drop than a 5-year
bond for the same rate increase.
 3. Price Sensitivity Varies by Coupon Rate
 Theorem: Bonds with lower coupon rates are more sensitive to changes in
interest rates.
 Meaning: Low-coupon bonds rely more on their principal repayment at
maturity, making them more affected by changes in discounting.
 Example: A zero-coupon bond is the most sensitive, as it has no periodic
payments.

4. Yield and Duration Relationship

 Theorem: Higher-duration bonds are more sensitive to interest rate
changes.
 Meaning: Duration reflects how long it takes to recover the bond's price.
A higher duration means higher sensitivity.
 Formula: ΔP/P=−Duration×ΔY\Delta P / P = - \text{Duration} \times
\Delta YΔP/P=−Duration×ΔY, where PPP is price, and ΔY\Delta YΔY is
the change in yield.
 Example: A bond with a duration of 10 will lose approximately 10% of its
price if yields rise by 1%.

5. Premium and Discount Bonds

 Theorem:
I. A bond priced above par (premium) has a YTM lower than its
coupon rate.
II. A bond priced below par (discount) has a YTM higher than its
coupon rate.
 Meaning: The relationship ensures fair pricing relative to the interest rate
environment.
 Example: A bond with a coupon of 6% and YTM of 5% will trade at a
premium.
Importance of These Theorems
 Provide a framework for bond valuation.
 Help assess interest rate risk.
 Aid in constructing immunization strategies for portfolios.
 Support the use of advanced metrics like duration and convexity for managing bond
investments.
These principles are critical for investors, portfolio managers, and financial analysts to make
informed decisions in the fixed-income market.
Bond Duration
Definition:
Bond duration measures the sensitivity of a bond's price to changes in interest rates. It is
expressed in years and represents the weighted average time it takes to recover the bond’s
cash flows (coupons and principal).
Types of Duration:
1. Macaulay Duration:
The weighted average time to receive all cash flows, including coupons and principal.
Used to estimate the time at which a bond’s cash flows are evenly distributed.
2. Modified Duration:
Measures the percentage change in a bond's price for a 1% change in interest rates.
Formula:

Where 𝑛 is the number of compounding periods in a year.

Modified Duration = Macaulay Duration/1+YTM/𝑛

3. Effective Duration:
Used for bonds with embedded options (e.g., callable or puttable bonds), as their cash flows
change with interest rate movements.
Key Characteristics:
Higher duration implies greater sensitivity to interest rate changes.
Duration is a useful measure for managing interest rate risk in bond portfolios.
Factors Affecting Duration:
1. Maturity:
 Longer maturities result in higher duration because cash flows are spread over a longer
period.
 Example: A 10-year bond will have a higher duration than a 5-year bond.
2. Coupon Rate:
 Lower coupon bonds have higher duration because a larger portion of their value comes
from the principal repayment at maturity.
 Example: A zero-coupon bond has the highest duration, equal to its maturity.
3. Yield to Maturity (YTM):
Higher yields reduce duration because cash flows are discounted more heavily, reducing their
present value.

Yield to Maturity (YTM)

Definition:
YTM is the internal rate of return (IRR) on a bond if held until maturity, assuming all
coupons are reinvested at the same rate. It represents the bondholder’s total expected return.
Key Features:
YTM accounts for:
I. Coupon Payments: The periodic interest paid by the bond.
II. Capital Gains or Losses: The difference between the bond's purchase price and its
face value at maturity.
Calculation:

The YTM is the discount rate that equates the bond's price to the present value of its future
cash flows:

𝑃: Current bond price

Where:

𝐹: Face value
C: Coupon payment

𝑛: Number of periods to maturity

Types of Yields:
1. Current Yield:
Measures annual coupon income relative to the bond’s current price.
Formula: Current Yield = Annual Coupon / Current Price
2. Yield to Call (YTC):
Similar to YTM but assumes the bond is called (redeemed early) at the first call date.
3. Nominal Yield (Coupon Rate):
The fixed percentage of the bond's face value paid as interest.
Key Insights:
Premium Bonds (Price > Face Value): YTM < Coupon Rate.
Discount Bonds (Price < Face Value): YTM > Coupon Rate.
Par Bonds (Price = Face Value): YTM = Coupon Rate.

Determinants of Interest Rates

Definition:
Interest rates represent the cost of borrowing money or the return on lending money. They are
influenced by a variety of economic, monetary, and market factors.
Key Determinants:
1. Inflation:
 Inflation erodes purchasing power, so lenders demand higher interest rates to
compensate.
 Fisher Effect: Nominal Interest Rate =Real Interest Rate + Expected Inflation
2. Economic Growth:
 In periods of strong economic growth, demand for credit increases, driving interest
rates higher.
 During recessions, central banks often lower rates to stimulate borrowing and
investment.
3. Monetary Policy:
 Central banks control short-term interest rates through tools like repo rates, reverse
repo rates, and open market operations.
 Tight monetary policy (rate hikes) curbs inflation but raises borrowing costs.
 Loose monetary policy (rate cuts) stimulates the economy but may lead to inflation.
4. Government Debt and Fiscal Policy:
 High government borrowing increases demand for funds, pushing rates higher
(crowding-out effect).
 Fiscal stimulus programs can also influence rate trends.
5. Supply and Demand in Credit Markets:
 High savings in the economy → More supply of loanable funds → Lower rates.
 High borrowing demand → Higher interest rates.
6. Credit Risk:
 Riskier borrowers must pay higher rates to compensate lenders for default risk.
7. Liquidity Preference:
 Investors demand a premium for locking their money into long-term investments,
leading to higher rates for longer maturities.
8. Global Economic Factors:
 International capital flows, currency exchange rates, and geopolitical events can
impact domestic interest rates.

Types of Interest Rates:

1. Nominal Interest Rate:
 The observed rate in the market, unadjusted for inflation.
2. Real Interest Rate:
 Adjusted for inflation to reflect the true cost of
borrowing: Real Rate = Nominal Rate − Inflation Rate
3. Risk-Free Rate:
 The return on investments with zero default risk, such as government securities.
4. Market Interest Rate:
 Combines the nominal rate, inflation expectations, and a risk premium.

Asset Allocation Techniques

1. Strategic Asset Allocation
Definition:
A long-term approach where fixed target allocations are set for asset classes based on an
investor’s risk tolerance, financial goals, and time horizon.
Key Features:
1. Fixed Targets: Predetermined percentage weights for each asset class.
2. Rebalancing: Periodic adjustments to return to target allocations.
3. Focus on Stability: Prioritizes long-term goals over short-term fluctuations.
4. Risk Management: Balances risk and return based on investor profile.
5. Minimal Active Management: Requires infrequent changes, suitable for passive
investors.
Key Features:
1. Market Timing: Allocations shift based on expected market performance.
2. Dynamic Adjustments: Adjustments are frequent, reflecting changing conditions.
3. Opportunistic: Seeks to outperform static strategies through active decision-making.
4. Higher Risk: Relies on market predictions, increasing potential risk and reward.
5. Active Involvement: Demands constant monitoring and expertise.

2. Dynamic Asset Allocation

Definition:
An active strategy where portfolio weights are continually adjusted to respond to market
changes and economic cycles.
Key Features:
1. Flexible Approach: Adapts to market trends and economic conditions.
2. Risk Mitigation: Reduces exposure to underperforming assets.
3. Economic Cycle Adaptation: Aligns investments with growth, recession, or
recovery phases.
4. Frequent Adjustments: Requires active management and regular portfolio reviews.
5. Short- to Medium-Term Focus: Suitable for volatile market conditions.

3. Core-Satellite Asset
Allocation Definition:
Combines a passive "core" for stability with active "satellite" investments for growth.
Key Features:
1. Core Stability: Majority invested in diversified, low-cost index funds or ETFs.
2. Satellite Growth: Smaller portion allocated to high-risk, high-reward investments.
3. Cost Efficiency: Keeps costs low for the core, with limited active management.
4. Controlled Risk: Core minimizes volatility, while satellite seeks higher returns.
5. Diversified Strategy: Balances passive stability and active growth.

4. Insured Asset Allocation

Definition:
A strategy that prioritizes preserving a minimum portfolio value while seeking growth.
Key Features:
1. Capital Protection: Ensures portfolio doesn’t fall below a predefined threshold.
2. Risk-Averse Approach: Focuses on safety, sacrificing some potential returns.
3. Portfolio Floor: Sets a minimum acceptable portfolio value.
4. Active Monitoring: Regular adjustments to safeguard capital.
5. Suitable for Conservative Investors: Ideal for those nearing retirement or with low
risk tolerance.
 Managing Equity and Bond Funds
Common Techniques for Equity and Bond Fund Management
1. Asset Allocation:
o Balancing equity and bond exposure to match investment goals and risk tolerance.
2. Rebalancing:
o Periodic adjustments to maintain target asset mix due to market fluctuations.
3. Liquidity Management:
o Ensuring sufficient liquid assets to meet redemption demands.
4. Macro and Micro Analysis:
o Macro Analysis: Economic trends, monetary policy, inflation, and GDP growth.
o Micro Analysis: Company financials, credit ratings, and market positioning.
5. Performance Metrics:
o Equity Funds: Alpha, beta, Sharpe ratio.
o Bond Funds: Yield to maturity (YTM), duration, and credit spread.

Comparison of Equity vs. Bond Fund Management

Aspect Equity Fund Bond Fund
Objective Capital growth Income and capital preservation
Risk High Moderate to low
Return Potential High (market-dependent) Moderate (interest rate-
dependent)
Key Metrics Alpha, beta, Sharpe ratio Duration, YTM, credit rating
Market Impacted by economic and company Highly sensitive to interest rates
Sensitivity factors
Discounted Cash Flow Techniques:
The discounted cash flow methods provide a more objective basis for evaluating and
selecting an investment project. These methods consider the magnitude and timing of cash-
flows in each period of a project’s life. Discounted cash-flow methods enable us to isolate the
differences in the timing of cash-flows of the project by discounting them to know the present
value. The present value can be analysed to determine the desirability of the project. These
techniques adjust the cash-flows over the life of a project for the time value of money.
Time Value of Money:
Sound decision making demands logical comparability of cash-flows, which differ in timing
and risk. Recognition of time value of money and risk by adjusting cash-flows for their
differences in timing and risk is extremely vital in financial decision making. Most financial
decisions, such as buying assets or borrowing funds involve cash-flows at different periods of
time. For example, if a firm purchases any machinery which will be used to produce a certain
type of product; the firm will have an immediate cash outflow; and a series of cash inflows
will be there for many future periods as the finished products will be sold. Similarly, if an
individual borrows money, she will have an immediate cash inflow and a series of cash
outflows as she will commit an obligation to service the debt for many future periods. These
cash-flows which differ in timing are not directly comparable. And, sound decision making
demands logical comparability of cash-flows.
The reasons attributed to time preference for money are:
1. Risk: Uncertainty about future cash receipts leads an individual to prefer receiving
cash now as “a bird in hand is worth two in the bush”.
2. Preference for Present Consumption: Individuals has subjective preference for
present consumption over future consumption of goods and services. The reason for
the same may be its urgency of present want, not being in a position to enjoy future
consumption due to illness, death or inflation.
3. Investment Opportunity: Individuals has preference for present cash to future cash
because of the available investment opportunities. If the cash is received at present, it
could be invested to reap returns in future.

To determine the desirability of the project, these techniques adjust the cash-flows over the
life of a project for the time value of money.
a) Net Present Value (NPV)
b) Internal Rate of Return (IRR)
c) Profitability Index (PI)
 Net Present Value Method:
The net present value method is a classic method of evaluating the investment proposals. It is one
of the methods of discounted cash flow techniques. It recognises the importance of time value
of money. It correctly postulates that cash flows arising at different time periods differs in
value and are comparable only with their equivalents i.e., present values are found out.

“It is a present value of future returns, discounted at the required rate of return minus the
present value of the cost of the investment.” Ezra Solomon

NPV is the difference between the present value of cash inflows of a project and the initial cost
of the project.
Steps for computing net present value:
1. An appropriate rate of interest should be selected to discount the cash flows. Generally,
this will be the “Cost of Capital” of the company, or required rate of return
2. The present value of inflows and outflows of an investment proposal has to be computed
by discounting them with an appropriate cost of capital
3. The net present value is the difference between the present value of cash inflows and the
present value of cash outflows

Decision Criteria: According the NPV technique, for accept-reject type of decision, if the
project has a positive NPV, the project is acceptable. If a project(s) NPV is less than ‘Zero’. It
gives negative NPV. Hence, it must be rejected. For mutually exclusive projects (i.e., only
one project will be selected) the project with highest positive NPV should be selected.

Merits:
1. It recognizes the time value of money.
2. It is based on the entire cash flows generated during the useful life of the asset.
3. It is consistent with the objective of maximization of wealth of the owners.
4. The ranking of projects is independent of the discount rate used for determining the present
value.
Demerits:
1. It is difficult to understand and use.
2. The NPV is calculated by using the cost of capital as a discount rate. But, the concept of
cost of capital itself is difficult to understood and determine.
3. It does not give solutions when the comparable projects are involved in different amounts
of investment.
4. It does not give correct answer to a question whether alternative projects or limited funds
are available with unequal lines.
Internal Rate of Return:
This method advocated by Joel Dean, takes into account the magnitude and timing of cash
flows. This is another important discounted cash flow technique of capital budgeting
decisions. IRR can be defined as that rate which equates the present value of cash inflows
with the present value of cash outflows of an investment proposal. It is the rate at which the
net present value of the investment proposal is zero.
“The internal rate as the rate that equates the present value of the expected future receipts to
the investment outlay”---------Weston and Brigham

If the IRR is greater than the cost of capital the funds invested will earn more than their cost,
when IRR of a project equal the cost of capital, the management would be indifferent to the
project as it would be expected to change the value of the firm. It is computed by the formula

Internal Rate of Return (IRR) = L + [(P1 - C) x D/(P1 - P2) x 100]

Where; L=Lower rate of interest
P1=Present value at lower rate of interest
P2=Present value at higher rate of
interest C= Capital Investment
D= Difference in rate of interest
Computation: The internal rate of return is to be determined by trail and error method. The
following steps can be used for its computation:
1. Compute the present value of the cash flows from an investment, by using an arbitrary
selected interest rate
2. Then compare the present value so obtained with capital outlay
3. If the present value is higher than the cost, then the present value of inflows is to be
determined by using higher rate
4. This procedure is to be continued until the present value of the inflows from the investment
is approximately equal to its outflow
5. The interest rate that brings about this equality is the internal rate of return.
If the internal rate of return exceeds the required rate of return, then the project is accepted. If
the project’s IRR is lower that the required rate of return, it will be rejected. In case of
ranking the proposals, the technique of IRR is significantly used. The projects with higher
rate of return will be ranked as first compared to the lowest rate of return projects. Thus, the
IRR acceptance rules are
Accept if r>k

Reject if r<k

May accept or reject if r=k

Where; r = internal rate of return

k=cost of capital

Merits:
1. It considers the time value of money
2. It takes into account the cash flows over the entire useful life of the asset.
3. It has a psychological appear to the user because when the highest rate of return projects
are selected, it satisfies the investors in terms of the rate of return and capital
4. It always suggests accepting to projects with maximum rate of return. 5. It is inconformity
with the firm’s objective of maximum owner’s welfare.
Demerits:
1. It is very difficult to understand and use.
2. It involves a very complicated computational work.
3. It may not give unique answer in all situations.

Probability Index Method (PI)

The method is also called benefit cost ratio. This method is obtained after a slight
modification of the NPV method. In case of PI the present value of cash out flows are divided
by the present value of cash out flows. While NPV is a absolute measure, the PI is a relative
measure.
If the PI is more than one (>1), the proposal is accepted else rejected. If there are more than
one investment proposal with the more than one PI, the one with the highest PI will be
selected. This method is more useful in case of projects with different cash outlays and hence
is superior to the NPV method.

The formula for PI is

Gross Profitability Index (PI) = Total Present Value of Cash Inflow / Total Present Value of Cash Outflow

Net Profitability Index (PI) = Net Present Value of Cash Inflow / Net Present Value of Cash Outflow

Merits:

1. It requires less computational work than IRR method

2. It helps to accept / reject investment proposal on the basis of value of the index.
3. It is useful to rank the proposals on the basis of the highest/lowest value of the index.
4. It takes into consideration the entire stream of cash flows generated during the useful
life of the asset.
Demerits:
1. It is very difficult to understand the analytical part of the decision on the basis
of probability index.