Valuation of bonds

1. VALUATION OF
BONDS AND EQUITY

2. CAPITAL STRUCTURE
Capital structure refers to how a company chooses to finance its operations and investments. It includes the long-term liabilities and equity shown on the balance sheet.
Long-term liabilities may include things like loans or bonds that the company has taken out for a specific period of time. Equity refers to the ownership interest in the
company, which can come from common shares, preferred shares, or retained earnings.
The capital structure of a company can suggest the proportion of debt and equity financing that it uses. A company with a higher proportion of debt financing has more
borrowed money on its balance sheet, while a company with more equity financing has a higher ownership stake from shareholders.
Choosing the right financing mix is important for a company to achieve its goals. Debt financing can offer tax benefits, but it also requires regular interest payments and
repayment of principal. Equity financing doesn't require interest payments, but it does dilute ownership and can be more expensive than debt financing in the long run.
It is Long-term Liability and Equity of Balance Sheet
It suggests the Financing proportion for company
Financing Mix:
Long term liability: Debt (Bonds), Term
Loan from Bank
Equity: Common Equity shares,
Preference Shares, Retained earnings
The financing mix refers to the types of funding a company uses to run its operations and
make investments.
Long-term liability refers to the money a company borrows and has to pay back over a long
period of time. This can include things like bonds, which are essentially loans taken out by the
company that pay a fixed interest rate over a set period of time, or term loans from banks.
Equity, on the other hand, refers to ownership in the company. This can come from common
equity shares, which are publicly traded shares of the company that can be bought and sold
by investors, or preference shares, which have certain preferences over common shares such
as receiving dividends before common shareholders. Retained earnings are profits that the
company has earned and kept instead of paying out as dividends to shareholders.
By using a mix of debt and equity financing, companies can balance the benefits and
drawbacks of each type of financinincreases the company's risk if they cannot repay the
borrowed money. Equity financing can provide a company with more flexibility, but it can also
be more expensive in the long run due to the potential dilution of ownership. g. Debt financing
can provide a company with a lower cost of capital, but it also can also be more expensive in
the long run due to the potential dilution of ownership.

3. Measuresforcapital Structure: Debt/Equityratio,D ebt ratio,Proprietor ratio
Measures for capital structure are used to evaluate the proportion of debt and equity financing that a company uses.
The debt/equity ratio compares the amount of debt a company has to the amount of equity. This shows how much debt a company has compared to its
ownership interest. A higher debt/equity ratio means the company is relying more on borrowed money than equity.
The debt ratio compares the total debt a company has to its total assets. This shows how much of the company's assets are financed through debt. A
higher debt ratio means the company is relying more on borrowed money to finance its operations.
The proprietor ratio compares the equity interest in a company to the total assets. This shows how much of the company's assets are owned by the
shareholders. A higher proprietor ratio means the shareholders have a larger ownership interest in the company.
These measures are important because they can help investors and analysts evaluate a company's financial health and risk. For example, a high
debt/equity ratio may indicate that a company is taking on too much debt and may struggle to pay it back in the future. On the other hand, a high
proprietor ratio may indicate that the company is well-funded by its shareholders and has a lower risk of default.
Importance:
Solvency of firm (Interest coverage)
Overall cost of capital
The capital structure of a company is important because it can affect two key factors: the solvency of the firm and the overall cost of capital.
Solvency refers to a company's ability to meet its long-term financial obligations, such as paying back loans or bonds. A company with a high level of
debt and a low level of equity financing may have difficulty meeting these obligations, especially if interest rates rise. This is where interest coverage
comes into play - it measures a company's ability to pay its interest expenses. If a company has low interest coverage, it may be at risk of defaulting on
its debts.
The overall cost of capital is another important factor in a company's capital structure. Cost of capital refers to the total cost of financing a company's
operations and investments. A company's cost of capital is affected by the proportion of debt and equity financing it uses. Debt financing can be less
expensive due to tax benefits, but it can also increase a company's risk if it cannot pay back the borrowed money. Equity financing can be more
expensive in the long run but can also provide more flexibility and less risk.
Finding the right balance between debt and equity financing is important for maximizing shareholder value while also maintaining the company's
financial health and solvency. A company with too much debt and high interest coverage may struggle to grow, while a company with too much equity
financing may be leaving money on the table due to high costs.

4. NEED OFVALUATION
• We need to record Equity and Debt at F
AIRVALUE
• We need to compute Cost of Capital at F
AIRVALUE
Valuation is the process of determining the fair value of an asset or liability. In the context of equity and debt financing, valuation is
important for two main reasons: recording equity and debt at fair value and computing the cost of capital at fair value.
Recording equity and debt at fair value means that the value of these financial instruments on a company's balance sheet should
reflect their true market value. For example, if a company's stock is publicly traded, its value should reflect the current market
price of the stock. Similarly, if a company has issued bonds, the value of those bonds should reflect the current market interest
rates and credit risk. By recording equity and debt at fair value, companies can provide more accurate financial statements and
make better decisions based on the true value of their assets and liabilities.
Computing the cost of capital at fair value is important because it affects a company's ability to raise capital for its operations and
investments. The cost of capital is the total cost of financing a company's operations and investments. By using fair value for
equity and debt, a company can more accurately compute its cost of capital, which can help it make better decisions about
financing and investing. This can ultimately lead to increased shareholder value and better long-term financial health for the
company.
In summary, valuation is important for recording equity and debt at their true market value and computing the cost of capital at fair
value. By doing so, companies can provide more accurate financial statements and make better decisions about financing and
investing, which can ultimately lead to increased shareholder value and better long-term financial health.

5. VALUATION AND COST OF CAPITAL FOR
BONDS
Fixed Income/P
riced Security
Valuation and cost of capital are important concepts when it comes to fixed income securities, such as bonds. A bond is a type of debt security that
represents a loan made by an investor to a borrower, usually a company or government entity. Bonds pay a fixed interest rate to the investor, and the
principal is repaid at the end of the bond's term.
Valuation refers to the process of determining the fair market value of a bond. This involves considering factors such as the bond's interest rate, term, credit
risk, and current market conditions. The fair value of a bond is important for investors because it helps them make informed decisions about buying, selling,
or holding the bond.
Cost of capital refers to the total cost of financing a company's operations and investments. For a company that has issued bonds, the cost of capital
includes the interest payments it makes to bondholders. The cost of capital is an important factor for companies because it affects their ability to raise funds
and make investments.
For investors, the cost of capital is important because it affects the return they can expect to receive on their investment.
When it comes to bonds, the valuation and cost of capital are closely related. The fair value of a bond affects its yield, which is the return an investor can
expect to receive on the bond. The cost of capital for a company that has issued bonds depends on the interest rate it must pay to bondholders, which is
based on the bond's yield.
In summary, valuation and cost of capital are important concepts when it comes to bonds. Valuation helps investors determine the fair market value of a
bond, while the cost of capital is the total cost of financing a company's operations and investments, including interest payments to bondholders. The fair
value of a bond affects its yield, which in turn affects the cost of capital for the company that issued the bond.

6. USUAL TERMINOLOGY RELATED TO BONDS
• PAR VALUE:It is the face value of Bond.
• MARKET PRICE: It is the price at which bond is bought and sold in the market
• COUPON: It is amount which company agrees to payto bond holder ateachtime
period.It is mentioned in percentage of par value or face value.This may be paid annually
,
quarterly,or semi-annually.
• INTEREST RATE: it is the rate which is prevalent in market at a point of time
• TERM to MATURITY: It is the time period for which coupons may be paid by
company

7. In the context of bonds, there are several key terms to understand. These include par value, market price, coupon,
interest rate, and term to maturity.
Par value is the face value of a bond. It represents the amount that the bond will be worth at maturity. For example,
if a bond has a par value of $1,000, this means that the bond will be worth $1,000 when it reaches maturity.
Market price is the price at which a bond is currently trading in the market. This price may be higher or lower than
the bond's par value, depending on a variety of factors such as current market conditions, interest rates, and the
creditworthiness of the bond issuer.
Coupon refers to the interest payments that a bond issuer agrees to make to bondholders at regular intervals. The
coupon is typically expressed as a percentage of the bond's par value, and may be paid annually, quarterly, or
semi-annually. For example, if a bond has a coupon rate of 5% and a par value of $1,000, this means that the bond
issuer will pay $50 in interest payments each year.
Interest rate is the prevailing rate in the market at a given point in time. This rate may be influenced by a variety of
factors, such as inflation, economic growth, and monetary policy.
Term to maturity refers to the length of time that a bond will remain outstanding until it reaches its maturity date.
This is the point at which the bond issuer will repay the bond's par value to the bondholder.
In summary, par value represents the face value of a bond, while market price is the price at which the bond is
currently trading in the market. Coupon refers to the interest payments that a bond issuer agrees to make to
bondholders, while interest rate is the prevailing rate in the market. Term to maturity is the length of time that a bond
will remain outstanding until it reaches maturity.

8. SOMETYPES OF BONDS
• Plain vanillabond
• Zero Coupon Bonds
• Embedded options bonds
• Inflation Indexed Bonds
There are several types of bonds, including plain vanilla bonds, zero coupon bonds, embedded options bonds, and inflation
indexed bonds.
A plain vanilla bond is the most basic type of bond, which pays a fixed rate of interest at regular intervals until maturity, when
the principal is repaid.
A zero coupon bond, on the other hand, does not pay regular interest payments. Instead, it is sold at a discount to its face value
and repays the full face value at maturity. The difference between the purchase price and the face value represents the interest
earned on the bond.
Embedded options bonds have additional features or "options" that can impact the bond's value. For example, a callable bond
gives the issuer the right to redeem the bond before maturity, while a putable bond gives the holder the right to sell the bond
back to the issuer before maturity.
Inflation indexed bonds are designed to protect investors against inflation. The interest payments and principal amount of these
bonds are adjusted for changes in the consumer price index, which helps to maintain the purchasing power of the investment
over time.
In summary, plain vanilla bonds are basic bonds that pay regular interest and return the principal at maturity, while zero coupon
bonds do not pay regular interest and are sold at a discount to their face value. Embedded options bonds have additional
features that can impact their value, while inflation indexed bonds are designed to protect against inflation.

9. EXAMPLE OF PLAIN VANILLA BOND
• A 5-year 6% bond is available in the market at price of INR 450
• A 5-year semi-annual 6% bond is available at the market price of INR 700
• A 10-year 7% quarterly paid coupon is available.Current interest is 5%.The bond
will be redeemed at par
.
• A 5-year 5% annual coupon bond is available which will be redeemed at premium
of INR 100.The par value of bond is INR 1000.Current market interest rate is
6%.

10. COMPUTING FAIRVALUE (SHOULD BE PRICE) OF
BOND
T=0 T=1 T=2 T=3 T=4
P= 𝑎[
1
1−
(1+𝑟)𝑛
]+ 𝐹
𝑟 (1+𝑟)𝑛
Coupon=a Coupon=a Coupon=a Coupon=a
+
FinalValue=F
Where,a=coupon amount
r=market interest rate
n=term to maturity
F=redemption value or final value
P=Fair value of bond/Price

11. The fair value or price of a bond is the current market value of the bond. This value is calculated based on several factors, including
the bond's coupon rate, interest rate environment, credit rating of the issuer, and time to maturity.
The formula for computing the fair value or price of a bond is:
PV = (C / r) x [1 - (1 / (1 + r)^n)] + (F / (1 + r)^n)
Where: PV = Present value or fair value of the bond C = Coupon payment r = Discount rate or yield to maturity n = Number of
periods or time to maturity F = Face value or par value of the bond
In this formula, the first part calculates the present value of the bond's coupon payments, while the second part calculates the
present value of the bond's face value. The sum of these two parts gives us the fair value or price of the bond.
To compute the fair value or price of a bond, you need to know the bond's coupon rate, face value, time to maturity, and the
prevailing interest rates in the market. Using these inputs, you can calculate the bond's yield to maturity, which is used as the
discount rate in the formula. Once you have the yield to maturity, you can use the formula to compute the fair value or price of the
bond.
The formula you are referring to is used to calculate the fair value or price of a bond, and is commonly known as the present value formula. It can be expressed as:
P = (A x [1 - (1 / (1 + R)^n)] + F / (1 + R)^n)
Where: P = Fair value or price of the bond A = Coupon payment or interest payment R = Yield to maturity or discount rate n = Number of periods or time to maturity F = Face
value or par value of the bond
To understand the formula, let's break it down into its component parts:
The first part of the formula (A x [1 - (1 / (1 + R)^n)]) calculates the present value of the bond's interest payments. This is done by dividing the coupon payment (A) by the
discount rate (R) and multiplying it by the present value factor [1 - (1 / (1 + R)^n)]. The present value factor represents the present value of the bond's cash flows, taking into
account the time to maturity (n) and the prevailing interest rates.
The second part of the formula (F / (1 + R)^n) calculates the present value of the bond's face value. This is done by dividing the face value (F) by the discount rate (R) and
multiplying it by the present value factor (1 / (1 + R)^n).
The sum of these two parts gives us the fair value or price of the bond (P), which represents the market value of the bond at a given point in time.
In summary, the present value formula is used to calculate the fair value or price of a bond based on its coupon rate, yield to maturity, time to maturity, and face value. The
formula takes into account the present value of the bond's cash flows and adjusts them for the prevailing interest rates in the market.

12. COMPUTE BOND PRICE
• What will be the bond price of 5%, 5-year bond? Current interest rate is
8%
• What will be the bond price of 5 year semi-annual 5% bond? Current
interest rate is 8%
• If above bond is available in market at Rs 950,should we buy this bond?

13. To compute the bond price using the present value formula, we can use the following formula:
P = (A x [1 - (1 / (1 + R)^n)] + F / (1 + R)^n)
Where: A = Annual coupon payment = 5% x Par Value R = Yield to maturity or discount rate = 8% n = Number of periods or time
to maturity = 5 years F = Face value or par value of the bond = 100
Using the formula, we can calculate the bond price as follows:
P = (5 x [1 - (1 / (1 + 8%)^5)] + 100 / (1 + 8%)^5) P = (5 x [1 - (1 / 1.4693)] + 100 / 1.4693) P = (5 x 0.3203 + 68.06) P = 69.08
Therefore, the bond price of a 5%, 5-year bond with a current interest rate of 8% is Rs. 69.08.
For a semi-annual bond, we need to adjust the coupon rate and the number of periods accordingly. The annual coupon payment
will be split into two semi-annual payments, each equal to 2.5% of the par value. The number of periods will be twice as much, or
10 semi-annual periods. The formula becomes:
P = (A x [1 - (1 / (1 + R/2)^n)] + F / (1 + R/2)^n)
Where: A = Semi-annual coupon payment = 2.5% x Par Value R = Yield to maturity or discount rate = 8% n = Number of periods
or time to maturity = 10 semi-annual periods F = Face value or par value of the bond = 100
Using the formula, we can calculate the bond price as follows:
P = (2.5 x [1 - (1 / (1 + 8%/2)^10)] + 100 / (1 + 8%/2)^10) P = (2.5 x [1 - (1 / 1.4238)] + 100 / 1.4238) P = (2.5 x 0.2986 + 70.18) P
= 77.47
Therefore, the bond price of a 5-year semi-annual 5% bond with a current interest rate of 8% is Rs. 77.47.
If the bond is available in the market at Rs. 950, we can compare its market price to its fair value (calculated using the present
value formula) to determine whether it is a good investment. In this case, the fair value of the bond is Rs. 77.47, which is higher
than the market price of Rs. 950. This indicates that the bond is undervalued and may be a good investment opportunity.
However, other factors such as the creditworthiness of the issuer and the prevailing market conditions should also be taken into
account before making an investment decision.

14. DETERMINANTS OF BOND PRICE
• The Price of bond decreases with increase in interest rate
• Bonds sell at premiumwhen coupon rate > interest rate
• Bonds sell atdiscount when coupon rate < interest rate
• Price of bond increases with increase in coupon rate
• Price of bond increases with increase in term to maturity
The price of a bond depends on several factors. First, when the interest rate in the market increases, the price of the
bond decreases because investors demand a higher yield to compensate for the increased interest rate. Second, if
the coupon rate of the bond is higher than the interest rate, the bond will sell at a premium because investors will be
willing to pay more to receive a higher return. Third, if the coupon rate is lower than the interest rate, the bond will
sell at a discount because investors will not be willing to pay as much for a lower return. Fourth, the price of a bond
increases with an increase in the coupon rate, as investors demand a higher yield for higher coupon payments.
Finally, the price of a bond also increases with an increase in the term to maturity, as investors demand a higher
yield for the longer period of time they must hold the bond.

15. DETERMINANTS OF BOND PRICE
• The effect of rise interest rate will be more on bond with high term to maturity (when coupon rate is same)
• The effect of rise in interest rate will be more on bond with higher term to maturity (when coupon rate is same)
• The effect of rise in interest rate will be more on bond with higher coupon rate (when term to maturity is same
• The effect of same rise and fallof interest rate is not same on price of bond. There is convexity in bond price and interest rate relationship
There are several determinants of bond price, and how they interact with changes in interest rates can be complex.
First, when the interest rate rises, the price of a bond with a longer term to maturity will be affected more compared to a bond with a
shorter term to maturity (assuming the coupon rate is the same). This is because the longer the term to maturity, the more sensitive
the bond is to changes in interest rates.
Second, a bond with a higher term to maturity will be affected more by changes in interest rates compared to a bond with a lower term
to maturity (assuming the coupon rate is the same). This is because the investor is committing to hold the bond for a longer period of
time, and therefore will demand a higher yield to compensate for the additional risk.
Third, a bond with a higher coupon rate will be affected less by changes in interest rates compared to a bond with a lower coupon rate
(assuming the term to maturity is the same). This is because the higher coupon payments provide a cushion against the decrease in
price resulting from the increase in interest rates.
Finally, there is convexity in the relationship between bond prices and interest rates. This means that the effect of the same rise and
fall in interest rates on bond prices is not symmetrical. In other words, a decrease in interest rates will increase the price of a bond
more than the price will decrease with the same increase in interest rates. This is because the relationship between bond prices and
interest rates is curved, not linear.

16. MEASURING RETURN ON BONDS (YIELD ON
BOND)
• CurrentYield:
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐶𝑜𝑢𝑝𝑜𝑛
𝑀𝑎𝑟𝑘𝑒𝑡 𝑃𝑟𝑖𝑐𝑒 𝑜𝑓 𝐵𝑜𝑛𝑑
• T
otal Return:𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐶𝑜𝑢𝑝𝑜𝑛 +𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑔𝑎𝑖𝑛𝑠
𝑀𝐴𝑟𝑘𝑒𝑡 𝑃𝑟𝑖𝑐𝑒 𝑜𝑓 𝐵𝑜𝑛𝑑
• Yield to Maturity: It is the average rate of return on bond if held till maturity. It is the
rate which equates payments (Coupon and redemption value) by bond to its
market price. We will compute this like IRR
• Yield to call: It is the average rate of return on bond if held till call for bond is made by
company

17. Current Yield: This is a simple way of measuring the return on a bond. It is calculated by dividing the annual coupon payment by
the market price of the bond. So, if a bond pays an annual coupon of $50 and is currently trading at a market price of $1000, the
current yield would be 5% (50/1000).
Formula: Current Yield = Annual Coupon Payment / Market Price of Bond
Total Return: This is a more comprehensive way of measuring the return on a bond, as it takes into account both the coupon
payments and any capital gains or losses from changes in the market price of the bond. It is calculated by adding the annual
coupon payment to the change in the market price of the bond over a given period, and then dividing the result by the initial
market price of the bond.
Formula: Total Return = (Annual Coupon Payment + Capital Gains or Losses) / Initial Market Price of Bond
Yield to Maturity: This is the average rate of return on a bond if it is held until it matures. It takes into account the timing and size
of all the bond's cash flows, including the coupon payments and the redemption value at maturity. It is the discount rate that
equates the present value of all these cash flows to the market price of the bond. Yield to maturity is similar to Internal Rate of
Return (IRR) used in finance.
Formula: Yield to Maturity = IRR(Bond's Cash Flows, Market Price of Bond)
Yield to Call: This is the average rate of return on a bond if it is held until it is called for redemption by the issuer before maturity.
It is similar to yield to maturity, but instead of using the maturity date, it uses the call date as the end point for the cash flows.
Yield to call is used for callable bonds that have a call feature (option for issuer to retire bonds before maturity).
Formula: Yield to Call = IRR(Bond's Cash Flows until Call Date, Call Price of Bond)
Note that the cash flows used in calculating the yields are the coupon payments and the redemption value (or call price),
discounted to present value using the appropriate discount rate. Also, bond prices may fluctuate in the market, and so yields
may change over time

18. PROBLEM
• 5% 5-year bond is available in the market atRs. 950.What is the
YTM of bond?
• If above bond will be called after three years at Rs.970.What is
theYTC of bond?
• A person purchases above bond at Rs.950 and sells it next year
at Rs 960.What is current yield and total return?

19. 1.To calculate YTM (yield to maturity) of the bond, we need to solve for the discount rate that equates the present value of the future cash flows (coupons and
principal) with the bond's current market price.
The formula for YTM is:
Market Price = (Coupon Payment / YTM) x [1 - 1 / (1 + YTM)^n] + Face Value / (1 + YTM)^n
Where: Market Price = Rs. 950 , Coupon Payment = 5% x Face Value = 5% x 1000 = Rs. 50 , Face Value = Rs. 1000
n = number of years to maturity = 5
YTM = Yield to Maturity (unknown)
By substituting the given values into the above formula, we can solve for YTM as follows:
950 = (50/YTM) x [1 - 1/(1+YTM)^5] + 1000/(1+YTM)^5
We can use trial and error or the Excel function "RATE" to solve for YTM, which turns out to be approximately 7.37%.
Therefore, the YTM of the 5% 5-year bond is 7.37%.
If above bond will be called after three years at Rs. 970. What is the YTC of bond?
YTC or Yield to Call is the rate of return on a bond if it is held until it is called by the issuer. In this case, the bond is called after three years at Rs. 970.
To calculate YTC, we need to use the formula:
YTC = (C + ((F - P) / n)) / ((F + P) / 2)
Where: C = annual coupon payment F = face value of the bond P = purchase price of the bond n = number of years until the bond is called
Using the given information, we have: C = 5% * Rs. 1000 = Rs. 50 F = Rs. 1000 P = Rs. 950 n = 3 years
So, YTC = (50 + ((1000 - 950) / 3)) / ((1000 + 950) / 2) YTC = 12.61%
Therefore, the Yield to Call on this bond is 12.61%.
A person purchases above bond at Rs. 950 and sells it next year at Rs 960. What is current yield and total return?
The current yield is the annual return on the bond relative to its current market price. To calculate the current yield, we can use the formula:
Current Yield = Annual Coupon Payment / Market Price of Bond
In this case, the annual coupon payment is Rs. 50 (5% of Rs. 1000 face value) and the market price of the bond is Rs. 950. So, the current yield is:
Current Yield = 50 / 950 Current Yield = 5.26%
The total return is the sum of the current yield and the capital gains yield (or loss). The capital gains yield is the change in the market price of the bond relative to its
purchase price, expressed as a percentage. To calculate the capital gains yield, we can use the formula:
Capital Gains Yield = (Selling Price - Purchase Price) / Purchase Price
In this case, the purchase price is Rs. 950 and the selling price is Rs. 960. So, the capital gains yield is:
Capital Gains Yield = (960 - 950) / 950 Capital Gains Yield = 1.05%
Therefore, the total return is:
Total Return = Current Yield + Capital Gains Yield Total Return = 5.26% + 1.05% Total Return = 6.31%
So, the person who purchased the bond at Rs. 950 and sold it at Rs. 960 earned a total return of 6.31% over one year.

20. COMPUTING BOND PRICE AND YTM
WITH DIFFERENT INTEREST RATE EACH
YEAR

21. SPOT RATE
• Spot rate: The interest rate prevalent in the market for current year are technically known
as SPOT RATE. These are usually deduced from ZCB. These are discounting factor for each
year
E.g, Spot rate for current year is 6%. Spot rate for one year zero-coupon bond (ZCB) is 6%.
Spot rate for two-year ZCB is 7%.Spot rate for three year ZCB is 8%
• Forward rate: These are forward looking interest rates and are deduced from spot rates.
The second year forward rate will be deduced from one-year and two-year spot rates
𝐹01 =
(1 + 𝑟2)2
1
(1 + 𝑟 )1
− 1
In general,(1 + 𝑟1)1∗ (1 + 𝑓01) ∗ (1 + 𝑓02) ∗−−−−−−−−∗ (1 + 𝑓0𝑛) = (1 + 𝑟𝑛)𝑛

22. Spot rate refers to the current interest rate in the market for a particular year. For example, if the current year's
spot rate is 6%, it means that the interest rate prevailing in the market for a one-year zero-coupon bond is 6%.
Similarly, the spot rate for a two-year zero-coupon bond would be 7% and for a three-year zero-coupon bond
would be 8%.
Now, let's talk about forward rate. These are interest rates that we estimate will apply in the future. We can
calculate forward rates based on the current spot rates. For example, the two-year forward rate is the interest
rate that we expect
will apply in two years' time, based on the current spot rates for one and two-year bonds.
To calculate the two-year forward rate, we use this formula: 𝐹01 = (1 + 𝑟2)2 / (1 + 𝑟1) - 1
This formula tells us that the two-year forward rate (F01) is equal to (1 + the two-year spot rate) squared, divided
by (1 + the one-year spot rate), minus one.
We can also use spot rates to calculate the prices of bonds with different maturities. The formula we use for this
is: (1 + 𝑟1)1∗ (1 + 𝑓01) ∗ (1 + 𝑓02) ∗−−−−−−−−∗ (1 + 𝑓0𝑛) = (1 + 𝑟𝑛)𝑛
This formula helps us find the price of a bond with a certain maturity, using the spot rates for different maturities.
The formula essentially tells us that the product of the (1 + spot rate) for each year, raised to the power of the
number of years, is equal to the price of the bond.
In the formula for forward rate, F01 represents the forward rate for the period between year 1 and year 2, which is calculated using the spot rates
for year 1 and year 2.
The formula for calculating F01 is:
𝐹01 = (1 + 𝑟2)^2 / (1 + 𝑟1) − 1
Where r1 is the spot rate for year 1 and r2 is the spot rate for year 2. The result is the implied interest rate for the period between year 1 and year
2.

23. LET’S UNDERSTAND SPOT RATE

24. TERM STRUCTURE OF SPOT RATE AND YIELD
CURVE
• Relationship between spot rate and their
term to maturity
• Curve shows expectations of investors in
market
• We first plot spot rates  compute
market price of bonds with different rate
for each year  based this computeYTM
for bond
• Curve showing relationship betweenYTM
and term to maturity isYIELD CURVE

25. The term structure of spot rate and yield curve show us how the interest rates in the market change
over time. Spot rates are the interest rates that are currently being offered for different terms or periods
of time. We can use these spot rates to calculate the market price of bonds with different maturities or
terms. Once we know the market price of these bonds, we can calculate the yield to maturity (YTM) of
each bond.
The yield curve shows us the relationship between the yield to maturity and the term to maturity of the
bonds. It's a graph that shows us the expectations of investors in the market. For example, if investors
expect interest rates to go up in the future, then the yield curve will slope upwards, indicating that bonds
with longer maturities will have higher yields than bonds with shorter maturities.
In summary, the term structure of spot rate and yield curve can help us understand how interest rates
are changing over time and how this affects the value of bonds with different maturities.

26. PROBLEM
The spot rate available in market are:
A 5%,5-year annual coupon bond is available in the market.
a) Compute price of bond.
b) ComputeYTM of bond.
r1 r2 r3 r4 r5
5% 5.25% 5.5% 5.75% 6%

27. COST OF CAPITAL FOR DEBT
• 𝐾𝑑 = 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡
𝐷𝑒𝑏
𝑡
𝑑 𝐷𝑒𝑏
𝑡
• After tax cost of debt 𝑘 = 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡
∗ (1 − 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒)
The cost of debt is the interest rate a company pays to borrow money. It is a measure of how much it costs a company to use debt financing,
which is borrowing money rather than issuing equity (selling ownership in the company). The formula for cost of debt (kd) is simple: it is the
interest rate (I) paid by the company divided by the amount of debt (De) it has borrowed, expressed as a percentage:
kd = I/De
For example, if a company has borrowed $100,000 at a 5% annual interest rate, the cost of debt would be:
kd = 0.05 x $100,000 / $100,000 = 0.05 or 5%
This means that the company must pay an annual interest rate of 5% on the $100,000 borrowed, which represents the cost of debt for the
company. The cost of debt is an important factor in calculating a company's weighted average cost of capital (WACC), which is the average cost
of all of the company's capital sources (debt and equity) weighted by the proportion of each source in the company's capital structure.

28. PRACTICE QUESTIONS: CHAPTER 3
• 1,2,3,4,6,8,9,10,11,12,13,15,16 (a),19,20

29. VALUATION AND COST OF CAPITAL FOR
EQUITY
Variable Income Security Variable income security is a type of financial instrument whose income or returns
vary and are not fixed or predetermined. Examples of variable income securities include stocks, mutual
funds, exchange-traded funds (ETFs), real estate investment trusts (REITs), and some bonds.
The income or returns on variable income securities fluctuate based on various factors such as market
conditions, interest rates, economic performance, and company performance. For example, the value of a
stock may increase or decrease based on the performance of the company, the industry, or the broader
economy. Similarly, the dividend payout on a stock may vary depending on the company's profitability and
dividend policy.
Investors who are willing to take on higher risks in exchange for potentially higher returns may invest in
variable income securities. However, these investments are subject to market volatility and can result in
significant losses as well. It is important for investors to carefully evaluate the risks and potential rewards
before investing in variable income securities.

30. USUAL TERMINOLOGY RELATED TO EQUITY
• Earnings per share (EPS): (PAT-preference dividend)/no.of common equity shareholders
• Dividend per share (DPS):Amount declared by company to pay its each common shareholder
• Payout ratio: Dividend per share as Proportion of EPS (DPS/EPS)
• Retention ratio or Plough back ratio: 1-payout ratio,proportion of net profit retained by company
• Return on Equity:P
AT/Equity capital or EPS/Book value per share
• Market capitalization rate or Cost of Equity: expected rate of return by equity share holders of same risk class
• DividendYield: D1/P0
• Primary Market or Initial Public Offer:When company first issues shares to common public
• Secondary Market:Market where shares (already issued) are traded.This provides liquidity.

31. Earnings per share (EPS): This is the amount of profit that a company has earned for each share of common stock.
To calculate EPS, you take the company's net income (profit after taxes) and subtract any preferred dividends (if
applicable), then divide that number by the total number of outstanding common shares.
Dividend per share (DPS): This is the amount of money that a company pays out to its shareholders for each share
of common stock they own.
Payout ratio: This is the proportion of a company's earnings that are paid out as dividends to shareholders. It is
calculated by dividing DPS by EPS.
Retention ratio or Plough back ratio: This is the proportion of a company's earnings that are retained and
reinvested back into the company instead of being paid out as dividends. It is calculated by subtracting the payout
ratio from 1.
Return on Equity: This is a measure of how much profit a company generates with the money that shareholders
have invested in it. It is calculated by dividing the company's net income by its total equity capital or by dividing
EPS by the book value per share.
Market capitalization rate or Cost of Equity: This is the expected rate of return that equity shareholders require to
invest in a company of similar risk. It is the return that investors demand on their investment in the company's
equity shares.
Dividend Yield: This is the ratio of the annual dividend payment per share to the current market price of the share. It
tells you how much income you can expect to earn from holding the stock.
Primary Market or Initial Public Offer: This is the market where a company first issues its shares to the public in
order to raise capital.
Secondary Market: This is the market where shares that have already been issued by a company are traded
among investors. This market provides liquidity to investors who want to buy or sell shares.

32. APPROACHES TO EQUITY VALUATION
Fundamental Approach
Price of equity in market is based on
fundamentals,that is,earnings of the
firm and to equity shareholders vis-à-vis
its risk
TechnicalApproach
Given market price is the best price
and future price will depend upon
path of past prices
Discounted Cash Flow Method
Price is the PV of all future cash benefits
received by equity share holder
RelativeValuation or Comparatives
Based on principle of“Law of one Prices”.
Price of company’
s share will be similar to
its peers
Based on Market
Expected Price can be computed based
on market and risk class withAsset
Pricing Models (CAPM or Market Model)

33. The technical approach to equity valuation is based on analyzing past market prices and patterns to predict
future prices. This approach assumes that market prices accurately reflect all available information and that
future prices can be predicted based on the path of past prices.
On the other hand, the fundamental approach looks at the earnings of the company and its risk to determine the
price of its shares. This approach uses methods such as the discounted cash flow method, which calculates the
present value of all future cash flows that an investor can expect to receive from owning the shares.
The relative valuation approach compares the company's share price with its peers in the same industry to
determine if the share is overvalued or undervalued. This approach is based on the principle of the "Law of one
Prices" which states that the price of a company's share will be similar to that of its peers.
Finally, the market approach to equity valuation calculates the expected price of a share based on the market
and the risk class with the use of Asset Pricing Models such as the Capital Asset Pricing Model (CAPM) or the
Market Model.
In summary, each approach to equity valuation has its own advantages and limitations. Investors may use one
or a combination of these approaches to determine the value of a company's shares before making an
investment decision.

34. DISCOUNTED CASH FLOW METHOD
Considering Dividends as Cash Flows to Equity shareholders
Considering one year
time period
𝑃0 =
𝐷1 + 𝑃1
1 + 𝑟𝑒
Considering‘H’ time period
𝑃
𝐷1 𝐷2 𝐷𝐻 + 𝑃𝐻
0 =
(1 + 𝑟)1 +
(1 + 𝑟)2 + ⋯ +
(1 + 𝑟)𝐻
Considering Perpetuity
0
𝐷1
𝑃 =
𝑟

35. The Discounted Cash Flow (DCF) method is a financial valuation technique used to estimate the intrinsic value of an investment
or asset. This method involves forecasting the future cash flows that an investor can expect to receive from the investment and
discounting them back to their present value using an appropriate discount rate.
When considering dividends as cash flows to equity shareholders, the DCF formula for a one-year time period is:
𝑃0 = 𝐷1 + 𝑃1 / (1 + 𝑟)
where P0 is the present value of the investment, D1 is the dividend expected to be paid out in the first year, P1 is the expected
price of the investment at the end of the first year, and r is the discount rate.
To extend this formula to multiple years (H time period), we add the present value of all the expected dividends and the final
price at the end of the investment period, discounted by the appropriate factors for each year. The formula becomes:
𝑃 = 𝐷1 / (1 + 𝑟)^1 + 𝐷2 / (1 + 𝑟)^2 + … + 𝐷𝐻 + 𝑃𝐻 / (1 + 𝑟)^𝐻
where P is the present value of the investment, D1 to DH are the expected dividends for each year, and PH is the expected
price of the investment at the end of the investment period.
In the case of a perpetuity, where the dividends are expected to continue indefinitely, the formula simplifies to:
𝑃 = 𝐷1 / 𝑟
where P is the present value of the investment, D1 is the expected dividend for the first year, and r is the discount rate. This
formula assumes that the dividend will remain constant indefinitely.
In summary, the DCF method is a valuable tool for estimating the intrinsic value of an investment or asset based on its expected
future cash flows. By discounting these cash flows to their present value, investors can make more informed investment
decisions and ensure that they are paying a fair price for the investment.

36. ASSUMING DIVIDENDSWITH KNOW N GROWTH
RATE
Considering dividends grow in
future at known growth rate
‘g’such that
𝐷1 = 𝐷0(1 + 𝑔)1
𝐷2 = 𝐷1(1 + 𝑔)1 = 𝐷0(1 + 𝑔
)2
𝐷3 = 𝐷2(1 + 𝑔)1 = 𝐷0(1 + 𝑔
)3
… … …
𝐷𝑛 = 𝐷𝑛−1(1 + 𝑔)1 = 𝐷0(1 +
𝑔)𝑛
When dividends grow at a known rate 'g', the future dividends can be calculated based on the current
dividend and the growth rate. This is useful when projecting future cash flows and valuing an investment
using the DCF method.
Let's assume that the current dividend is D0, and the growth rate is g. The expected dividend in the first
year, D1, can be calculated as:
𝐷1 = 𝐷0(1 + 𝑔)1
This formula shows that the expected dividend in the first year will be the current dividend (D0) multiplied
by one plus the growth rate (g).
The expected dividend in the second year, D2, can be calculated by applying the same formula to D1, as
follows:
𝐷2 = 𝐷1(1 + 𝑔)1 = 𝐷0(1 + 𝑔)2
This formula shows that the expected dividend in the second year will be the expected dividend in the first
year (D1) multiplied by one plus the growth rate (g). Alternatively, we can use the formula to calculate the
expected dividend in any year n:
𝐷𝑛 = 𝐷𝑛−1(1 + 𝑔)1 = 𝐷0(1 + 𝑔)𝑛
This formula shows that the expected dividend in any year n will be the expected dividend in the previous
year (Dn-1) multiplied by one plus the growth rate (g).
By using these formulas, investors can project the expected future dividends of an investment and
calculate the present value of those cash flows using the DCF method. This allows investors to estimate
the intrinsic value of the investment and determine whether the current market price is fair.

37. DISCOUNTED CASH FLOW METHOD
Considering one year time period
𝑃0
𝐷1 + 𝑃1
=
1 + 𝑟
𝑒
𝐷1(1 + 𝑔)
𝑃1 =
𝑟 − 𝑔
Considering‘H’ time period
𝑃0 = +
𝐷1 𝐷2
(1 + 𝑟)1 (1 + 𝑟)2
𝐷𝐻 + 𝑃𝐻
+ ⋯ +
(1 + 𝑟)𝐻
𝐷𝐻(1 + 𝑔)
𝑃𝐻 =
𝑟 − 𝑔
Considering Perpetuity
0
𝐷1
𝑃 =
𝑟
𝑃0 = 𝐷0(1+𝑔)
𝑟−
𝑔
or
𝐷1
𝑟−𝑔

38. The Discounted Cash Flow (DCF) method is a technique used to estimate the value of an investment based on its future cash flows. The formula you have
provided is used to calculate the value of an investment after one year, using the following variables:
P0: the current price of the investment
D1: the cash flow expected to be generated by the investment in the next year
r: the required rate of return, or the minimum rate of return investors expect to receive for investing in the security
g: the expected growth rate of the cash flow.
The first part of the formula (D1 + P / (1 + r)) calculates the present value of the expected cash flow generated by the investment over the next year,
discounted at the required rate of return. This value is added to the current price of the investment to get the total estimated value of the investment after one
year (P1).
The second part of the formula (D1(1+g) / (r-g)) is used to estimate the value of the investment at some point in the future beyond one year. This formula
assumes that the cash flow generated by the investment will grow at a constant rate of g per year, and discounting those future cash flows at the required rate
of return provides the estimated value of the investment at that future point in time (P1).
So, in summary, the formula you provided is used to estimate the current and future value of an investment based on its expected cash flows, required rate of
return, and expected growth rate of those cash flows.

39. CONSIDERING TWO GROWTH RATES
Suppose initial growth rate g1 and sustainable growth g2 (with g1>g2)
Considering‘H’ time period
𝐷0(1 + 𝑔1)1 𝐷0(1 + 𝑔1)2 (𝐷0(1 + 𝑔1)𝐻) + 𝑃𝐻
𝑃0 =
(1 + 𝑟)1 +
(1 + 𝑟)2 + ⋯ +
(1 + 𝑟)𝐻
𝐻
𝐷𝐻(1 + 𝑔2)
𝑃 =
𝑟 − 𝑔2

40. LET’S UNDERSTAND
• XYZ Co.Ltd.is expected to paydividend of Rs 20 and
expected price next year will beRs 150.How much price
should I paynow to buy this share?
• XYZ Co. Ltd.has paid Rs 20 as dividend this year
.The
dividend is expected to grow attherateof 5% p.a.How much
price should I paynow to buythis shareifmyhorizon period
is a) one-year b) five years
c) perpetuity
• XYZ Co. Ltd has paid Rs. 20 as dividend this year
.The company
may have higher growth rate of 5% for initial three years and
sustainable growth rate of 3% after that. How mush should I pay
now to buy this share if my horizon period is a) one year b) five
years
c) perpetuity

41. FUNDAMENTAL GROWTH RATE
g = ROE * Retention rate
(This assumes that financing is only available from retained earnings)
In general,Market capitalization rate,r = Dividend yield + g
1. The company usually declares 60% of earnings as dividend.The PAT is Rs 5lakhs and Equity
capital is Rs 10 lakhs with face value of 1000.Compute growth rate for company.
2. If Dividend yield of above company is 5% then what will be cost of equity or market
capitalization rate?
The fundamental growth rate is a financial metric used to
calculate the maximum rate of growth a company can achieve
without the need for additional external funding. It is the growth
rate a company can maintain using only its own earnings to
finance expansion. In other words, it is the rate at which a
company can grow while still being able to pay dividends,
maintain its current level of debt, and make necessary
investments in fixed assets, research and development, and
other capital expenditures. The fundamental growth rate is an
important metric for investors and analysts to evaluate a
company's financial health and future growth potential.

42. CONSIDERING ‘EARNINGS’
INSTEAD OF ‘DIVIDEND’
• There can be some stocks which don’t pay regular dividend
• Dividend policy of company is usually sticky
• There can be stocks which don’t pay dividend at all (Growth stocksVs Income Stocks)
0
𝐷1 𝐸1
𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛, 𝑟 =
𝑃
=
𝑃0
Assumption is all earnings are
reinvested back and must provide
return equal to cost of equity or
market capitalization rate
Corollary
The E/Pis cost of
capital only when
future project
NPV=0

43. When we talk about stocks, there are two main types of stocks: growth stocks and income stocks.
Income stocks are those that provide regular income to investors in the form of dividends. These stocks are usually issued by well-
established companies that have a stable earnings history and don't need to reinvest all their earnings back into the business. These
stocks are generally less volatile and less risky than growth stocks.
On the other hand, growth stocks are those that are expected to grow at a faster rate than the overall market. These stocks may not
pay dividends or may pay a lower dividend, as the company needs to reinvest its earnings back into the business to fuel growth.
These stocks are generally riskier and more volatile than income stocks, but they have the potential to generate higher returns.
When we consider earnings instead of dividends, we are looking at the profitability of the company. Earnings are the amount of profit
a company makes after deducting all expenses. Investors who focus on earnings growth look for companies that are reinvesting their
profits back into the business to fuel future growth. These investors believe that companies that are growing their earnings at a fast
pace will eventually increase in value, leading to higher stock prices.
Overall, whether an investor chooses to focus on dividends or earnings depends on their investment objectives and risk tolerance.
Income stocks are a good option for those who want regular income from their investments, while growth stocks are a good option for
those who are willing to take on more risk for the potential of higher returns.
The formula "expected return, r = dividend/purchase price = earnings/purchase price" assumes that all the earnings or dividends are
reinvested back into the company, and that this reinvestment provides a return that is equal to the cost of equity or the market
capitalization rate.
The corollary to this is that the earnings-to-price (E/P) ratio is only equal to the cost of capital when the net present value (NPV) of
future projects is zero. In other words, if a company is able to invest its earnings in projects that have a positive NPV, then the E/P
ratio will be higher than the cost of capital. On the other hand, if a company's future projects have a negative NPV, then the E/P ratio
will be lower than the cost of capital.
In simple terms, this means that if a company is able to invest its earnings into profitable projects, then its stock will be worth more
than its cost of capital. However, if the company's future projects are not profitable, then its stock will be worth less than its cost of
capital. Therefore, investors should carefully evaluate a company's potential for future profitability before deciding whether to invest in
its stock.

44. LET’S UNDERSTAND IMPLICATIONS……..1/2
A company has EPS = Rs 10 and current market price is 100.The cost of equity = 0.1 or
10%
When this Rs 10 per share is invested back then company expects to earns Rs 1 per share
(additional) on this (let’s say) leading to EPS = Rs 11
So company would expect price as EPS = 11 and r =0.1 so price should be 110
But NPV of investment = -10 + (1/0.1) = 0
So,for present sacrifice made by investors they receive future
benefits  this leads to no rise in share price

45. LETS UNDERSTAND IMPLICATIONS………….2/2
But usually market
favours such companies
and
𝑃0 > 𝐸1
𝑟
0 𝑟
𝑃 = 𝐸1
+ PVGO
A company has r=10% and ROE = 15%. It has payout ratio = 60%.
Therefore g= 6% (=0.15*(1-0.6)).The dividend expected next year
is Rs 5.
0
𝑃 =
5
0.1−0.06
= 125 (Price with dividend declared)
8.33
If company does not declare dividend at all.EPS = DPS/payout ratio
= 5/0.6 = 8.33
𝑃0 = 0.1−0.06
= 208.33 (with growth)
𝑃0 = 8.33
0.1
= 83.33 (with no growth)
PVGO = 208.33 – 83.33 = 125

46. RELATIVEVALUATION
Peers Price to BookValue Price to Earnings Price to Sales
A 200 5 0.5
B 250 6 0.2
C 300 8 0.6
D 275 3 0.1
Mean 256.25 5.5 0.35
For XYZ Co.Compute Price based on its peers.
Information available is
BookValue of per share= 25
Earnings per share= 20
Sales per share = 1000

47. COST OF CAPITAL BASED ON ASSET PRICING
MODELS
Computing ‘expected rate of return’ based on CapitalAsset Pricing Model
𝑟𝑖 = 𝑟𝑓 + 𝛽(𝑟𝑚 − 𝑟𝑓)
Computing ‘expected rate of return’ based on Market Model
𝑟𝑖 = 𝛼𝑓 + 𝛽(𝑟𝑚)

48. PRACTICE QUESTIONS
Chapter-4 (EquityValuation):1,3,4,5,6,7,9,10,16,17,18,

49. OVERALL COST OF CAPITAL (WACC)
WeightedAverage Cost of Capital (WACC)
𝑟𝑜 = 𝑟𝑒 𝑤𝑒 + 𝑟𝑑 𝑤𝑑 (before tax)
𝑟𝑜 = 𝑟𝑒 𝑤𝑒 + 𝑟𝑑 𝑤𝑑 ∗ (1 − 𝑡𝑐 ) (after tax)
A company has raised 40% of its finance from debt and rest from equity.The cost of capital
for debt is 8% and cost of equity is 12%.What is WACC for company? If interests paidby
company has tax exemption and current tax rate is 30% then what isWACC of company?

50. LEVERAGE RATIO AND COST OF
CAPITAL
The leverage ratio is a measure of a company's debt level relative to its equity. It tells us how much of the company's
assets are financed through debt compared to equity. A higher leverage ratio means that the company is using more
debt to finance its operations, which can be both good and bad. On the one hand, debt can be cheaper than equity
because interest on debt is tax-deductible, and it can also help increase returns on equity. On the other hand, too much
debt can be risky because it increases the company's financial obligations, which can be difficult to meet if the
company's profits decline.
The cost of capital is the minimum return that investors require to invest in a company. It represents the cost of financing
a company's operations through a combination of debt and equity. The cost of debt is the interest rate that the company
pays on its debt, while the cost of equity is the return that investors expect to receive in exchange for investing in the
company's stock.
The leverage ratio can affect the cost of capital because it influences the level of risk that investors perceive in the
company. A higher leverage ratio means that the company has more debt and is therefore riskier for investors. As a
result, investors may demand a higher return to compensate for the increased risk. This higher return increases the
company's cost of capital, making it more expensive for the company to finance its operations.
In summary, the leverage ratio and the cost of capital are closely related. A higher leverage ratio can increase the cost of
capital because it increases the perceived risk of the company. Therefore, companies must carefully manage their debt
levels to balance the benefits of debt financing with the increased cost of capital that comes with it.

51. COST OF CAPITAL AND LEVERAGE RATIO
• Should company have debt?
• Does Debt enhances value of company?
• Does Debt enhances value of equity shares?
• Does Level of Debt affects Overall cost of capital (WACC)?
• Does Level of Debt affects Cost of Equity?
• What should be optimum level of debt in company?
• Is there any optimum Debt/Equity?