Principle 1.

Investment Basics …
• What is investing?
The giving up of something important to us now (money or time) in order to get
something better in the future.

• What is sacrifice? “saving”

The giving up of something important to us now (money or time) in order to get
something better in the future.

• Do we all invest?
With every choice we make each day, we are investing (generally) our time.

• Why should we learn to invest?

A- From our view:
1- To accomplish our personal and family goals.
2- To have resources for retirement, education, etc.
3- To grow our financial assets to serve and bless our families and others.

B- From a spiritual view:

1- To teach us to sacrifice.
2-To teach us the “law of the harvest”.
3- To teach us to be “wise stewards”.
4- To allow us to help and bless others.

• What is the difference between investing and gambling?

* Investing: The odds are in your favor
1- There is a favorable risk-return tradeoff.
2- It is part of a long-term plan.
3- You have done your homework.
4- It involves the creation of wealth.

* Gambling: The odds are in another’s favor

1- There is no favorable risk-return tradeoff.
2- There is no long-term plan.
3- There is no homework, only chance.
4- It is a zero-sum game—no wealth is created.
2. Savings vs. Investing. “define”

Savings: It is the part of current income that is not spent on consumption.

Investments: is the purchase of assets with the goal of increasing future income.

Risk, Return, and Liquidity:

• Risk: Chance of investment loss.

• Return: Profit/gain from investment.

• Liquidity: Ease of converting investment to cash.

• Savings • Investments
• Low risk • High risk
• Low return • High return
• High liquidity • Low liquidity

Time Value of Money (Complete …)

• The time value of money refers to the fact that a dollar in hand today is
worth more than a dollar promised at some future time.

Future Value (Complete …)

• Refers to the amount of money an investment will grow over a specific period
of time at a specific interest rate.

future value is the cash value of an investment at a given time in the future.

Risk and Return

• What is the relationship between risk and return?
3. Financial institutions:
3. Saving, Investment, and the Financial System

• The financial system (Complete …) consists of the group of institutions in the

economy that helps to match one person’s saving with another person’s
investment.

• Financials flow: It moves the economy’s scarce resources from savers to

borrowers.

Financial institutions in the economy

coordinate the actions of savers and borrowers.

• Financial institutions can be grouped into two different categories: “v.i.p”

1.Financial markets.
2.Financial intermediaries.

Q. Define …
1. Financial markets >>> are the institutions through which savers can directly
provide funds to borrowers.

2. Financial intermediaries >>> are financial institutions through which savers can
indirectly provide funds to borrowers.

1. *Financial Markets 2. * Financial Intermediaries

1.Stock Market. 1. Banks.
2.Bond Market. 2.Mutual Funds.

1. *Financial Markets:
1.* The Stock Market (Complete …)

1. Stock represents a claim to partial ownership in a firm and is therefore, a

claim to the profits that the firm makes.

• The sale of stock to raise money is called equity financing.

- Compared to bonds, stocks offer both higher risk and potentially higher
returns.
2. Most newspaper stock tables provide the following information:
1. Price (of a share).
2. Volume (number of shares sold).
3.Dividend (profits paid to stockholders).
4. Price-earnings ratio.

2.* The Bond Market (Complete …)

A bond is a certificate of indebtedness that specifies obligations of the borrower
to the holder of the bond.

* Characteristics of a Bond: (Complete …)

1- Term: The length of time until the bond matures.

2- Credit Risk: The probability that the borrower will fail to pay some of the
interest or principal.

3- Tax Treatment: The way in which the tax laws treat the interest on the
bond.
o Municipal bonds are federal tax exempt.

2. * Financial Intermediaries

1. * Banks (Complete …)

• Take deposits from people who want to save and use the deposits to make loans
to people who want to borrow… CR.

• Pay depositors interest on their deposits and charge borrowers slightly higher
interest on their loans… DEP.

• Help create a medium of exchange by allowing people to write checks against

their deposits.
- A medium of exchange is an item that people can easily use to engage in
transactions.

• Facilitate the purchases of goods and services.

 2. * Mutual Funds (Complete …)

• A mutual fund is an institution that sells shares to the public and uses the
proceeds to buy a portfolio, of various types of stocks, bonds, or both.

• Mutual funds allow people with small amounts of money to easily diversify.

• Other Financial Institutions:

1. Credit unions 3. Insurance companies
2. Pension funds 4. Loan sharks

Saving and investment in the national income accounts (Complete …)

• Recall that GDP is both total income in an economy and total expenditure on
the economy’s output of goods and services:
Y = C + I + G + NX

• Consider a closed economy – an economy that does not engage in international

trade:
Y=C+I+G

Some Important Identities

1. Now, subtract C and G from both sides of the equation:

2. Y – C – G = I

3. National saving (S) = income left after consumption & government spending.

4. Substituting S for Y – C – G, the equation can be written as:

5. S = I
Some Important Identities
National saving, or saving, is equal to:
S=I
S=Y–C–G
S = (Y – T – C) + (T – G)
 The Meaning of Saving and Investment (Complete …)

A- National Saving

• National saving is the total income in the economy that remains after paying for
consumption and government purchases.

B- Private Saving

• Private saving is the amount of income that households have left after paying
their taxes and paying for their consumption.

• Private saving = (Y – T – C)

4.introo
* Bond Market Overview
• Bond market exists to help governments, corporations, and other borrowers
intersect with capital providers.
• Bonds are considered safer than stocks or many other assets.
• Bonds are a science, stocks are an art.
• Bonds trade over the counter - no central exchange.
• Bond markets lack transparency.
• Largely dominated by institutional investors.

* Yield & Price Inversely Related

* Key Terms:
Bond characteristics:
➢Issuer. ➢Price.
➢Maturity. ➢Yield.
➢Coupon. ➢Callable or non-callable (bullet)?
➢Rating. ➢Basis point (1/100 of 1%).

• Why an Investment Policy?

▪ Defines the investment program.
o Legal &permitted activities.
o Who's responsible for the portfolio.
o Measurement of results.
▪ Provides structure to investment program.
▪ Dynamic process-can evolve over time.
• local Agency Investment Objectives:
• Primary objectives of local agency investing.
➢Safety.
o Protect principle
➢Liquidity.
o Meet anticipated cash flow requirements Since all possible demands
cannot be anticipated, hold securities that have active secondary markets.

➢Yield/Rate of Return.
o Earn a reasonable return relative to the risk being assumed.

• Why Prepare a Cash Flow Forecast?

1. Projection of anticipated receipts & disbursements.

2. Ensures liquidity for disbursements.
3. Warns of impending budget problems.
4. Identifies short-term cash deficits.
5. Estimate of investable cash balances Liquid funds Core funds.
• Investment and Economic Analysis
5. Investment Appraisal

Compounding vs. Discounting “Example:”

• Invest sum over years, how much will it be worth?

• Terminal Value after n years @ r:

o TVn = p (1+r) n.
Example:
• p = 1000, r = 10%, n = 2.
Solution:
TVn = 1000(1+10%)2 =1210.

• Offer a final sum in n years, how much should I get now?

𝑻𝑽𝒏
o Discounted Present Value: DPV =
(𝟏+𝒓)𝒏

EXAMPLE:
• p = 1000, r = 10%, n = 2.
SOLUTION:
DVP = 1210 / (1+10%)2 =1000.

“MDAM EL DPV LESS THAN EL TVn kda yb2a Don’t investment “

• Discounting is the inverse or mirror image of compounding.
 Investment Appraisal
(a.k.a. Capital Budgeting)
• Central concepts:
o Capital cost (KC). o Discounted Present Value
o Opportunity cost of capital (DPV).
(typically r). o FACE VALUE (F).
o Net Present Value (NPV). o DISCOUNT RATE (r).
o Internal Rate of Return (IIR) o Time to maturity (T).
(IRP).

NPE (Net present value)

note: Kol power y3ny sana kdeda, y3ny Kol ma hnzod wahda hnzod
power.

o DPVCF= CF1 / (1+r) + CF2 / (1+r)2 =

Note:
o DPV – KC < 0, Do not invest.
o DPV – KC >0, invest.
 Rule >>> DPVCF = =

o DPVCF= 1100 / (1+10%) + 1210 / (1+10%)2 =2000.

o Kc = 2100.

o o DPV – KC < 0
o Do not invest, because opportunity cost of capital not
compensated for Equivalently,

IRR (Internal Rate of Return) IIR

• IRR is that rate of interest that equates an initial outlay with the
DPV of an income stream.

o 2000 = 1100 / 1+y + 1210/(1+y)2

o Y=0.1 = 10%.
• Implicit assumptions:
• y is an average growth rate. (T OR F).
• All payments received before the terminal investment are re-
invested at y. (T OR F) And why?]

Valuation of Bonds and Stock

• First Principles:
o Value of financial securities = PV of expected future cash flows.

• To value bonds and stocks, we need to:

o Estimate future cash flows: size (how much) and timing (when).
o Discount future cash flows at an appropriate rate.
 Bond Features
• What is (a bond – (Complete …), Define….).
o debt issued by a corporation or a governmental body.

o A bond represents a loan made by investors to the issuer.

o in return for his/her money, the investor receives a legal claim on future
cash flows of the borrower.

• The issuer promises to:

o makes regular coupon payments every period until the bond matures,
and.
o pay the face (par) value of the bond when it matures.

• Default (Complete …)
o an issuer who fails to pay is subject to legal action on behalf of the
lenders (bondholders).

Pure-Discount (Zero-Coupon) Bonds “Example”

• Information needed for valuing pure discount bonds:

o Time to maturity (T):

o T = Maturity date - today’s date.
o Face value (F).
o Discount rate (r).
6. FINANCIAL MARKETS AND INSTITUTIONS
Functions of Financial Markets

1.*Mechanism for raising funds!

o Done in primary financial markets (e.g., IPOs) with the assistance of

investment banking firms.
• Mechanism for converting financial assets into cash before maturity.

o Done in secondary financial markets (e.g., ARE, NYSE, OTC bond markets)

2.*
Provides the means for entities to protect (hedge) their
financial/commercial positions.
- Done in derivatives markets (Options, futures, forwards, credit default swaps).

* Mechanism for generating …. (a return on surplus funds (Investing).).

- Return occurs through interest, dividends, capital Appreciation.

3.*
• Allocates “limited” financial resources among competing users.
• And, we assume, if done so in the most efficient manner (i.e., to the most
productive users):

- The process will improve economic efficiency and

- Result in highest possible economic growth!

4.*
* Provides financial signals to market participants
- (Interest rates, stock prices, exchange rates):
as measures of market’s perception of risk and changing risk assessments:

• - We can use financial market signals as a leading indicator of

economic activity. (T. F.)
• Yield curves, stock prices, central bank rates
 * Classification of Financial Markets

1. • Primary Financial Market

- The financial market in which new issues of a security, such as a bond or

a stock, are sold to initial buyers by a corporation or a government.

• Important financial institution that assists in the initial sale of

securities in the primary market are investment banks.

• They do this by “underwriting securities,” i.e., (usually) guaranteeing a

price for a corporation’s securities and then selling them to the public (an
IPO).

• Thus, primary financial markets are important for raising new capital.

2. • Secondary Financial Market

• The financial market in which securities that have been previously issued
can be resold.

• Examples:
The Egyptian Stock Exchange … The New York Stock Exchange (NYSE) and
National Association of Securities Dealers Automated Quotation System
(NASDAQ) are examples for secondary markets

• Secondary markets provide liquidity for previously issued securities:

• Liquidity refers to the ease of conversion of a financial asset into cash

(prior to maturity if there is a maturity date) and how stable the price of the
asset is while being held in a form other than cash.
 Classification of Financial Markets

A- Money Markets

1- Short-term debt markets (under 1 year) offer safer, more liquid

investments with smaller price swings.

2- Commercial banks use Treasury bills for their “secondary reserves” to

meet deposit withdrawals and increases in loan demands.

3- Corporations and banks use money markets to manage working capital.

4- Money market instruments include: A.R.E. Treasury bills, Commercial

Paper, Bank Certificates of Deposit, and Bankers’ Acceptances.

B- Capital Markets

1- The financial market for longer-term debt (generally those with

maturities greater than one year) and equity (common stock).

2- Financial intermediaries with predictable cash flows hold long-term

securities.

3- These assets are also less liquid (in terms of price stability) than money
market instruments.

4- Capital market instruments include: Common Stock, A.R.E Treasury

bonds, corporate bonds, and Mortgages
* Flow of Funds Through a Financial System “Complete “…

A- Indirect Finance:

• Funds that flow through financial intermediaries, (such as depository

institutions, insurance companies and mutual funds).

• These intermediaries fuel businesses by channeling savers' money into

investments and loans.

B- Direct Finance:

• Funds that flow directly lenders to borrowers with the help of

institutions that provide brokerage services (research and advice,
retirement planning, tax tips, execution of trades).

• These institutions facilitate direct financing between businesses and

governments and lenders in financial markets (IPOs)

Q. Draw Circular Flow of Income in A Simple Economy

Q. Draw Flow of Funds Through a Financial System

* Why are Financial Intermediaries Important in Financial Markets?

1- Transaction cost:

Refers to the time and money spent in carrying out financial transactions.
Financial intermediaries’ lower transaction costs through expertise and
scale

2- Risk sharing:

Financial intermediaries sell assets with risk characteristics that people

are comfortable with and
then use the money to buy other assets that may involve much greater
risk.

3- Asymmetric information (i.e., where one party has more or better

information):

Financial intermediaries are usually better at credit risk screening than

individuals, therefore reducing losses due to wrong investment decision
making.
 REVISION MID-TERM
(Complete …)
1- The financial system consists of….
the group of institutions in the economy that help to match one person’s saving
with another person’s investment.

2- The financial system is made up of financial institutions that ….

coordinate the actions of savers and borrowers.

3- Financial institutions ….
can be grouped into two different categories ….
1- Financial markets
2- Financial intermediaries

4- Financial Markets CONTENTS OF ….

1- Stock Market.
2- Bond Market.

5- Financial Intermediaries CONTENTS OF ….

1- Banks.
2- Mutual Funds.

6- Financial intermediaries are financial institutions through which (…. savers) can
(…. indirectly) provide funds to (…. borrowers).

7- sacrifice is ….
(The giving up of something important to us now (money or time) to get something
better in the future).

8- stock tables provide the following informa0on ….

1-Price (of a share).
2- Volume (number of shares sold).
3- Dividend (profits paid to stockholders).
4- Price-earnings ratio.
9- The most banks operations ….
1- Take deposits from people who want to save and use the deposits to make
loans to people who want to borrow… CR.

2- Pay depositors interest on their deposits and charge borrowers slightly

higher interest on their loans… DEP.

3- Help create a medium of exchange by allowing people to write checks against

their deposits. A medium of exchange is an item that people can easily use to
engage in transactions. ….

4- Facilitate the purchases of goods and services.

10- A mutual fund is

An institution that sells shares to the public and uses the proceeds to buy a
portfolio, of various types of stocks, bonds, or both.

11- Intermediaries financial institution …

1- Credit unions.
2- Pension funds.
3- Insurance companies.
4- Loan sharks.

12- Financial Intermediaries Important in Financial Markets because of …

1- Transaction cost:
Refers to the time and money spent in carrying out financial transactions.

2- Risk sharing:
Financial intermediaries sell assets with risk characteristics that people are
comfortable with and then use the funds to purchase other assets that may have
far more risk.

3- Asymmetric information (i.e., where one party has more or better information):
Financial intermediaries are usually better at credit risk screening than
individuals, therefore reducing losses due to wrong investment decision making.

13- Transaction cost Refers to…

the time and money spent in carrying out financial transactions.
14- Risk sharing in financial intermediaries sell assets with …
risk characteristics that people are comfortable with and then use the funds to
purchase other assets that may have far more risk.

15- To value bonds and stocks we need to…

A- Estimate future cash flows, size (how much) and timing (when)
B- Discount future cash flows at an appropriate rate

16- A bond is …
Debt issued by a corporation or a governmental body.

17- A bond represents …

a loan made by investors to the issuer.

18- Money Markets….

The financial markets for short-term debt instruments (generally those with
original maturity of one year or less).

19- Capital Markets ….

The financial market for longer-term debt (generally those with maturi0es
greater than one year) and equity (common stock).

20- Direct Finance ….

Funds that directly flow lenders to borrowers with the assistance of institutions
that provide brokerage services (research and advice, retirement planning, tax
tips, execution of trades)

21- Indirect Finance …

Funds that flow through financial intermediaries, such as depository institutions,
insurance companies and mutual funds
 True or false:

1- A bond is a certificate of indebtedness that specifies obligations of the

borrower to the holder of the bond. (. )

2- Credit Risk is the probability that the borrower will fail to pay some of the
interest or principal. (. )

3- Stock represents a claim to partial ownership in a firm and is therefore, a

claim to the profits that the firm makes. (. )

4- The sale of stock to raise money is called equity financing. (. )

5- Compared to bonds, stocks offer both higher risk and potentially higher
returns. (. )

6- Mutual funds allow people with small amounts of money to easily diversify. (. )

7- Y = C + I + G + NX (. )

8- National saving is the total income in the economy that remains after paying
for consumption and government purchases. (. )

9- Private saving is the amount of income that households have left after paying
their taxes and paying for their consumption. (. )

10- Savings is the portion of current income not spent on consumption. (. )

11- Investing is the purchase of assets with the goal of increasing future income.
(. )

12- Future Value Refers to the amount of money to which an investment will grow
over a finite period of time at a given interest rate. (. )

13- There is no different between trade and investment. (. )

14- In market we briefer gambling vs investment. (. )

15- Primary Financial Market IS The financial market in which new issues of a
security, such as a bond or a stock, are sold to initial buyers by a corporation or a
government. (. )
16- The financial market in which securities that have been previously issued can
be resold (. )

17- Secondary markets provide liquidity for previously issued securities. (. )

18- Money Markets (The financial markets for short-term debt instruments
(generally those with original maturity of one year or less). (. )

19- Capital Markets (The financial market for longer-term debt (generally those
with maturities greater than one year) and equity (common stock). (. )
20- Indirect Finance ( Funds that flow through financial intermediaries, such as
depository institutions, insurance companies and mutual funds.) (. )

21- Direct Finance (Funds that flow directly lenders to borrowers with the
assistance of institutions that provide brokerage services (research and advice,
retirement planning, tax tips, execution of trades) . (. )

22- Value of financial securities = PV of expected future cash flows (. )

23- Savings is the portion of current income not spent on consumption. (. )

24- Investing is the purchase of assets with the goal of increasing future income.
(. )

25- Risk = The chance that the value of an investment will decrease.(. )

26- Return= The profit or yield from an investment. (. )

27- Liquidity=The ability of an investment to be converted into cash quickly

without loss of value. (. )

28- Future value (FV) refer to the amount of money to which an investment will
grow over a finite period of time at a given interest rate.(. )

29- future value is the cash value of an investment at a particular time in the
future. (. )

30- Functions of Financial Markets provides financial signals to market

participants such as Interest rates, stock prices, exchange rates . (. )
31- We can use financial market signals as a leading indicator of economic activity.
(. )

32- Stock prices and interest rates may tell us something about the market’s
assessment of companies, financial institutions, and even overall financial markets
(.)

33- Primary Financial Market is the financial market in which new issues of a
security, such as a bond or a stock, are sold to initial buyers by a corporation or a
government. (. )
34- Secondary Financial Market is the financial market in which securities that
have been previously issued can be resold. (. )

35- Liquidity refers to the ease of conversion of a financial asset into cash (prior
to maturity if there is a maturity date) and how stable the price of the asset is
while being held in a form other than cash. (. )

Q.3: Draw Circular Flow of Income

in A Simple Economy

Q.4: Draw Flow of Funds

Through a Financial System
Q.5:
Invest sum OF (1000 LE) over years (2 Y), how much will it be
worth? • Find:
1- Terminal Value?
o TVn = p (1+r) n.
o TVn = 1000 (1.1)2 = 1210.

2- Discounted Present Value?

B: Discounting is the inverse or mirror image of compounding.

Q. 6: If you in charge in a project proposal with current data

11-2023
o CF1 = 1100 o R= % 10
o CF2 = 1210 o KC=2100

o A- Should you invest? Ans.

o Total CF = 1100+1210= 2310
o KC= 2100 •
o (TOTAL CF )2310 > (KC) 2100 •
o Invest

B- Find NPV? AND Explain Your Design Opinion?

Ans.

o DPV (2000) – KC (2100) = ( -100) < 0 Do not invest, because

opportunity cost of capital not compensated for Equivalently.
Q.7: Consider a zero-coupon bond, with a face value of $1,000,
maturing in 5 years. Suppose that the appropriate discount rate is
8%. What is the current value of the bond?

PV = F / (1 + r) T = 1,000 / (1.08)5 = $( )

Q8: Suppose 6 months have past. What is the bond value now?
Ans.
PV = F / (1 + r) T = 1,000 / (1.08)4.5 = (. _. )$

Q.9: Compare between (Saving and Investment) according to …

1- Risk, 2- Return, 3- and Liquidity
7. Financial Products, Markets & Services

1. Investing in bonds - Advantages of investing in bonds

o A regular and certain flow of income (bonds with a fixed coupon).

o Relative security of capital for more highly rated bonds.
o For many bonds (not all!) they have a fixed maturity date.
o A range of income yields to suit different investment and tax situations.

2.Investing in bonds – Disadvantages and risks of investing in bonds.

o Inflation risk
If inflation rises, the ‘real’ value of the bond’s coupon and redemption
payment are eroded

o Liquidity Risk
The ease with which a security can be converted into cash.

o Default risk
There is a possibility that the issuer will not be able to pay the coupon or
capital back

o Exchange rate risk

Foreign currency bonds risk losing value due to exchange rate swings.

o Price risk/Market risk

Fluctuations in interest rates cause bond prices to change accordingly
when they are traded.

o Seniority Risk
Newer bonds can jump the queue if a company can't pay, leaving older ones
at the back.
There is an inverse relationship between interest rates and
bond prices:

Price Risk/Market Risk – A closer look

o If interest rates increase, bond prices will decrease.

o If interest rates decrease, bond prices will increase.

Price Risk/Market Risk – Complete ….

o Highly rated government bonds are said to have only price risk, as
there is little or no risk that the government will fail to pay the coupons
or repay the capital on the bonds.

o The prices of their bonds fell significantly as a result.

Bond yields – Flat Yields

o An investor may not have paid the par value – they may have
paid a different amount to purchase the bond, so a method of
calculating the true return to him or her is needed.
8.Interest Rates and Bond Valuation
Present Value of Cash Flows as Rates Change
• Bond Value = PV of coupons + PV of par
• Bond Value = PV of annuity + PV of lump sum
• As interest rates increase, present values decrease
• So, as interest rates increase, bond prices decrease and vice versa
Valuing a Discount Bond with Annual Coupons
• Consider a bond with a coupon rate of 10% and annual coupons. The par value is
$1,000, and the bond has 5 years to maturity. The yield to maturity is 11%. What
is the value of the bond?
Solution:
– Using the formula:
• B = PV of annuity + PV of lump sum
• B = 100[1 – 1/(1.11)5] / .11 + 1,000 / (1.11)5
• B = 369.59 + 593.45 = 963.04.

Valuing a Premium Bond with Annual Coupons

• Suppose you are reviewing a bond that has a 10% annual coupon and a face value
of $1000. There are 20 years to maturity, and the yield to maturity is 8%. What
is the price of this bond?
Solution:
– Using the formula:
• B = PV of annuity + PV of lump sum
• B = 100[1 – 1/(1.08)20] / .08 + 1000 / (1.08)20
• B = 981.81 + 214.55 = 1196.36
 Bond Prices: Relationship Between Coupon and Yield
• If YTM = coupon rate, then par value = bond price.

• If YTM > coupon rate, then par value > bond price.
– Why? The discount provides yield above coupon rate.
– Price below par value, called a discount bond.

• If YTM < coupon rate, then par value < bond price.
– Why? Higher coupon rate causes value above par.
– Price above par value, called a premium bond.

The Bond Pricing Equation

Example
• Find present values based on the payment period
C=7%, t=14, r=8%, FV=1000
– How many coupon payments are there?
– What is the semiannual coupon payment?
– What is the semiannual yield?
– B = 70[1 – 1/ (1.08)14] / .08 + 1,000 / (1.08)14 = 917.56
Interest Rate Risk (Complete or T/F)
Price Risk
• Change in price due to changes in interest rates
• Long-term bonds have more price risk than short-term bonds
• Low coupon rate bonds have more price risk than high coupon rate bonds

Reinvestment Rate Risk

• Uncertainty concerning rates at which cash flows can be reinvested
• Short-term bonds have more reinvestment rate risk than long-term bonds
• High coupon rate bonds have more reinvestment rate risk than low coupon rate
bonds
 Computing Yield to Maturity

• Yield to Maturity (YTM) is the rate implied by the current bond price
• Optional …
- Finding the YTM requires trial and error if you do not have a financial
calculator and is similar to the process for finding r with an annuity
- If you have a financial calculator, enter N, PV, PMT, and FV, remembering
the sign convention (PMT and FV need to have the same sign, PV the opposite
sign)
YTM with Annual Coupons

Consider a bond with a 10% annual coupon rate, 15 years to maturity and a
par value of $1,000. The current price is $928.09.
– Will the yield be more or less than 10%?
– N = 15; PV = -928.09; FV = 1,000; PMT = 100
– CPT I/Y = 11%
YTM with Semiannual Coupons
Suppose a bond with a 10% coupon rate and semiannual coupons, has a face
value of $1,000, 20 years to maturity and is selling for $1,197.93.
Complete…
– Is the YTM more or less than 10%? ….
– What is the semiannual coupon payment? …
– How many periods are there? ….
– PV = 1,197.93; FV = 1,000; CPT I/Y = 4% (Is this the YTM?)
– YTM = 4%*2 = (((8%)))

Current Yield vs. Yield to Maturity

• Current Yield = annual coupon / price
• Yield to maturity = current yield + capital gains yield
Example:
• 10% coupon bond, with semiannual coupons, face value of 1,000, 20 years
to maturity, $1,197.93 price

1- Current yield = 100 / 1,197.93 = .0835 = 8.35%

2- Price in one year,
_ Assuming no change in YTM = 1,193.68
– Capital gain yield = (1,193.68 – 1,197.93) / 1,197.93 = -.0035 = -.35%
– YTM = 8.35 - .35 = 8%, which is the same YTM computed earlier
 Bond Pricing Theorems

• Bonds of similar risk (and maturity) will be priced to yield about the same
return, regardless of the coupon rate
• If you know the price of one bond, you can estimate its YTM and use
that to find the price of the second bond
• This is a useful concept that can be transferred to valuing assets other
than bonds