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Lecture 2 - Bond Valuation

Findings on the management of financial

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Strategic Management (BBMN 3233)

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Bond valuations

LECTURE 2

Recap

Last week
Companies invest in value creating long-term investments to maximize firm and

####### shareholder value

Companies pay for these investments by raising money through bonds and equity
This week
Focus on bonds – Financial managers evaluate these financial decisions through

####### comparison of cash payments at different dates

Sources of capital: Bonds

Financial markets

Money market

Capital markets

Raise long-term sources of funds

Debt Equity

Bonds • Stocks

Raise short-term sources of funds

CAPITAL MARKETS

What are bonds?

Bonds are issued by corporations and governments to raise funds by selling

bonds to market participants.

What are the bonds issued for?
Companies issue bonds to raise funds to expand their operations, and development
Government raise funds by issuing bonds to build schools, roads and other public infrastructures
Bonds are fixed income securities which pays fixed amount on regular time

intervals

Bonds are a type of debtinstruments, which means they must be paid back
When a company or government issue bonds, they are essentially borrowing money from the investors, and promises them repayment (like a loan)

Type of bonds

There are two types of bonds

What is the difference between both type of bonds?

Coupon bonds pay regular fixed coupon payments for specified time period
Zero coupon bonds does not pay coupons

Type of Bonds

(1) Coupon Bonds

(2) Zero Coupon Bonds

Coupon bonds

Typically, corporate bond pays coupons
The amount of each coupon payment is determined by the coupon rate of the

bond.

Coupon rate is set by the issuer and stated in the bond certificate.
Coupon rate is expressed as annual percentage rate (APR)

Therefore, the amount of each coupon payment, CPN, is

Coupon Rate Face Value Number of Coupon Payments per Year

 CPN 

Identify two types of bonds

What is the timeline of payments?

01234

Figure 1: Promised cash flow of $1,000 face value 10% 4-year Bond with annual coupon payments

Understanding bond terminology

$100 $100 $100 $100+ $

What is the timeline of payments if McDonalds pays

semiannual coupons?

Calculate the semi-annual coupon payment

0 2 3 6 8

Figure 2: Promised cash flow of $1,000 face value 10% 4-year Bond with semi-annual coupon payments

1 4 5 7

####### What is the timeline of payments?

Coupon payment paid every 6 months is _____$

$50 $50 $50 $50 $50 $50 $50 $50+$

Understanding bond terminology

BOND VALUATION

1 1

1 (1 ) (1 )

 

     

   

N N

FV

P CPN

y y y

####### The promised cash flow associated with bonds is equivalent to the sum of two cash flows:

####### (1) the coupon payment is an annuityand

####### (II) Final price or face value payment is a singlecash flow

Annuity Face Value

Yield to maturity (YTM)

Calculate the present value of a bond’s future interest payments, and bonds face value upon maturity

####### Find the price of the bond if the Yield-To-Maturity is 4% annually

####### Consider at 20-year, 6% Corporate bond with the face value equal

####### to $100 that pays annual coupon

1 1

1 (1 ) (1 )

 

     

   

N N

FV

P CPN

y y y

(a)What is the annual coupon payment? (b)Use formula to calculate bond price

$ 0.

1 −

1 (1 + 0)

100 (1 + 0)

= $𝗏𝗐𝗕.𝗏𝗖( Premium bond)

Bond valuation (Coupon bonds)

Bond Valuation

Find the value of a 1-year zero coupon bond with $1000 par

####### value and a yield to maturity of 5%

0 1

𝕃 =

𝔹𝕉 (1 + 𝕦)

Using the formula below, what is the bond price?

$1,000 still returned upon maturity

𝕃 =

$ ( 1. 05 )𐀀

= $952.

$952 $

Although the bond pays “no interest” directly, as an investor you are compensated for the time value of money by purchasing the bond at a discount to its face value

Yield to Maturity

Yield to Maturity (YTM) is the total return anticipated on the bond if the bond is held until

####### maturity

The yield to maturity of a bond is the discount rate that sets the present value of the promised

####### bond payments equal to the current market price of the bond

𝕃 =

𝔹𝕉 1 + 𝕌𝕇𝕀

𝕌𝕇𝕀=

𝔹𝕉 𝕃

𐀀/ − 1

Zero coupon bonds

Understanding YTM

YTM: Coupon Bonds

Similar to zero-coupon bonds, the yield to maturity of coupon bonds can be computed
Because the coupon payments represent an annuity, the yield to maturity is the interest

####### rate that solves the following equation

Rearranged, we can compute YTM for coupon bonds

𝔴𝕝𝕝𝕟𝕜𝕥 𝕌𝕇𝕀 =

𝔶𝕃𝕁 +

𝔹𝕉 − 𝕃 𝕁 𝔹𝕉 + 𝕃 2

𝕃 = 𝔶𝕃𝕁 ×

1 𝕦

1 −

1 1 + 𝕦 𐀀

𝔹𝕉 1 + 𝕦 𐀀

Understanding YTM

Example: Compute YTM for coupon bonds

𝔴𝕝𝕝𝕟𝕜𝕥 𝕌𝕇𝕀 =

𝔶𝕃𝕁 + 𝔹𝕉 − 𝕃 𝕁 𝔹𝕉 + 𝕃 2

####### Consider at 20-year, 6% Corporate bond with the face value equal to

####### $100 that pays annual $6 coupon. Find the Yield to Maturity

𝔴𝕝𝕝𝕟𝕜𝕥 𝕌𝕇𝕀 =

$6 +$100 − 127 20 100 + 127. 2

= 4%

Understanding YTM

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