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BUS235: PRINCIPLES OF BUS235: PRINCIPLES OF FINANCIAL ANALYSISFINANCIAL ANALYSIS

Lecture 5Lecture 5

Lecturer: Kleanthis Zisimos Lecturer: Kleanthis Zisimos

Characteristic of BondsCharacteristic of Bonds Bond ValuationBond Valuation Discount BondDiscount Bond Premium BondPremium Bond Yield to maturityYield to maturity

Lecture Topic ListLecture Topic List

Ways for raising capitalWays for raising capital Corporations raise capital in two primary formsCorporations raise capital in two primary forms1.1. DebtDebt2.2. Common equityCommon equity

A bond is a basic way to raise capital through A bond is a basic way to raise capital through dept because is a long term promissory note dept because is a long term promissory note issued by a business or governmental unit.issued by a business or governmental unit.

Stocks are the basic way to raise capital through Stocks are the basic way to raise capital through common equity.common equity.

The main difference between the two of them is The main difference between the two of them is that bonds have a steady maturity date and that bonds have a steady maturity date and coupon rate while stocks do notcoupon rate while stocks do not

Characteristics of Bonds Characteristics of Bonds Par valuePar value. The par value is the stated face . The par value is the stated face

value of the bond. The par value generally value of the bond. The par value generally represents the amount of money the firm represents the amount of money the firm borrows and promises to repay at some future borrows and promises to repay at some future date.date.

Coupon interest rateCoupon interest rate. The bond requires . The bond requires the issuer to pay a specified number of euro of the issuer to pay a specified number of euro of interest each year. When this coupon interest each year. When this coupon payment is divided by the par value, the result payment is divided by the par value, the result is the coupon interest rate.is the coupon interest rate.

Maturity dateMaturity date. Bonds generally have a . Bonds generally have a specified maturity date on which the par value specified maturity date on which the par value must be repaidmust be repaid

Characteristics of BondsCharacteristics of Bonds

Draw a time line of a bond with par value Draw a time line of a bond with par value 1000, maturity date 3 years and coupon 1000, maturity date 3 years and coupon rate 5%rate 5%

00 1 2 31 2 3

50 50 50+100050 50 50+1000

Bond ValuationBond Valuation

If we know the par value (M), the maturity If we know the par value (M), the maturity date (n), the coupon (C) and the interest date (n), the coupon (C) and the interest rate (k) of the market then we can rate (k) of the market then we can calculate the value of the bond today with calculate the value of the bond today with the following equation:the following equation:

-n-n -n-n

BV=CBV=C((1-(1+k) 1-(1+k) ))+ M (1+k)+ M (1+k) kk

As can see the value of the coupons is As can see the value of the coupons is found with the present value annuity found with the present value annuity formula and the value of the par value formula and the value of the par value with the present value formulawith the present value formula

Call provisionCall provision

Most bonds have provision whereby the Most bonds have provision whereby the issuer may pay the holder prior to issuer may pay the holder prior to maturity. Usually the payment is 5% maturity. Usually the payment is 5% higher than the par value.higher than the par value.

Companies use callable bonds because if Companies use callable bonds because if the interest rate in the economy decline the interest rate in the economy decline then they retire the old one and issue a then they retire the old one and issue a new bond with lower coupon ratenew bond with lower coupon rate

Discount BondsDiscount Bonds

When the value of the bonds are smaller When the value of the bonds are smaller than their par value then we call them than their par value then we call them discount bonds.discount bonds.

Example. What is the value of a bond with Example. What is the value of a bond with par value 1000, coupon rate 4,5%, par value 1000, coupon rate 4,5%, maturity 3 years and interest rate 6%maturity 3 years and interest rate 6%

-3-3 -3-3

BV=45BV=45((1-(1+0,06) 1-(1+0,06) ))+ 1000 (1+0,06)+ 1000 (1+0,06) 0,060,06 BV=959,91BV=959,91

Premium BondsPremium Bonds

When the value of the bonds are higher When the value of the bonds are higher than their par value then we call them than their par value then we call them Premium bonds.Premium bonds.

Example. What is the value of a bond with Example. What is the value of a bond with par value 1000, coupon rate 6%, maturity par value 1000, coupon rate 6%, maturity 10 years and interest rate 4%10 years and interest rate 4%

-10-10 -10 -10

BV=45BV=45((1-(1+0,04) 1-(1+0,04) ))+ 1000 (1+0,04)+ 1000 (1+0,04) 0,040,04 BV=1162BV=1162

Premium vs. Discount BondsPremium vs. Discount Bonds

From our examples we can conclude the From our examples we can conclude the following:following:

1.1. When c < k => Discount BondWhen c < k => Discount Bond

2.2. When c > k => Premium BondWhen c > k => Premium Bond

3.3. When c = k => Bond value=par valueWhen c = k => Bond value=par value

C=coupon rateC=coupon rate

K=interest rate of the marketK=interest rate of the market

Finding the interest rate or Yield to Finding the interest rate or Yield to maturity (YTM)maturity (YTM)

Suppose you were offered a 14-year, 15% Suppose you were offered a 14-year, 15% coupon, 1000 par value bond of 1368 coupon, 1000 par value bond of 1368 euro. What rate of return you earn on your euro. What rate of return you earn on your investment if you buy the bond. The investment if you buy the bond. The interest rate otherwise called yield to interest rate otherwise called yield to maturity can be found by the bond maturity can be found by the bond valuation equationvaluation equation

-14 -14-14 -141368=1501368=150((1-(1+YTM) 1-(1+YTM) ))+ 1000 (1+YTM)+ 1000 (1+YTM)

YTMYTM YTM=10% (found by substituting values of YTM=10% (found by substituting values of

k until you find the correct value which k until you find the correct value which forces the equalityforces the equality

Yield to callYield to call

The yield to call is the interest rate of a The yield to call is the interest rate of a callable bond.callable bond.

Find the YTC of a 10-year, 8% coupon, 1000 Find the YTC of a 10-year, 8% coupon, 1000 par value bond of 1003,3 euro. The call par value bond of 1003,3 euro. The call price is 1050 in year 4price is 1050 in year 4

-4 -4-4 -41003,3=801003,3=80((1-(1+YTC) 1-(1+YTC) ))+ 1050 (1+YTC)+ 1050 (1+YTC)

YTCYTC YTC=9% (found by substituting values of k until YTC=9% (found by substituting values of k until

you find the correct value which forces the equalityyou find the correct value which forces the equality

Current yieldCurrent yield

Current yield is the annual coupon rate Current yield is the annual coupon rate divided by the bond value\divided by the bond value\

Find the CY of a 10-year, 9% coupon, 1000 Find the CY of a 10-year, 9% coupon, 1000 par value bond of 1200 euro. par value bond of 1200 euro.

CY= 90/1200= 7,5%CY= 90/1200= 7,5%

Interest rate riskInterest rate risk An increase in interest rates leads to a decline An increase in interest rates leads to a decline

in the values of outstanding bonds. Since in the values of outstanding bonds. Since interest rates can rise, bondholders face the interest rates can rise, bondholders face the risk of losses in the values of their portfolios. risk of losses in the values of their portfolios. This risk is called interest rate price risk.This risk is called interest rate price risk.

Many bondholders buy bonds to build funds for Many bondholders buy bonds to build funds for some future use. These bondholders reinvest some future use. These bondholders reinvest the cash flows. If interest rates decline, the the cash flows. If interest rates decline, the bondholders will earn a lower rate of return on bondholders will earn a lower rate of return on reinvested cash flows, and this will reduce the reinvested cash flows, and this will reduce the future value of their portfolios relative to the future value of their portfolios relative to the values they would have had if interest rates values they would have had if interest rates had not fallen. This is called interest rate had not fallen. This is called interest rate reinvestment rate risk.reinvestment rate risk.