1. CDA COLLEGE BUS235: PRINCIPLES OF FINANCIAL ANALYSIS Lecture 5 Lecture 5 Lecturer: Kleanthis Zisimos

2. Characteristic of Bonds Characteristic of Bonds Bond Valuation Bond Valuation Discount Bond Discount Bond Premium Bond Premium Bond Yield to maturity Yield to maturity Lecture Topic List

3. Ways for raising capital Corporations raise capital in two primary forms Corporations raise capital in two primary forms 1. Debt 2. Common equity A bond is a basic way to raise capital through dept because is a long term promissory note issued by a business or governmental unit. A bond is a basic way to raise capital through dept because is a long term promissory note issued by a business or governmental unit. Stocks are the basic way to raise capital through common equity. Stocks are the basic way to raise capital through common equity. The main difference between the two of them is that bonds have a steady maturity date and coupon rate while stocks do not The main difference between the two of them is that bonds have a steady maturity date and coupon rate while stocks do not

4. Characteristics of Bonds Par value. The par value is the stated face value of the bond. The par value generally represents the amount of money the firm borrows and promises to repay at some future date. Par value. The par value is the stated face value of the bond. The par value generally represents the amount of money the firm borrows and promises to repay at some future date. Coupon interest rate. The bond requires the issuer to pay a specified number of euro of interest each year. When this coupon payment is divided by the par value, the result is the coupon interest rate. Coupon interest rate. The bond requires the issuer to pay a specified number of euro of interest each year. When this coupon payment is divided by the par value, the result is the coupon interest rate. Maturity date. Bonds generally have a specified maturity date on which the par value must be repaid Maturity date. Bonds generally have a specified maturity date on which the par value must be repaid

5. Characteristics of Bonds Draw a time line of a bond with par value 1000, maturity date 3 years and coupon rate 5% Draw a time line of a bond with par value 1000, maturity date 3 years and coupon rate 5% 0 1 2 3 0 1 2 3 50 50 50+1000 50 50 50+1000

6. Bond Valuation If we know the par value (M), the maturity date (n), the coupon (C) and the interest rate (k) of the market then we can calculate the value of the bond today with the following equation: If we know the par value (M), the maturity date (n), the coupon (C) and the interest rate (k) of the market then we can calculate the value of the bond today with the following equation: -n -n -n -n BV=C ( 1-(1+k) ) + M (1+k) BV=C ( 1-(1+k) ) + M (1+k) k As can see the value of the coupons is found with the present value annuity formula and the value of the par value with the present value formula As can see the value of the coupons is found with the present value annuity formula and the value of the par value with the present value formula

7. Call provision Most bonds have provision whereby the issuer may pay the holder prior to maturity. Usually the payment is 5% higher than the par value. Most bonds have provision whereby the issuer may pay the holder prior to maturity. Usually the payment is 5% higher than the par value. Companies use callable bonds because if the interest rate in the economy decline then they retire the old one and issue a new bond with lower coupon rate Companies use callable bonds because if the interest rate in the economy decline then they retire the old one and issue a new bond with lower coupon rate

8. Discount Bonds When the value of the bonds are smaller than their par value then we call them discount bonds. When the value of the bonds are smaller than their par value then we call them discount bonds. Example. What is the value of a bond with par value 1000, coupon rate 4,5%, maturity 3 years and interest rate 6% Example. What is the value of a bond with par value 1000, coupon rate 4,5%, maturity 3 years and interest rate 6% -3 -3 -3 -3 BV=45 ( 1-(1+0,06) ) + 1000 (1+0,06) BV=45 ( 1-(1+0,06) ) + 1000 (1+0,06) 0,06 0,06 BV=959,91 BV=959,91

9. Premium Bonds When the value of the bonds are higher than their par value then we call them Premium bonds. When the value of the bonds are higher than their par value then we call them Premium bonds. Example. What is the value of a bond with par value 1000, coupon rate 6%, maturity 10 years and interest rate 4% Example. What is the value of a bond with par value 1000, coupon rate 6%, maturity 10 years and interest rate 4% -10 -10 -10 -10 BV=45 ( 1-(1+0,04) ) + 1000 (1+0,04) BV=45 ( 1-(1+0,04) ) + 1000 (1+0,04) 0,04 0,04 BV=1162 BV=1162

10. Premium vs. Discount Bonds From our examples we can conclude the following: 1. When c Discount Bond 2. When c > k => Premium Bond 3. When c = k => Bond value=par value C=coupon rate K=interest rate of the market

11. Finding the interest rate or Yield to maturity (YTM) Suppose you were offered a 14-year, 15% coupon, 1000 par value bond of 1368 euro. What rate of return you earn on your investment if you buy the bond. The interest rate otherwise called yield to maturity can be found by the bond valuation equation Suppose you were offered a 14-year, 15% coupon, 1000 par value bond of 1368 euro. What rate of return you earn on your investment if you buy the bond. The interest rate otherwise called yield to maturity can be found by the bond valuation equation -14 -14 -14 -14 1368=150 ( 1-(1+YTM) ) + 1000 (1+YTM) 1368=150 ( 1-(1+YTM) ) + 1000 (1+YTM) YTM YTM YTM=10% (found by substituting values of k until you find the correct value which forces the equality YTM=10% (found by substituting values of k until you find the correct value which forces the equality

12. Yield to call The yield to call is the interest rate of a callable bond. The yield to call is the interest rate of a callable bond. Find the YTC of a 10-year, 8% coupon, 1000 par value bond of 1003,3 euro. The call price is 1050 in year 4 Find the YTC of a 10-year, 8% coupon, 1000 par value bond of 1003,3 euro. The call price is 1050 in year 4 -4 -4 -4 -4 1003,3=80 ( 1-(1+YTC) ) + 1050 (1+YTC) 1003,3=80 ( 1-(1+YTC) ) + 1050 (1+YTC) YTC YTC YTC=9% (found by substituting values of k until you find the correct value which forces the equality YTC=9% (found by substituting values of k until you find the correct value which forces the equality

13. Current yield Current yield is the annual coupon rate divided by the bond value\ Current yield is the annual coupon rate divided by the bond value\ Find the CY of a 10-year, 9% coupon, 1000 par value bond of 1200 euro. Find the CY of a 10-year, 9% coupon, 1000 par value bond of 1200 euro. CY= 90/1200= 7,5% CY= 90/1200= 7,5%

14. Interest rate risk An increase in interest rates leads to a decline in the values of outstanding bonds. Since interest rates can rise, bondholders face the risk of losses in the values of their portfolios. This risk is called interest rate price risk. An increase in interest rates leads to a decline in the values of outstanding bonds. Since interest rates can rise, bondholders face the risk of losses in the values of their portfolios. This risk is called interest rate price risk. Many bondholders buy bonds to build funds for some future use. These bondholders reinvest the cash flows. If interest rates decline, the bondholders will earn a lower rate of return on reinvested cash flows, and this will reduce the future value of their portfolios relative to the values they would have had if interest rates had not fallen. This is called interest rate reinvestment rate risk. Many bondholders buy bonds to build funds for some future use. These bondholders reinvest the cash flows. If interest rates decline, the bondholders will earn a lower rate of return on reinvested cash flows, and this will reduce the future value of their portfolios relative to the values they would have had if interest rates had not fallen. This is called interest rate reinvestment rate risk.