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FINE 2000 (79)
Chapter 5


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FINE 2000

CHAPTER 5 VALUING BONDS Then companies need money to make long-term investments they issue bonds, which are simply long- term loans. When companies issue bonds, they promise to make a series of fixed interest payments and then to repay the debt. As long as the company generates sufficient cash, the payments on a bond are certain. In this case bond valuation involves simple straight-forward time value of money computations. However, investors take default risk into account when they price the bonds and demand a higher interest rate to compensate when risk is higher. 5.1 Bond Characteristics  Companies raise capital to finance long-term investments by issuing bonds to investors. The money they collect when the bond is issued, or sold to the public, is the amount of the loan. In return, they agree to make specified payments to the bondholders, who are lenders.  Coupon: the interest payments paid to the bondholders each year until the bond matures.  Face Value: payment at the maturity of the bond. Also called par value, or maturity value (principal of the loan)  Bond Market Data: bond prices are reposted on the financial web sites of major newspapers and are always for the previous day’s trading activity.  The bid price: the price you receive if you sell the bond to a bond dealer. Prices are quoted as percentages of face value.  Asked price: if you want to buy the bond you pay this  Spread: dealers need to sell bonds for higher than they purchased them. This additional cost is called the spread.  Ask yield: measures the return that investors will receive if they buy the bond at the asked price and hold it to maturity  Accrued interest: Coupon interest earned form the last coupon payment to the purchase date of the bond Accrued interest= coupon payments X (number of days form last coupon to purchase date/ number of days in coupon period)  Clean bond: bond price excluding accrued interest  Dirty bond: bond price including accrued interest 5.2 Interest Rates and Bond Prices  The value of a security is the present value of the cash flows it will pay to its owners  Calculate the present value of the bond by discounting the cash flows at a given interest rate  Bond prices are usually expressed as a percentage of their face value  The coupon payments on the bond are an annuity and ay maturity the bond holder gets an additional payment. Therefore you can use the annuity formula to value the coupon payments and then add on the present value of the final payment of face value PV(bond)- PV (coupons) +PV(face value) = (coupon X annuity factor) + (face value x discount factor) ** Most coupon payments are semi-annually*** ** This interest rate compounded semi-annually is the bonds APR= use formula to find the EAR** How Bond Prices vary with Interest  As interest rates change, so do bond prices  When interest rate= coupon ate, bond sells for its face value  When the cash flows are discounted at a rate that is higher than the bond’s coupon rate, the bond is worth less than its face value  When market interest rate is below the coupon rate, bonds sell for more than face value.  When the interest rate rises, the present value of the payments to be receives by the bondholder’s falls, and bond prices fall. Conversely, declines in the interest rate increase the present value of those payments and result in higher bond prices ** Note that payments are fixed, regardless of changes in the interest rate. Only the PV changes not the payment itself** 5.3 Current Yield and Yield to Maturity 1. Bonds Priced at Face Value  The rate of return is the coupon rate 2. Discount Bond  Bond that sells for less than its face value  Investors face capital gain over the life of the bond, the return on these bonds is greater than the current yield 3. Premium Bond  Bond that sells for more than its face value  Investors face capital loss over the life of the bond, so the return on these bonds is always less than the bond’s current yield. Current yield= annual coupon payment divided by bond price  Overstates return of premium bonds and understates that of discount bonds because it focused only on current income and ignores prospective price increases  Yield of maturity: interest rate for which the present value of the bond’s payments equals the price. Measure of bond’s total return, including both coupon income and capital gain. Determined through trial and error 5.4 Bond Rates of Return  Can make a capital gain or loss as rates change (rate of return: total income per period per dollar invested) The rate of return= (coupon income + price change)/ investment  Rate of return also fluctuates with the market. This is why we say bonds are subject to interest rate risk  In contrast to the yield to maturity, the rate of return can be calculated for any particular holding period and is based on the actual income and the capital gain or loss on the bond over that period  Connection between the two arises if the bond’s yield to maturity remains unchanged during an investment period, its rate or return will equal that yield. Taxes and Rates of Return  Taxes reduce the rate of return on an investment. Interest income is fully taxable and 50% of capital gains are taxable  To figure out the after tax rate of return on the investment, convert the cash flows to their after- tax calues by subtracting the relevant taxes After tax rate of return= (after tax coupon income + after ta
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