【文章內(nèi)容簡介】 oan. The interest may not be expressed, but it is there. ? The IRS agrees and will require the tax payer to calculate interest payments even if the contract does not specifically state a rate of interest (called implicit or imputed interest). ? GAAP agrees and requires that long term liabilities be recorded at their present value and that repayments be separated into interest expense and reduction of the liability. ? Where interest rates are not stated, they can be puted using present value methods and using the know payments with – An estimate of market value (which bees the PV), or – An estimate of the interest rate for similar debt. If you are confused with this slide, please skip and return after Finishing this chapter. 23 Bonds ? Bonds are debt instruments sold to the investing public. ? Some bonds carry no collateral（擔(dān)保） and are called debenture bonds. ? Bonds backed by collateral are called collateral trust bonds. ? Bonds that can be converted to mon shares of the issuing pany are called convertible bonds. ? Bonds are recorded as a longterm liability. 24 How to define a bond? 1. A piece of paper 2. Face value (or par value): for example $1,000 3. A nominal （名義上的） interest rate: for example 10% (the rate is annual rate if not stated otherwise. Semiannual rate is half of it at 5%). 4. Duration: number of years before the principle is due, for example, 5 years 5. Frequency of nominal interest payment in a year: annually pays once a year。 semiannually pays twice a year (so a fiveyear bond would have ten semiannual periods) 25 How to define a bond? The definition of a bond is the pattern of its cash payments to the bondholders, nothing else (STOP: This is the first important concept in bond accounting, you must understand before you go on) The bond in the previous slide is defined as: This bond is defined by ten $50 payments of nominal interests every half a year (semiannually)。 and a payment of par value $1,000 at the end of the fifth year. $50 $50 $50 $50 $50 $50 $50 $50 $50 $50 $1,000 26 How much will this bond sell for? Like any investment vehicles, the price of a bond is the present value of its future cash payments (NPV) The bond price and the par value of the bond are totally two different things, they do not have to be the same. The previous bond can be sold more than or less than the par value $1,000. (STOP: This is the second important concept in bond accounting, you must understand before you go on) I assume you have learnt NPV calculations, and The use of present value tables. 27 How much will this bond sell for? The rate of return that we use to discount the cash flows to get NPV of the bond is called discount rate（折現(xiàn)率） . Discount rate is decided, at the time of the bond sale, by the risk associated with the bond. If it is more (less) likely for the bond seller to default in the future, the discount rate will higher (lower). Microsoft’ s bond discount rate may be %, while a small food chain’ s bond discount rate has to be %. Discount rate has nothing to do with the bond’ s nominal interest rate。 nominal interest rate only determines the cash payments ($50 each in this case).(STOP: This is the third important concept in bond accounting, you must understand before you go on) 28 How much will this bond sell for?sold at par Let us assume the previous bond’ s discount rate is 10% (this 10% has nothing to do with the 10% nominal interest rate). Then the bond price is = 50/(1+5%) + 50/(1+5%)2 + 50/(1+5%)3 + 50/(1+5%)4 + …… 50/(1+5%) 10 + 1000/(1+5%)10 = $1,000 Why we use 5% discount rate not the 10%? Because the $50 nominal interest payment is for half a year. We use 10 periods because five years make up ten halfayears. When bond price is equal to bond face value, we say it is sold at par. You should not rely on any calculator or tables to pute the bond price in the above equation. When nominal interest rate (5%) is the same as discount rate (5%), the bond is sold at par value. (STOP: This is the fourth important concept in bond accounting, you must understand before you go on) 29 How much will this bond sell for?sold at premium Let us assume the previous bond’ s discount rate is 8% (that is, it is less riskier than in the previous slide to lend to the pany so a lower discount rate is used). Then the bond price is = 50/(1+4%) + 50/(1+4%)2 + 50/(1+4%)3 + 50/(1+4%)4 + …… 50/(1+4%) 10 + 1000/(1+4%)10 = $50* + $1,000*=$1,081 1 Stickney and Weil page 855, 4% at n=10 2 Stickney and Weil page 853, 4% at n=10 Premium = $1,081 – 1,000 = $81 When bond price is more than bond par value, we say it is sold at premium. 30 How much will this bond sell for?sold at discount Let us assume the previous bond’ s discount rate is 12% (that is, it is more riskier than in the previous two slide to lend to the pany so a higher discount rate is used). Then the bond price is = 50/(1+6%) + 50/(1+6%)2 + 50/(1+6%)3 + 50/(1+6%)4 + …… 50/(1+6%) 10 + 1000/(1+6%)10 = $50*** + $1,000****=$926 ** Stickney and Weil page 855, 6% at n=10 *** Stickney and Weil page 853, 6% at n=10 Discount = $1,000 – 926 = $74 When bond price is less than bond par v