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# Introduction to Business Finance FINC 331

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This 6 page Class Notes was uploaded by Maudie Walter on Monday October 19, 2015. The Class Notes belongs to FINC 331 at Radford University taught by Steven Beach in Fall. Since its upload, it has received 29 views. For similar materials see /class/224671/finc-331-radford-university in Finance at Radford University.

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Date Created: 10/19/15

FIN 331 Business Finance CHAPTER 6 Interest Rates and Bond Valuation How the time value equations can be used for the valuation of Bonds Zero coupon bonds Pure Discount Bonds Example of Pure Discount Loan Treasury Bill Describe them and draw time line Q What equation do we use here Present value of a future cash ow PVFV1rt Example Consider a 10year zero coupon bond it is priced to yield 9 What is the current price Note that I said priced to yield What I am implying is that the market forces have determined that 9 is required on a particular security with its particular risk and payment structure That required return is established in the market place YTM is the IRR on a bond We ll discuss IRR in detail a little later Example Say we have a 20year zerocoupon bond that is selling for 275 What is its yieldtomaturity Pricing and YTM for CouponPavinq Corporate Bonds Coupon paying bonds pay an interest payment every 6 months and return the principle usually 1000 at the end ofthe loan Example Assume we have a 20year bond paying a 1025 annual coupon rate gt 102510002 or 5125 every six months If it is priced to yield 11 what is its price all at 5125 1000 1 2 3 4 39 40 months PV r112 For equations use 1 pv of annuity and 2 pv of future cash ow PV Coupon PVIFArYt 1000 PVlFryt General solution for Bond Price For calculator What if the required return goes up Say to 12 then PV Bond is at a discountll What if required return goes down Say to 10 then PV Bond is at a premiumll Solving for yield However when we try to calculate the YTM for a coupon paying corporate bond we do not have a closed form solution We must solve for YTM using trialand error or have our nancial calculator solve for us Let s try another price and see what the yield is lfthe PV 1035 YTM Interest Rate Risk Discussion in Class Interest Rate Levels What is a rate of return or interest rate Simple I offer to give you 115 in one year if you give me 100 now Return on your 100 investment ie Given a 100 investment and a 15 rate of return we have What elements contribute to your required return INFLATION IS A COSTLY THING EXAMPLE Your usual basket of groceries cost 150 last year this year the same basket costs 160 Ifthat basket is used to measure inflation then inflation forthe year was We see that inflation reduces the purchasing power of money ie the dollar Note in the example that one dollar last year bought 1150 of your basket while now one dollar only buys 1160 of your basket NOMINAL VERSUS REAL RATES Nominal rates of return an observed rate of return that is not adjusted for inflation like the 15 mentioned in the preceding discussion Although the investment yielded a 15 return if inflation was 15 we cannot buy any more goods than before Real rates of return are inflation adjusted In the example above our nominal rate was 15 but since we can only buy the same amount of goods we received a 0 real return from that investment The relationship between nominal and real interest rates is given in the Fischer Equation Nominal Interest Rate real rate expected inflation Which is often used to show the real rate of return as The exact formulation that is much more useful in more complex analysis is The real rate has been about 3 for much of the 1900s Nominal rates have fluctuated from 4 to 18 over the time though As a result much of the variation in nominal interest rates is due to changes in expected inflation In the example where you lend me 100 your nominal rate of return was 15 but your real return on that investment was rloan to SLB rloan to SLB Term Structure of Interest Rates R Default riskfree rate of return Real rate of return lnflation Premium Interest Rate Risk Premium Term structure of interest rates considers R for pure discount bonds R is compared for different maturities lnflation Premium based on expected inflation investors must be compensated for inflation Interest Rate Risk the risk that higher interest rates will reduce the value of the security alternatives Upward sloping term structure Downward sloping term structure Yield curve looks at R for securities of similar default risk usually Treasury Yield Curve Upward sloping yield curve Downward sloping yield curve Define R1 as the required return YTM on security 1 R1 Specifically a risk premium is the return required on a risky investment in excess of the return required on a riskless investment Where DRP TaxP and LP are a function of the individual security Specifically a risk premium is the return required on a risky investment in excess of the return required on a riskless investment DRP additional return demanded for default risk TaxP additional return demanded for tax cost LP additional return demanded for lack of liquidity risk that you cannot sell quickly without loss in value

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