Chapter 4 – Understanding Interest RatesChapter 4 – Understanding Interest RatesPresent Value – Today’s value of a paymentto be received in the future when the interestrate is i.Why is a dollar you receive today more valuable to you than a dollar you might receive a month from now?Suppose that you want to have $500 two years from now. If you can obtain a 5% interest rate, then you would need to set aside $453.51 today. A simple formula isPV = CF/(1 +i)n$453.51 = $500.00/(1 + .05)2If you could get a 10% interest rate, then you would need to set aside $413.22 today.$413.22 = $500.00/(1 + .10)2If you would like to have $500.00 four yearsfrom now, you would need to set aside $341.51 today.$341.51 = $500.00/(1 + .10)4Note that the higher the interest rate the lower the present value. Also, the longer thetime period the lower the present value.Types of Credit Market InstrumentsSimple loan – a credit market instrument providing the borrower with an amount of funds that must be repaid to the lender at thematurity date along with an additional payment (interest).Fixed payment loan – a credit market instrument that provides a borrower with an amount of money that is repaid by making a fixed payment periodically for a set number of years.Coupon bond – a credit market instrument that pays the owner of the bond a fixed periodic every year until the maturity date when a specified final amount is repaid.Maturity date (term) – the date the loan expires or when the final payment must be paid.Par (face) value – the final specified amount that is paid to the owner of a couponbond at the maturity date.Coupon rate – the percentage of the par value that is paid to the bondholder on a regular basis.Coupon payment – the periodic payment the holder of the coupon bond receives. It iscalculated by multiplying the coupon rate times the par value.Discount bond (zero-coupon bond) – a credit market instrument that is bought at a price below its face value and whose face value is repaid at the maturity date. It does not make any periodic payments.Yield to maturity – the interest rate that equates the present value of a debt instrument’s cash flow payments to today’s value.Yield to Maturity on a Simple LoanFor a simple loan, the simple interest rate equals the yield to maturity. Page 70.Yield to Maturity on a Fixed-Payment LoanPage 71Yield to Maturity on a Coupon BondPage 73Bond prices and yields are inversely (negatively) related. When bond price goes up, the yield to maturity decreases. The yield to maturity is equal to the coupon rate when the bond price is equal to the par value.Consol(perpetuity) -- a bond with no maturity date and no repayment of principal that pays fixed coupon payments forever.The yield to maturity of a consol isic = C/PcThe formula for the yield to maturity of a perpetuity is often used to approximate the yield to maturity for a long-term coupon bond. When used in this manner, the calculation is called the current yield.Yield to maturity on a Discount Bond Page 76Key FactCurrent bond prices and interest rates are negatively related. When interest rates rise, bond prices fall. When bond prices are rising, interest rates are falling.Rate of return -- payments to the owner of a security plus the change in the security's value, expressed as a fraction of its purchaseprice.The return on a security is not necessarily equal to the yield to maturity of that security.Key Findings- If a bond is held to maturity, the return equals the initial yield to maturity.- An increase in interest rates means a decrease in bond prices and a capital lossfor bonds not held to maturity.- The longer the time to maturity the larger the bond's price change when the interest rate changes.- The longer the time to maturity the larger the change in the rate of return when the interest rate changes.- Even a bond with a high initial yield can have a negative return if interest rates rise.Interest-rate risk -- the possible reduction in returns associated with changes in interestrates.Prices and returns for long-term bonds are more volatile than those for shorter-term bonds. Long-term bonds have greater interest-rate risk.If there is a decline in interest rates, which would you rather be holding, long-term bonds or short-term bonds? Why?Nominal interest rate -- current or market interest rate.Real interest rate -- interest rate adjusted for expected changes in the price level.Fisher equationi = r + πewhere i = nominal interest rater = real interest rateπe = expected rate of inflationWhen the real interest rate is low, there are greater incentives to borrow and fewer incentives to
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