Review Chapter fourFinancial markets A market for financial instruments.Financial Instruments or claims money market capital marketMarket makers

Summary of Part IPart I consists of fundamental introduction: 1.The economy and finance 2.Money 3.Credit 4.Financial markets ,instruments and market makers

Outline of Part IIPart II focuses on the price of money: 1.interest rate 2.exchange rate they represent the rental price and bought/sold price of money respectively.

Chapter 5Interest Rates and Bond Prices

Learning ObjectivesWhat is the interest rate? Simple interest ()and compound interest ()Compounding and discountingWhy interest rates and bond prices are inversely related?

Interest RateTwo methods to calculate interestDiscounting :present valueInterest Rates and bond prices

An question If you want to purchase goods and services but are short of the necessary funds , what will you do ?1) save now and purchase later 2) borrow now and purchase now

Interest rate

Money represents purchasing power ()If someone does not have money now and wants to make purchases, he can rent purchasing power by borrowing. The interest rate is the cost to borrowers of obtaining money.The interest rate is the return (or yield/) on money to lenders.

Willingness to lend/borrowOn the lender side, the interest rate is the reward for postponing purchases into the futurethe higher the interest rate, the more willing an individual will be to postpone purchases into the future and lend in the presentSimilar reasoning applies on the borrowing side.

present value / future valueThe interest rate links the present to the future and represents the time value of moneyspecifies the terms upon which an individual can trade off present purchasing powerpresent value) for future purchasing power (future value).(

Two methods to calculate interestSimple interest: refers to interest earned only on the principal. ( Compound interest: involves earning interest on interest in addition to the interest earned on the principal .

Simple interest: future valuesExample: let us suppose that you lend someone $1,000 at 6% annual interest rate. How much would you get back at the end of the first year, the second year and the third year if you are only paid simple interest?

Simple interest: future valuesThe amount you would get back at the end of the first year would be: the principal(1000) + the interest (1000*6%=60) or a total future amount of $1060;

Simple interest: future valuesThe amount you would get back at the end of the second year would be: the principal(1000) + the interest (1000*6%*2=120) or a total future amount of $1120;

Simple interest: future valuesThe amount you would get back at the end of the third year would be: the principal(1000) + the interest (1000*6%*3=180) or a total future amount of $1180.

Simple interest: future valuesThere is a formula for calculating the amount of interest and future value: interest=Principal rate time future value=principal +interest =principal 1+(ratetime) expressed symbolically Vn = V0(1 + in) where Vn = the funds to be received by the lender at the end of year n ,note that this is a future value ; V0 = the funds lent (and borrowed) now, note that this is a present value

Compounding: Future Values

The general relationship is Future value=Amount repaid = principal + interestThe amount of interest at the end of year 1 isInterest = principal interest rateInterest = principal iSubstituting, we getAmount repaid = principal (1 + i)V1 = V0(1 + i)

Compounding: Future ValuesExample: if you agree to lend a friend $1,000 for one year at an interest rate of 6%V1 = V0(1 + i)V1 = $1,000 (1 + 0.06)V1 = $1,000 (1.06)V1 = $1,060

What if your friend wants to borrow the money for two years?assume that he makes no payments until the end of the loanThis is where compounding comes into play. V2 = V0 + iV0 + i(V0 + iV0)We can reduce this equation toV2 = V0(1 + i)2

CompoundingIn fact, this equation can be generalized for any maturity of n yearsVn = V0(1 + i)nIn our example, V0 = $1,000, i = 0.06, and n = 2V2 = $1,000(1 + 0.06)2V2 = $1,000(1.1236)V2 = $1,123.60

Compounding: The Future Value of Money Lent TodayPayment Today (present value)$1,000

Discounting: The Present Value of Money to Be Received in the FutureFuture Payment$1,060

Discounting: Present ValuesDiscounting answers the followingwhat is the present value of money that is to be received (or paid) in the future?To calculate present value, we can simply rearrange the formula for future valuethis time, we solve for V0

Discounting: Present ValuesExample: Suppose a movie star has been offered the following dealeither $6,000,000 today of $7,500,000 in five yearsthe interest rate is 6%

Discounting: Present ValuesAssume that the interest rate is 4% instead of 6%. Would you still advise the movie star to take the $6,000,000 today ,or does the change in the interest rate point to a different option?

Discounting: Present Values

present value of a stream of future paymentsWe have learned how to compute the present value of a single future payment, how does this help you understand the present value of a stream of future payments?

A single future payment

future payments at the end of 1st year and 2nd year

a stream of future payments

Interest Rates & Bond PricesThis will help us to understand the prices of bonds which generally share the following characteristics:have a maturity > 10 yearshave a face or par value (F) of $1,000 per bond the issuer agrees to make periodic interest payments over the term to maturity and to repay the face value at maturitythe periodic payments are called coupon payments

Interest Rates & Bond PricesA bond represents a stream of future paymentsTo find its present value (the price it will trade at in financial markets) we need to compute the present value of each future coupon paymentcompute the present value of the final repayment of the face value on the maturity date

Interest Rates & Bond PricesThe appropriate formula is

ExampleSuppose that you are about to buy a bond that will mature in one yearthe face value is $1,000the coupon payment is $60 (the coupon rate 6%)the prevailing market interest rate is 6%How much will you be willing to pay

When the interest rate risesSuppose that the market interest rate rises to 8%The price of the bond now becomes

you would be buying the bond for a price below its par value (981.48

Conclusion 1As the market interest rate rises, the price of existing bonds fallspotential purchasers can purchase newly issued bonds with higher yields to maturitythe yield to maturity on existing bonds must rise to remain competitivethis occurs when the price on existing bonds fallsthe price will fall until the yield to maturity of the bond is equal to the current interest rate

When the interest rate fallsSuppose that the market interest rate falls to 4%The price of the bond now becomes

You would be buying the bond for a price above its par value (1,019.23>1,000)this is called a premium above par lowers the yield to maturity on the bond

Conclusion 2As the market interest rate falls, the price of existing bonds risesthe higher yields to maturity of existing bonds are attractive to potential investorsthis raises the price of these bondsthe process continues until the yield to maturity on existing bonds is equal to the current interest rate

RecapThe price of a bond is the discounted value of the future stream of income over the life of the bond. When the interest rate increases, the price of the bond decrease. When the interest rate decreases, the price of the bonds increases.