1 Review Chapter four  Financial markets （金融市场） A market for financial instruments.  Financial Instruments or claims money market capital market  Market makers （做市商）

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

3 Outline of Part II  Part 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 5 Interest Rates and Bond Prices

5 Learning Objectives  What is the interest rate?  Simple interest ( 单利 )and compound interest ( 复利 )  Compounding and discounting （贴现）  Why interest rates and bond prices are inversely related?

6  Interest Rate Interest Rate  Two methods to calculate interest Two methods to calculate interest  Discounting :present value Discounting :present value  Interest Rates and bond prices Interest Rates and bond prices

7 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

8 Interest rate  Money represents purchasing power ( 购买力 )  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/ 收益 ) on money to lenders.  利率是借方今天借入资金（以后偿还）的成本， 是对贷方今天贷出资金（以后消费）的回报。

9 Willingness to lend/borrow  On the lender side, the interest rate is the reward for postponing purchases into the future  the higher the interest rate, the more willing an individual will be to postpone purchases into the future and lend in the present  Similar reasoning applies on the borrowing side.

10 present value / future value  The interest rate links the present to the future and represents the time value of money ：  specifies the terms upon which an individual can trade off present purchasing power （ present value) for future purchasing power (future value). ( 货币的时间价值：将现在的购买力换算成未来购 买力的换算条件 —— 利率）

11 Two methods to calculate interest  Simple interest: refers to interest earned only on the principal. ( 本金：最初借出的资 金数额） 单利：只对初始本金计算利息的方法。  Compound interest: involves earning interest on interest in addition to the interest earned on the principal. 复利：将上期利息并入本金一并计算利息的方法。

12 Simple interest: future values  Example: 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?

13 Simple interest: future values  The 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;

14 Simple interest: future values  The 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;

15 Simple interest: future values  The 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.

16 Simple interest: future values  There is a formula for calculating the amount of interest and future value: interest=Principal× rate× time future value=principal +interest =principal × 〔 1+(rate×time) 〕 expressed symbolically V n = V 0 (1 + i × n) where V n = the funds to be received by the lender at the end of year n,note that this is a future value ; V 0 = the funds lent (and borrowed) now, note that this is a present value

17 Compounding: Future Values  The general relationship is Future value=Amount repaid = principal + interest  The amount of interest at the end of year 1 is Interest = principal  interest rate Interest = principal  i  Substituting, we get Amount repaid = principal  (1 + i) V 1 = V 0 (1 + i)

18 Compounding: Future Values  Example: if you agree to lend a friend $1,000 for one year at an interest rate of 6% V 1 = V 0 (1 + i) V 1 = $1,000  ( ) V 1 = $1,000  (1.06) V 1 = $1,060

19  What if your friend wants to borrow the money for two years?  assume that he makes no payments until the end of the loan  This is where compounding comes into play. V 2 = V 0 + iV 0 + i(V 0 + iV 0 )  We can reduce this equation to V 2 = V 0 (1 + i) 2

20 Compounding  In fact, this equation can be generalized for any maturity of n years V n = V 0 (1 + i) n  In our example, V 0 = $1,000, i = 0.06, and n = 2 V 2 = $1,000( ) 2 V 2 = $1,000(1.1236) V 2 = $1,123.60

21 Compounding: The Future Value of Money Lent Today Payment Today (present value) $1,000 Future Value $1,060

22 Discounting: The Present Value of Money to Be Received in the Future Future Payment $1,060 Value Today $1,000

23 Discounting: Present Values  Discounting answers the following  what is the present value of money that is to be received (or paid) in the future? 贴现：计算未来收入的某一笔资金的现在价值的方法。  To calculate present value, we can simply rearrange the formula for future value  this time, we solve for V 0

24 Discounting: Present Values  Example: Suppose a movie star has been offered the following deal  either $6,000,000 today of $7,500,000 in five years  the interest rate is 6%

25 Discounting: Present Values  Assume 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?

26 Discounting: Present Values

27 present value of a stream of future payments  We 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?

28 A single future payment

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

30 a stream of future payments

31 Interest Rates & Bond Prices  This will help us to understand the prices of bonds which generally share the following characteristics:  have a maturity > 10 years  have a face or par value (F) of $1,000 per bond 面值：债券的票面价值。  the issuer agrees to make periodic interest payments over the term to maturity and to repay the face value at maturity  the periodic payments are called coupon payments 息票支付：定期支付的利息，即债券的票面利率乘以票面金额。

32 Interest Rates & Bond Prices  A bond represents a stream of future payments  To find its present value (the price it will trade at in financial markets) we need to  compute the present value of each future coupon payment  compute the present value of the final repayment of the face value on the maturity date

33 Interest Rates & Bond Prices  The appropriate formula is

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

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

36  you would be buying the bond for a price below its par value (981.48<1,000)  this is called a discount from par 折价：债券发行后，利率提高导致债券售价低于票面价 值。 raises the yield to maturity on the bond 到期收益率：持有债券到期后的回报率，包括利息 和资本利得或资本损失两部分。

37 Conclusion 1  As the market interest rate rises, the price of existing bonds falls  potential purchasers can purchase newly issued bonds with higher yields to maturity  the yield to maturity on existing bonds must rise to remain competitive  this occurs when the price on existing bonds falls  the price will fall until the yield to maturity of the bond is equal to the current interest rate

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

39  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 溢价：债券发行后，利率降低导致债券售价高于 票面价值。  lowers the yield to maturity on the bond

40 Conclusion 2  As the market interest rate falls, the price of existing bonds rises  the higher yields to maturity of existing bonds are attractive to potential investors  this raises the price of these bonds  the process continues until the yield to maturity on existing bonds is equal to the current interest rate

41 Recap  The 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.