1. TOPIC 4 INTEREST RATES AND RATES OF RETURN

2. 2 CHAPTER PREVIEW Objective: To develop better understanding of interest rate; its terminology and calculation. Topics include: 1.Measuring Interest Rates 2.Distinction Between Real and Nominal Interest Rates 3.Distinction Between Interest Rates and Returns Interest rate – one of most closely watched variables in economy; it is imperative to know what it means exactly -Directly affect everyday lives -Health of the economy -Personal Decision: save or consume -Business Decision In this chapter, we will see that yield to maturity (YTM) is the most accurate measure of interest rates, because: - Different debt instruments have different steams of cash flows with very different timing. -Compare the value of one kind of debt instruments with another. So, concept of Present Value is important to understand -

3. 3 PRESENT VALUE CONCEPT (PV) Comparing returns across debt types is difficult since timing of repayment differs –Apply the PV concept: find a common measure for funds at different times, present each in today’s dollars The PV of $1 received n years in the future is $1/(1 + i ) n Interest rate is important in valuation of various investment instruments

4. 4 PRESENT VALUE CONCEPT Concept of PV (or present discounted value) is based on notion –A dollar today is better than a dollar tomorrow –A dollar of cash flow paid one year from now is less valuable than a dollar paid today. That one dollar today could be invested in a savings account that earns interest and have more than a dollar in one year PV analysis involves –Finding the PV of all future payments that can be received from a debt instrument –PV of a single cash flow or sum of a sequence or group of future cash flows

5. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-5 Types of Debt Instruments Categories of bonds are used to identify variations in the timing of payments Simple loan –Involves the principal (P) and interest ( i ) –Total payment = P + iP = P(1 + i ) For example, commercial loans to businesses. Fixed-payment loan –Borrower makes regular periodic payments to the lender. –Payments include both interest and principal and no lump- sum payment at maturity. For example, if you borrowed $1,000, a fixed-payment loan might require you to pay $126 every year for 25 years. Installment loans (such as auto loans) and mortgages are frequently of the fixed-payment type.

6. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-6 Types of Debt Instruments Coupon bond –Borrowers make multiple payments of interest at regular intervals and repay the face value at maturity –Specifies the maturity date, face value, issuer, and coupon rate (equals the yearly payment divided by face value) Ex: A coupon bond with $1,000 face value, for example, might pay you a coupon payment of $100 per year for 10 years, and at the maturity date repay you the face value amount of $1,000. Discount bond –Repays in a single payment –Repays the face value at maturity, but receives less than the face value initially For example, a discount bond with a face value of $1,000 might be bought for $900; in a year’s time the owner would be repaid the face value of $1,000. U.S. Treasury bills, U.S. savings bonds, and long-term zero-coupon bonds are examples of discount bonds.

7. 7 PRESENT VALUE APPLICATIONS: 1. Simple Loan Loan Principal: amount of funds lender provides to borrower Maturity Date: date loan must be repaid; Loan Term is from initiation to maturity date Interest Payment: cash amount that borrower must pay lender for use of loan principal Simple Interest Rate –interest payment divided by loan principal –%of principal that must be paid as interest to the lender –conventionally expressed on an annual basis, irrespective of the loan term

8. What is the cost of borrowing?  Loan of RM100 today requires borrower to repay the RM100 a year from now and make an additional interest payment of RM10. Calculations of interest rates:- i = 10 = 0.10 = 10% 100 First Year  If you give out this loan, at the end of the year, you would receive RM110, which can be rewritten as: 100 x (1 + 0.10) = RM110 Second Year 110 x (1 + 0.10) = RM121 OR 100 x (1 + 0.10) x (1 + 0.10) = 100 x (1 + 0.10) 2 = RM121 Continuing the Loan 121 x (1 + 0.10) OR RM100 x (1 + 0.10) 3 = RM133 Today 0 Year 1Year 2Year 3 100110121133

9.  Can be generalized as: If the simple interest rate i is expressed as a decimal (0.10), then after making these loans for n years, you will receive a total payment of RM100 x (l +i) n or RM100 today = RM110 next year = RM121 next 2 years = RM133 next 3 years  Discounting the future Today Future RM100 100 (I + i) 3 = RM133 So that, 100= 133 (1 + i) 3  From here, we can solve for the Present Value (Present Discounted Value) – The value today of a future payment (FV) received n years from now

10. PV = FV (1 + i) n Q:- What is the present value of RM250 to be paid in two years if the interest rate is 15% PV = FV (1 + i) n FV = 250 i = 0.15 n = number of years PV = ? PV = 250 = 250 = RM189.04 (1 + 0.15) 2 1.3225 0 Today Yr 1 Yr 2 250 Answer = RM189.04

11. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-11 Present value is extremely useful because it allows us to figure out today’s value of a credit market instrument at a given simple interest rate i by just adding up the present value of all the future cash flows received. The present value concept allows us to compare the value of two instruments with very different timing of their cash flows.

12. 12 Yield to Maturity: Loans Yield to maturity = interest rate that equates today's value with present value of all future payments 1.Simple Loan Interest Rate (i = 10%) If Kamal borrows $100 from his sister and next year she wants $110 back from him, what is the yield to maturity on this loan? Solution: The yield to maturity on the loan is 10%. Of the several common ways of calculating interest rates, the most important is the yield to maturity

13. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-13

14. 14 PRESENT VALUE APPLICATION : 2. Fixed-Payment Loan Terms Fixed-Payment Loans are loans where the loan principal and interest are repaid in several payments, often monthly, in equal dollar amounts over the loan term. Installment Loans, such as auto loans and home mortgages are frequently of the fixed-payment type.

15. Example: The loan is RM1000, and the yearly payment is RM85.81 for the next 25 years. 1 st Year: PV = FV 1 + i PV = 85.81 1 + i 2 nd Year: PV = 85.81 (1 + i) 2 25 th Year: PV = 85.81 (1 + i) 25

16. - What makes today’s value of the loan RM1000? = Sum of the present value of all the yearly payments gives us:- 1000 = 85.81 + 85.81 + ………………. 85.81 (1 + i) (1 + i) 2 (1 + i) 25 More generally, for any fixed payment loan:- LV = FP + FP + FP + ……… FP (1 + i) (1 + i) 2 (1 + i) 3 (1 + i) 25 LV = Loan value FP = Fixed yearly payment n = Number of Years until maturity  For a fixed-payment loan amount, the fixed yearly payment and the number of years until maturity are known quantities, we can then solve for yield to maturity.

17. Fixed-Payment Loan You want to purchase a house and need a $100,000 mortgage. You take up a loan from a bank that has an interest of 7%. What is the yearly payment to the bank to pay off the loan in 20 years? LV = FP + FP ……………. + FP (1 + i) (1 + i) 1 (1 + i) n LV = loan value amount = 100,000 i = annual interest rate = 0.07 n = number of years = 20 1000,000 = FP + FP + …………………. FP (1 + 0.07) (1 + 0.07) 2 (1 + 0.07) 20

18.  Solving Using Finance Calculator: n = number of years = 20 PV = amount of the loan (LV) = -100,000 FV = amount of the loan after 20 years = 0 i = annual interest rate = 0.07 Yearly payment to bank is:- RM9,439.29 Then push the PMT button = fixed yearly payment (FP ) = $9,439.29 Help: Home Mortgage Payment Calculator Using an Excel Spreadsheet https://www.youtube.com/watch?v=mjqXAaQqFqs

19. 19 PRESENT VALUE APPLICATION : 3. Coupon Bond Pays owner of the bond a fixed interest payment (coupon payment) every year until maturity date, when face value/par value is repaid Three information: Issuer; maturity date; coupon rate-the value of yearly coupon payment expressed as a % of the face value Example: Find the price of a 10% coupon bond with a face value of $1000, a 12.25% yield-to-maturity, and 8 years to maturity Use formula Or use calculator P = price of coupon bond C = yearly coupon payment n = years to maturity date i=annual interest rate

20. Find the price of a 10% coupon bond with a face value of $1,000, a 12.25% yield to maturity and eight years to maturity Solution : - The price of bond is RM889.20 n = years to maturity = 8 FV = face value of the bond = 1000 i = annual interest rate = 12.25% PMT = Yearly coupon payments = 100

21. 21 Yield to Maturity: Bonds 3.Coupon Bond (Coupon rate = 10% = C/F) Consol/perpetuity: A perpetual bond with no maturity date and no repayment of principal. Fixed coupon payments of $C forever P = price of coupon bond C = yearly coupon payment F = face value of the bond n = years to maturity date i=annual interest rate

22. 22 PRESENT VALUE APPLICATION : 4. Discount Bond Zero-coupon bond: a bond that is bought at a price below its face value (at a discount), and the face value is repaid at the maturity date. Makes no interest payments-just pays off the face value Example: A one-year TBILL paying a face value of $1,000 in 1 year’s time. If current purchase price is $900, find the yield-to- maturity Use formula YTM formula similar to simple loan: PV= FV/(1+i) n

23. 23 Yield to Maturity: Bonds 4.One-Year Discount Bond (P = $900, F = $1000) P = price of coupon bond F = face value of the bond i= annual nterest rate

24. 24 Relationship Between Price and YTM For a coupon bond or discount bond, the yield to maturity is negatively related to the current bond price. For example, a rise in the bond price from $900 to $1000 means that the bond will have a smaller increase in its price over its lifetime, and the yield to maturity falls from 11.75% to 10.0%. Similarly, a fall in the yield to maturity means that the price of the discount bond has risen. Three observations: 1.When bond is at par, yield equals coupon rate 2.Price and yield are negatively related 3.Yield greater than coupon rate when bond price is below par value

25. Bottom Line: The concept of present value shows: A dollar in the future is not as valuable to you as a dollar today because you can earn interest on this dollar. A dollar received n years from now is worth only today. The present value of a set of future cash flows on a debt instrument equals the sum of the present values of each of the future cash flows. The yield to maturity for an instrument is the interest rate that equates the present value of the future cash flows on that instrument to its value today. Current bond prices and interest rates are negatively related: When the interest rate rises, the price of the bond falls, and vice versa. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4-25

26. 26 OTHER MEASURES OF INTEREST RATE 1. Current Yield Current yield: An approximation of YTM that equals to yearly coupon payment divided by price of a coupon bond Two characteristics 1.Is better approximation to yield to maturity, nearer price is to par and longer is maturity of bond 2.Change in current yield always signals change in same direction as yield to maturity

27. 27 Two characteristics: 1. Understates yield to maturity; longer the maturity, greater is understatement 2. Change in discount yield always signals change in same direction as yield to maturity OTHER MEASURES OF INTEREST RATE 2. Yield on a Discount Basis One-Year Bill (P = $900, F = $1000)

28. 28 Distinction Between Real and Nominal Interest Rates The real interest rate is the interest rate that is adjusted by subtracting expected changes in the price level (inflation) so that it more accurately reflects the true cost of borrowing. The Fisher equation states that the nominal interest rate i equals the real interest rate i r plus the expected rate of inflation e. Fisher hypothesis: change in expected inflation = change in nominal interest rate. Real interest rate more accurately reflects true cost of borrowing When real rate is low, greater incentives to borrow BUT less incentive to lend out/save

29. 29 Distinction Between Real and Nominal Interest Rates (cont.) If i = 5% and π e = 0% then If i = 10% and π e = 20% then

30. 30 U.S. Real and Nominal Interest Rates Figure 3-1 Real and Nominal Interest Rates (Three-Month Treasury Bill), 1953–2004 Sample of current rates and indexes http://www.martincapital.com/charts.htm

31. 31 Distinction Between Interest Rates and Returns How well a person does by holding a bond over time is accurately measured by rate of return RET is the payments to the owner plus the change in the value of the security Rate of Return R = return from holding the bond from time t to time t + 1 Pt = price of the bond at time t Pt+1 = price of the bond at time t 1 C = coupon payment

32. 32 Distinction Between Interest Rates and Returns What would the rate of return be on a bond bought for $1000 and sold one year later for $800? The bond has a face value of $1000 and a coupon rate of 8%.