Understanding Interest Rate (Ch3) -- Fin331 1

Understanding Interest Rates

1. Present Value

2. Calculating Yield to Maturity for different types of debt

3. Other Measures of Interest Rates

4. Real Interest Rate

5. Rate of Return

6. Interest Rate Risk and Reinvestment Risk

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Present Value

A loan of $1 at 10% interest

Year 1 2 3 n $1.10 $1.21 $1.33 $1x(1+i)n

PV of future $1 = $1 (1+i)n

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Types of Loans

1. Simple loan

2. Fixed-payment loan

3. Coupon bond

4. Discount bond

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Simple Loan: a loan that borrower repays lender principal and interest payment at the maturity date.

Fixed-Payment Loan: a loan that borrower repays lender same payment every month.

Coupon Bond: a bond/loan that pays the owner of the bond a fixed interest payment every year until maturity, when a specified final amount is repaid.

Discount Bond (Zero-Coupon Bond): a bond that is bought at a price below its face value, and face value is repaid at the maturity date.

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Yield to Maturity: Simple Loans

Yield to maturity = interest rate that equates today's value with present value of all future payments

1. Simple Loan

You borrowed $100 and agreed to return $110. Then the return is ___?

i =

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2. Fixed Payment Loan (i =?)

LV = FP + FP + FP + ... + FP (1+i) (1+i)2 (1+i)3 (1+i)N

$1000 = $126 + $126 + $126 + ... + $126 (1+i) (1+i)2 (1+i)3 (1+i)25

Yield to Maturity: Fixed Payment Loans

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You planned to buy a house for $350,000. You will pay 20 percent down payment. You will also arrange a 30-year 6% APR mortgage. What is your monthly payment?

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Yield to Maturity: Coupon Bonds

3. Coupon Bond (Coupon rate = 10% = C/F) P = $100 + $100 + $100 + ... + $100 + $1000 (1+i) (1+i)2 (1+i)3 (1+i)10 (1+i)10

P = C + C + C + ... + C + F (1+i) (1+i)2 (1+i)3 (1+i)N (1+i)N

Fixed coupon payments of $C foreverP = C i = C

i P

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Relationship Between Price and Yield to Maturity

Three Interesting Facts1. When bond is at par, yield equals coupon rate2. Price and yield are negatively related3. Yield greater than coupon rate when bond price is below

par value

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In-class Exercise

Quantitative Problem 3, Page 69

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4. One-year Discount Bond (P = $900, F = $1000)

i = F - P P

i =

Yield to Maturity: Discount Bonds

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Other Bonds Reporting

1. Current yield - Corporate Bonds

2. Yield on a discount basis - Treasury Bill

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Current Yield

ic = C P

Two Characteristics1. Is better approximation to yield to maturity, nearer price is

to par and longer is maturity of bond2. Change in current yield always signals change in same

direction as yield to maturity

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Yield on a Discount Basis

maturity) todays of (number

360x

F

P)-Fidb

(

Example: One-year bill, P = $900, F = $1000

Two Characteristics1.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

9.9%.099365

360x

$1000

$900-$1000idb

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Bond Page of the Newspaper

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Distinction Between Real and Nominal Interest Rates

Real interest rate: Interest rate that is adjusted for expected changes in the price level

ir = i - π e

1. Real interest rate more accurately reflects true cost of borrowing

2. When real rate is low, greater incentives to borrow and less to lend

if i = 5% and π e = 0% then: ir = 5% - 0% = 5%if i = 10% and π e = 20% then

ir = 10% - 20% = - 10%

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U.S. Real and Nominal Interest Rates

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Distinction Between Interest Rates and Returns

gain capitalP

Ppg

yieldcurrentP

Ci :where

giP

PPCRET

t

t1t

tc

ct

t1t

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Calculate One-year return for investing a 10 year 10% coupon rate bond when interest rise from 10% to 20%

Formula:

Assuming face value is $1000, then C =

P(t)

P(t+1)

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Key Facts about Relationship Between Rates and Returns

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Maturity and the Volatility of Bond Returns

1. Only bond whose return = yield is one with maturity =

holding period

2. For bonds with maturity > holding period, i P implying capital loss

3. Longer is maturity, greater is price change associated with interest rate change

4. Longer is maturity, more return changes with change in interest rate

5. Bond with high initial interest rate can still have negative return if i

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Maturity and the Volatility of Bond Returns

Conclusion from Table 2 Analysis1. Prices and returns more volatile for long-term

bonds because have higher interest- rate risk

2. No interest-rate risk for any bond whose maturity equals holding period

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Reinvestment Risk

1. Occurs if hold series of short bonds over long holding period

2. i at which reinvest uncertain

3. Gain from i , lose when i