MishkinCh04Alt.ppt

7/28/2019 MishkinCh04Alt.ppt

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Chapter 4

Understanding Interest Rates


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Present Value

One lira paid to you one year from nowis less valuable than one lira paid toyou today. Even if we assume inflation

zero, people prefer immediate money.People are impatient.

This is called time value of money.


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Present Value

If the government promises to pay you 100 lirasone year later, or alternatively pay you 100 lirasright now, which one would you prefer?

What If the government promises to pay you 115TL one year later, or alternatively pay you 100 TLright now, which one would you prefer?

What is the present value of 115 TL one yearlater for you? In other words, how many liras you

receive today would make you equally happy with115 TL received one year later? (assume infl. iszero)


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If your answer is 100 TL today, then yourdiscount rate is 15%:

The present value of 115 liras one year later isequal to 100 liras now. Notice that the present

value decreases as the discount (interest) rateincreases. If discount rate was 20%, then PV of115 liras next year would be _____liras now.

Present Value

TL100)15.01(

115uePresentVal


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Present Value

If we think of a longer time period such as twoyears, how much money two years later wouldbe equivalent to 100 liras now? With 15%annual discount=interest rate,

Cash Flow is the two-years-later value (or therepayment amount) of 100 TL (loan) today. Wefind CF = _132.25___ liras.

2)15.01(100

FlowCashFuture


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Present Value

Today Year 1 Year 2 Yearn

100 115 132.25 nx 15.01100


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Simple Present Value

yearsofnumberrateinterestannual

paymentflowcashfuture

valuepresent

where1

n

i

CF

PV

i

CFPV

n


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Simple Present Value

f there is more than one payment in thefuture, then we add the present value ofeach payment.

For example, if there are two payments:1000 TL one year later and 1500 TL threeyears later:

PV=(1000/(1+i))+(1500/(1+i)3)


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Four Types

of Credit Market Instruments

Simple Loan

Lender provides the borrower the loan amountat the present. Borrower must repay theprincipal + interest paymentwhen the

maturity date comes.

Ex: 100 TL loan at 50%simple interest rate,1 yr. maturity. Principal: 100 TL, interestpayment: 50 TL.


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Four Types


Fixed Payment Loan

Repayment of a certain loan is divided intoequal payments. Ex: You borrowed 100,000

TL now to buy a house. If the interest rate is10%, you will repay this loan by paying a fixedamount of 11,017 TL every year for thematurity of 25 years. Ex: Mortgages, car loans.

252 )1(

017,11..

)1(

017,11

)1(

017,11000,100

iii


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Four Types


Coupon Bond Issuer of this bond makes fixed interest (coupon)

payments to the holder every year until thematurity date. For example, assume you bought a

coupon bond with 1000 TL face value, 50%coupon rate, annual coupon payments and 5years maturity issued by the Treasury. Thetreasury will pay you 500 TL every year and willpay you the 1000 TL five years later.

5432 )1(

1500

)1(

500

)1(

500

)1(

500

)1(

500

iiiiiPV


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Four Types


Discount Bond(zero-coupon bond)

The issuer pays the holder the face value atthe maturity date. No coupon payments. The

current price of the bond is smaller than theface value.

Ex: Treasury discount bond with 1000 TLface value and one year maturity is currentlysold for 900 TL. then the interest rate is

(1000-900) / 900 = 11.1 %


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Simple LoanYield to Maturity

If one borrows 100 TL credit for one year,and repays 118 TL at the end of the year,YTM of this credit is

= (118-100)/100 = 0.18, i.e. 18%


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Fixed Payment Loan

Yield to Maturity

2 3

The same cash flow payment every period throughout

the life of the loan

LV = loan value

FP = fixed yearly payment

= number of years until maturity

FP FP FP FPLV = . . . +

1 + (1 + ) (1 + ) (1 + )n

n

i i i i


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Fixed Payment Loan

Yield to Maturity

You take out a 100,000 TL house mortgage withan annual interest rate (YTM) of 20% to be paidin 20 years. What is your payment every year?

Using a financial calculator, we find annualpayments (FP) as 20,536 TL. Total amount paidin 20 years: 410,720 TL. If the interest rate(YTM) increases, annual payments also increase(keeping maturity and loan value constant). For

example, if interest rate was 10%, then we wouldfind annual payments as FP = 11,746 TL.


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Coupon BondYield to Maturity

2 3

Using the same strategy used for the fixed-payment loan:

P = price of coupon bond

C = yearly coupon paymentF = face value of the bond

= years to maturity date

C C C C FP = . . . +1+ (1+ ) (1+ ) (1+ ) (1n

n

i i i i

+ )ni


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Coupon BondYield to Maturity

For a treasury coupon bond with 1000 YTLface value, ten years maturity and 100 TLcoupon payments every year: If the yield

to maturity is 10%, what is the currentprice of the bond?

The current price =present value is 1000TL.

102 )10.01(

1100...

)10.01(

100

)10.01(

1001000


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If the current price of the coupon bond is equal to itsnominal value, its yield to maturity equals the couponrate. In other words, if the YTM is equal to the couponrate, then its current price is equal to its nominal value.

The price of a coupon bond and the yield to maturity areinversely related

If yield to maturity is greater than the coupon rate thenthe current price is below its face value. IfYTM=20%,then current price = $581. (sold at a discount)


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Consol or Perpetuity

A bond with no maturity date. A consol never repays theprincipal but pays fixed coupon payments forever. But youcan sell it anytime.

Pc C / i

c

Pc price of the consol

C yearly interest payment

ic yield to maturity of the consol

Can rewrite above equation as ic C / Pc

For coupon bonds, this equation gives current yield

an easy-to-calculate approximation of yield to maturity


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Consols

The same consol formula can be used toapproximately calculate the YTM or FP of along-term coupon bond or a fixed payment loan.For example, consider a coupon bond with 1000

TL nominal value, 10% coupon rate, 10 yearsmaturity and present value of 1200 TL. Then YTMis ~ 8.3 % (exact 7.13%).

Or a fixed payment credit of 100,000 YTL with 20

years maturity has annual payments equal to20,536 YTL. YTM of this credit is approx. 20.5 %(exact 20%).

Di B d Yi ld


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Discount Bond

Yield to

Maturity

For any one year discount bond

i =F - P

P

F = Face value of the discount bond

P = current price of the discount bond

The yield to maturity equals the increase

in price over the year divided by the initial price.As with a coupon bond, the yield to maturity is

negatively related to the current bond price.

Di B d Yi ld


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Discount Bond

Yield to

Maturity

If a discount bond issued by the treasuryhas a face value of 1000 TL, maturity of oneyear, and is sold at the price of 900 TL, whatis its yield to maturity?

Answer:

%1.11111.0900

100

900

9001000

i


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Rate of Return

In case one does not hold an asset until maturity, rate

of return differs from YTM.

Consider a treasury coupon bond with 20% yield to

maturity (interest rate), 1000 TL face value, 200 TL

coupon payments and two years maturity (initial

price=1000) . One year later, a crisis breaks out and

the interest rate rises to 40%. If you need money and

sell the bond, price of the bond will be 857 TL

(=1200/(1.4)). (If the int. rate did not increase, pricewould be still 1200/1.2 = 1000 TL)

Your rate of return is :


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Rate of Return

Your rate of return is :

200/1000 + (857 - 1000)/ 1000 = 20 - 14.3= 5.7 % much less than 20%. The

bondholder faces interest rate risk.

25


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Rate of Return

More generally, rate of return R for holding abond from time tto time t+1 is

gaincapitalisandyieldcurrentis

paymentcouponis

1tat timebondtheofpricetheis

tat timebondtheofpricetheis

where

1

1

1

t

tt

t

t

t

t

tt

t

P

PP

P

C

C

P

P

P

PP

P

C

R

R f R


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Rate of Return

and Interest Rates

Rate of return is equal to yield to maturity onlyifyou hold the bond until the maturity date.

A rise in interest rates causes a fall in bond

prices, and results in a capital loss if the assetis sold before the time to maturity.

If the bond has a longer term (maturity),there is a greater risk of capital loss because of

a given interest-rate change. See Table 2. So,usually long term bonds have higher int. Ratesto compensate for the higher interest rate risk.


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Interest-Rate Risk

Prices and returns for longer-termbonds are more volatile than those forshorter-term bonds. There is more interest raterisk for long term bonds. This is why Turkish

Treasury had a hard time selling long termbonds.

There is no interest-rate risk for any bond if theowner holds it until the end of maturity. In that

case, YTM= rate of return and YTM is knownwhen the bond is purchased.


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Real and Nominal Interest Rates

Nominal interest rate is the rate quoted bybanks. It is not adjusted for inflation.

Real interest rate is adjusted for inflation so itmore accurately reflects the cost of borrowing

Ex antereal interest rate is calculated fromexpected rate of inflation at the beginning of theyear.

Ex postreal interest rate is calculated from

realized inflation at the end of the year.


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Fisher Equation

= nominal interest rate

= real interest rate

= expected inflation rate

When the real interest rate is low,

there are greater incentives to borrow and fewer incentives to lend.

The real inter

e

r

r

e

i i

i

i

est rate is a better indicator of the incentives to

borrow and lend.


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Real Interest Rates in Turkey

-40

-30

-20

-10

0

10

20

30

40

50

60

70

80

90

100

110

1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

NomIntRate

RealIntRate


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Real Interest Rates in USA

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MishkinCh04Alt.ppt