Bond

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◇ Typical Bond Feature

특징	설명	비고
Par value	The amount of loan to be repaid. This often referred to as the principal of the bond	$1,000
Time to maturity	The number of years left until the maturity	1year to 30 years
Call	The opportunity for the issuer to repay the principal before the maturity date, usually because the interest rate have fallen or issuer's circumstances have changed. When calling a bond, the issuer commonly pays the principal and one year of interest payment.	Many bonds are callable. For those that are, a common feature is that the bond called anytime after 10years of issuance
Coupon rate	The interest rate used to compute the bond's interest payment each year listed as a percentage of par value, the actual payment usually arrive twice per year	2 to 10 percent
Bond price	The bond's market price reported as a percentage of par value	80 to 120 per cent of par value

◇ Bond characteristics

Consider a bond issued ten years ago with an at issue time to maturity of 30 years. The bond's coupon rate is 8 % and it currently trades in the bond market for 109. Assuming a par value of $1,000, what is the bond's current time to maturity , semi annual interest payment, and bond price in dollars?

-Time to maturity =30 years-10 years=20 years

Annual payment=8% x $1,000=$80, so semi annual payment is $40

Bond price=109% x $1,000=$1,090

◇ Bond yields

-Current yields : The bond's annual coupon rate divided by the bond's current market rate

-Yield to maturity : The total rate of return that they might expect if the bond were bought to a particular price and held to maturity. (금융상품이 미래에 지급하는 금액을 현재의 가치(가격)와 일치시키는 이자율)

Consider 3.5% Treasury bond with 4 year left to maturity and a quoted price of 96:09

(1) First identify that the bond's price is $962.81(=96: 09/32% x $1,000)

(2) The annual $35 in interest payment is paid in two $17.50 semi annual payment. Therefore, the current yield of the bond is 3.64%(=$35 ÷ $962.81)

(3) The yield to maturity is computed using equation(Bond Price=PV of annuity(PMT, i,N) + PV(FV,i,N) and the financial calculator as N=8, PV=-962.81, PMT=17.50, and FV=1,000, Computing the interest rate(i) results in 2.26 % and multiplying by 2 gives the yield to maturity of 4.53%

(4) Note that the current yield is less than yield to maturity because it does not account for the capital gain to be earned if held to maturity.

Discounted Cash Flow(DCF)

-1년 후 미래가치가 $1,000, 현재 금리가 5%인 경우 현재가치는?

$952.38 x 0.05=$47.62

$952.38 + $47.62=$1,000

-현재 금리가 7%인 경우

$934.58 x 0.07=$65.42

$934.58 + $65.42=$1,000(금리와 미래가치는 음의 관계)

현재가치(present value)=할인가치(discounted value)

<Amount Problem>

1.The Future Value of an Amount

FV1 = PV +kPV

FV1 = PV(1 +k)-------------(1)

FV2 = FV1 (1 +k)

FV2 = PV(1 +k)2-------------(2)

FVn = PV(1 +k)n-------------(3)

ex1) $850 을 3년간 5%로 저축하는 경우 미래가치는?

FVn = PV(FVFk,n)------------(4)

FV3 =$850[FVF5,3]

the Future Value Factor for k and n

FVFk,n =(1+k)n

FV3 = $850[1.1576]

=$983.96

ex2) 매도가 $25,000 토지를 $15,000 은 선수금, 나머지는 매년 $5,000 씩 2년간 지급하는 경우 금리가 6%인 경우 실제 매수가격은?

FVn = PV(FVFk,n)

$5,000=PV(FVF6,1)

=PV[1.0600]

PV=$4,716.98

FVF6,2 =1.1236

PV=4,449.98

Actual Price=$15,000 +$4,716.98 +$4,449.98

=$24,166.96

FVn = PV(1 +k)n-------------(3)

PV = FVn [1 /(1 +k)n]--------(5)

PV = FVn (1+k)-n -------- (6)

PV = FVn [PVFk,n]-----------(7)

PVFk,n = 1 /PVFk,n -----------(8)

ex3) 3년 후에 $850 이 $983.96 이 되려면 이자율은 ?

PV = FVn [PVFk,n]

$850 = $983.96[PVF k,3]

PVF k,3 =$850/$983.96 =0.8639

Tablel을 통해 3년을 보면 5%

ex4) 금리14%로 투자했을 때 2배가 되는 기간은?

FVn = PV(FVFk,n)

FVF14,n = FVn / PV=2.000

Table에서 n=15%

5년 1.9254

6년 2.1950 따라서 5년이 접근, 실제 년 수 : 5.29 년