1 bond valuation issuer (seller) investors (buyers) $ $$ bond contract
TRANSCRIPT
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Bond Valuation
Issuer (Seller)Investors
(Buyers) $$$
Bond Contract
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Bond Contract
How much should you pay ? Bond Value = ?
Par
C C C C C1
2
41 2 3 n
Buy the bond today
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Value of Bond today
= C (PVIFA i, n) + Par (PVIF i,
n)Bond Value C = Coupon Payment = coupon rate x par
Par value or Face Value = $1,000
Par
C C C C C1
2
41 2 3 n
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An example
You buy bond with $1,000 par value, Coupon rate 9% paid once per year, 5 years until maturity. Assume interest rate is 3%. What is the value of this bond?
1,000
90 90 90 90 90
Vb = + PAR x PVIF i, nC x PVIFA i, n
+ 1,000 x PVIF 3%,590 x PVIFA 3%,51,274.77
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Find value of bond with $1,000 par value, Coupon rate
15% paid once per year, 4 years until maturity
Vb = C (PVIFA i,n) + Par (PVIF i,n)
$ 1,158.49
$ 1,000
$ 870.61
Bond Price
= 10%
= 15%
= 20%
If interest
Bond sold at Premium
Bond is sold at Par
Bond sold at Discount
Price-Yield relationship
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Semiannual coupon payment
Coupon per period = coupon per year ÷ 2
Find value of bond with 10% coupon rate paid semiannually, 10
years maturity. Interest rate is 6%
Bond Value = C (PVIFA i/2,nx2) + Par (PVIF i/2,nx2)
Coupon per period = 10% x 1,000 ÷ 2
= 50
Vb = 50 (14.8775) + 1,000 (0.5537)
Vb = 50 (PVIFA 3% , 20 ) + 1,000 (PVIF 3% , 20 )
Vb = 1,297.57
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Finding the interest rate (YTM)
= coupon per year + [(par – price) ÷ n]
(par + price) ÷ 2
***coupon per year = coupon rate x par
***par = $1,000
***price = market price
***n = number of years
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Finding the interest rate (YTM)
= coupon per year + [(par – price)
÷ n]
(par + price) ÷ 2
***coupon per year = 10% x 1000 = $ 100
***par = $1,000
***price = $ 850
***n = 5 years
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Finding the interest rate (YTM)
= $ 100 + [(1,000 – 850) ÷ 5]
(1,000 + 850) ÷ 2
***coupon per year = 10% x 1000 = $ 100
***par = $1,000
***price = $ 850
***n = 5 years
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Finding the interest rate (YTM)
= $ 100 + [(1,000 – 850) ÷ 5]
(1,000 + 850) ÷ 2
= $ 100 + 30
925
= 0.1405 = 14.05 %
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Finding the interest rate (YTM)
= $ 160 + [(1,000 – 1,100) ÷ 10]
(1,000 + 1,100) ÷ 2
***coupon per year = 16% x 1000 = $ 160
***par = $1,000
***price = $ 1,100
***n = 10 years
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Finding the interest rate (YTM)
= $ 160 + [(1,000 – 1,100) ÷ 10]
(1,000 + 1,100) ÷ 2
= $ 160 - 10
1,050
= 0.1429 = 14.29 %
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Exercise
1. A corporate bond with a coupon rate of 7% matures in 4 years. Its price is currently $1,150. - Calculate the current yield on this bond- Calculate the yield to maturity on this bond
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Current Yield Formula
The current yield refers simply to the annual
payment (coupon) divided by the price.
Yc = R/Pwhere
Yc is the current yield, R is the annual coupon payment in
dollars, P is the market price.
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Current Yield Example
Market price of 5-years treasury bond is $1,020. the bond is
paying a coupon of $50 per year. Find the current yield.
Yc = 501020
Yc = 0.049 or 4.9%
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Comparing bond value & market price
If the market price of Bond < Bond Value
Then the Bond is “Cheap” Bond is Undervalued (Underpriced) Investors will buy the Bond
Demand > Supply Price will increase
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Comparing bond value & market price
If the market price of Bond > Bond Value
Then the Bond is “Expensive” Bond is Overvalued (Overpriced) Investors will sell the Bond
Demand < Supply Price will decrease
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A bond will have a higher price if:
Interest rate (yield) is …………….(higher/lower)
Coupon rate, payment is …………….(higher/lower)
Maturity is ……….(longer/shorter)