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Bond Valuation. Bond Contract. Issuer (Seller). Investors (Buyers). $. $. $. Bond Contract. How much should you pay ? Bond Value = ?. Buy the bond today. 1. 2. 3. 4. n. C C C C C. 1. Par. 2. Value of Bond today. C = Coupon Payment = coupon rate x par

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Bond Contract

How much should you pay ? Bond Value = ?

Buy the bond today

1

2

3

4

n

C C C C C

1

Par

2

Value of Bond today

C = Coupon Payment = coupon rate x par

Par value or Face Value = $1,000

Bond Value

= C (PVIFA i, n) + Par (PVIF i, n)

1

2

3

4

n

C C C C C

1

Par

2

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?

90 90 90 90 90

1,000

Vb =

C x PVIFA i, n

+ PAR x PVIF i, n

90 x PVIFA 3%,5

+ 1,000 x PVIF 3%,5

1,274.77

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)

If interest

Bond Price

- Bond sold at Premium

= 10%

$ 1,158.49

- Bond is sold at Par

= 15%

$ 1,000

- Bond sold at Discount

= 20%

$ 870.61

- Price-Yield relationship

Semiannual coupon payment paid once per year, 4 years until maturity

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 (PVIFA 3% , 20 ) + 1,000 (PVIF 3% , 20 )

Vb = 50 (14.8775) + 1,000 (0.5537)

Vb = 1,297.57

Finding the interest rate (YTM) paid once per year, 4 years until maturity

= 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

Finding the interest rate (YTM) paid once per year, 4 years until maturity

= coupon per year + [(par – price) ÷ n]

(par + price) ÷ 2

***coupon per year = 10% x 1000 = $ 100

***par = $1,000

***price = $ 850

***n = 5 years

Finding the interest rate (YTM) paid once per year, 4 years until maturity

= $ 100 + [(1,000 – 850) ÷ 5]

(1,000 + 850) ÷ 2

***coupon per year = 10% x 1000 = $ 100

***par = $1,000

***price = $ 850

***n = 5 years

Finding the interest rate (YTM) paid once per year, 4 years until maturity

= $ 100 + [(1,000 – 850) ÷ 5]

(1,000 + 850) ÷ 2

= $ 100 + 30

925

= 0.1405

= 14.05 %

Finding the interest rate (YTM) paid once per year, 4 years until maturity

= $ 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

Finding the interest rate (YTM) paid once per year, 4 years until maturity

= $ 160 + [(1,000 – 1,100) ÷ 10]

(1,000 + 1,100) ÷ 2

= $ 160 - 10

1,050

= 14.29 %

= 0.1429

Exercise paid once per year, 4 years until maturity

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

Current Yield Formula paid once per year, 4 years until maturity

The current yield refers simply to the annual payment (coupon) divided by the price.

Yc = R/P

where

Yc is the current yield,

R is the annual coupon payment in dollars,

P is the market price.

Current Yield Example paid once per year, 4 years until maturity

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 = 50

1020

Yc = 0.049 or 4.9%

Comparing bond value & market price paid once per year, 4 years until maturity

If the marketprice of Bond < Bond Value

Then the Bond is “Cheap”

Bond is Undervalued (Underpriced)

Investors will buy the Bond

Demand > Supply

Price will increase

Comparing bond value & market price paid once per year, 4 years until maturity

If the marketprice of Bond > Bond Value

Then the Bond is “Expensive”

Bond is Overvalued (Overpriced)

Investors will sell the Bond

Demand < Supply

Price will decrease

A bond will have a higher price if: paid once per year, 4 years until maturity

Interest rate (yield) is …………….(higher/lower)

Coupon rate, payment is …………….(higher/lower)

Maturity is ……….(longer/shorter)

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