Question

5) a) Consider a 20-year 6 percent coupon bond.

i) What is the price of this bond if the market yield is 8%?

ii) What is the percentage change in the price of this bond if the market yield rises to 9%?

b) Consider a 20-year 7 percent coupon bond.

iii) What is the price of this bond if the market yield is 8%?

iv) What is the percentage change in the price of this bond if the market yield rises to 9%?

c) What is Theorem 5?

Answer 1

5.

Let, face value is $1000 ( since it is not specifically mentioned)

A.

i.

Coupon payment = 6%*1000 = $60

Time = 20 years

R = 8%

So,

Price of the bond = 60*(1- 1/1.08^20)/.08 + 1000/1.08^20

Price of the bond = $803.64 or $804

===

ii.

If R = 9%, then:

Price of the bond = 60*(1- 1/1.09^20)/.09 + 1000/1.09^20

Price of the bond = $726.14 or $726

So,

% change in price = (726.14-803.64)/803.64

% change in price = -9.64%

So, price decreases by 9.64% with yield increase from 8% to 9%.

====

B.

iii.

Coupon payment = 7%*1000 = $70

Time = 20 years

R = 8%

So,

Price of the bond = 70*(1- 1/1.08^20)/.08 + 1000/1.08^20

Price of the bond = $901.82 or $902

===

iv.

When R = 9%

Then,

Price of the bond = 70*(1- 1/1.09^20)/.09 + 1000/1.09^20

Price of the bond = $817.43 or $817

So,

% change in price = (817.43 - 901.82)/901.82

% change in price = -9.36%

So, price decreases by 9.36% with yield increase from 8% to 9%.

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C.

According to this theorem, when coupon rate and maturity period of the bonds are same, then a bond with a higher frequency of coupon payment, will be less sensitive to the change in price, when interest rate changes for the bond.

For example, bond A, has quarterly coupon payment, and bond B has annual coupon payment, then bond A will have lesser decrease in price when interest rate increases, than that of bond B, as per theorem 5.