Question

Assuming the standard US Par (Face) value of $1000,

Annual coupon = $100 x 6% = $60

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%?

Answer 1

A.

i.

Face value = $1000

Annual coupon = 1000*6% = $60

Time = 20 years

R = 8%

Then,

Price of the bond = 60*(1-1/(1+8%)^20)/.08 + 1000/(1+8%)^20

Price of the bond = $803.64 or $804

==

ii.

If R = 9% , then:

Price of the bond = 60*(1-1/(1+9%)^20)/.09 + 1000/(1+9%)^20

Price of the bond = 726.14

So,

% change in price ( with rise in R from 8% to 9%) = (726.14-803.64)/803.64

% change in price ( with rise in R from 8% to 9%) = -9.64%

So, there is a decrease in price by 9.64%.

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B.

iii

Face value = $1000

Annual coupon = 1000*7% = $70

Time = 20 years

R = 8%

Then,

Price of the bond = 70*(1-1/(1 + 8%)^20)/.08 + 1000/(1+8%)^20

Price of the bond = $901.82 or $902

==

IV

If R = 9% , then:

Price of the bond = 70*(1-1/(1+9%)^20)/.09 + 1000/(1+9%)^20

Price of the bond = $817.43

So,

% change in price ( with rise in R from 8% to 9%) = (817.43-901.82 )/901.82

% change in price ( with rise in R from 8% to 9%) = -9.36%

So, price decreases by 9.36%.