Consider the following 4 bonds A B C D:(a) What is the percentage change in the price of each bond if its yields to maturity falls from 6% to 5%

Answer is explained and solved in the explanation section below.

Explanation:

Note: This question is not complete and lacks necessary data to solve. But I have found a similar question on internet and will be using its's data to solve this question for the sake of concept and understanding.

Data Missing:

Bonds              Coupon Rates          Maturity

A                              0%                         15 years

B                              0%                          10 years

C                              4%                          15 years

D                               8%                         10 years

Par Value = $1000

Required = % age change in price of bonds, if yields to maturity falls from 6% to 5%.

New YTM = 5%

Old YTM = 6%

For Bond A:

Formula for Old Price = PV(6%, maturity, -annual coupon, -1000)

You need to put this function into Microsoft Excel to solve for old price.

Annual coupon formula = $1000 x coupon rate.

So,

We have,

Maturity = 15 years

Annual Coupon = $1000 x 0% = 0

Old price = PV(6%, maturity, -annual coupon, -1000)

Old price = PV(6%, 15, 0, -1000)

Old Price = $417.27

Now, for new price:

Formula for New Price = PV(5%, maturity, -annual coupon, -1000)

New Price = PV(5%, maturity, -annual coupon, -1000)

New Price = PV(5%, 15, 0, -1000)

New Price = $481.02

Now, we need to find the %age change of bond A.

%age change = (New Price - Old Price) divided by Old Price x 100

%age change = ( $481.02 - $417.27) / ($417.27) x 100

%age change = 15.28%

For bond B:

Old Price = PV(6%, maturity, -annual coupon, -1000)

Maturity = 10 years

Annual Coupon = $1000 x 0% = 0

Old Price = PV(6%, 10, 0, -1000)

Old Price = $558.39

For New Price:

New Price = PV(5%, maturity, -annual coupon, -1000)

New Price = PV(5%, 10, 0, -1000)

New Price = $613.91

%age change = (New Price - Old Price) divided by Old Price x 100

%age change = ( $613.91 - $558.39) / ($558.39) x 100

%age change = 9.94%

For Bond C:

Old Price = PV(6%, maturity, -annual coupon, -1000)

Maturity = 15 years

Annual Coupon = $1000 x 4% = 40

Old Price = PV(6%, 15, -40, -1000)

Old Price = $805.76

New Price = PV(5%, maturity, -annual coupon, -1000)

New Price = PV(5%, 15, -40, -1000)

New Price = $896.20

%age change = (New Price - Old Price) divided by Old Price x 100

%age change =  ( $896.20 - $804.76) / ($805.76) x 100

%age change = 11.23%

For Bond D:

Old Price = PV(6%, maturity, -annual coupon, -1000)

Maturity = 10 years

Annual Coupon = $1000 x 8% = 80

Old Price = PV(6%, 10, -80, -1000)

Old Price = $1,147.20

New Price = PV(5%, maturity, -annual coupon, -1000)

New Price = PV(5%, 10, -80, -1000)

New Price = $1,231.65

%age change = (New Price - Old Price) divided by Old Price x 100

%age change =  ( $1231.65 - $1147.20) / ($1147.20) x 100

%age change = 7.36%

Hence,

% age change of A = 15.28%

% age change of B = 9.94%

% age change of C = 11.23%

% age change of D = 7.36%

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