Answer:
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%
