Respuesta :
Answer:
The question is incomplete; the complete question is as follows;
A 20-year maturity bond with par value $1,000 makes semiannual coupon payments at a coupon rate of 9%.
a.
Find the bond equivalent and effective annual yield to maturity of the bond if the bond price is $940.(Round your intermediate calculations to 4 decimal places. Round your answers to 2 decimal places.)
Bond equivalent yield to maturity %
Effective annual yield to maturity %
b.
Find the bond equivalent and effective annual yield to maturity of the bond if the bond price is $1,000.(Do not round intermediate calculations.Round your answers to 2 decimal places.)
Bond equivalent yield to maturity %
Effective annual yield to maturity %
c.
Find the bond equivalent and effective annual yield to maturity of the bond if the bond price is $1,060.(Round your intermediate calculations to 4 decimal places. Round your answers to 2 decimal places.)
Bond equivalent yield to maturity %
Effective annual yield to maturity %
Explanation:
PMT= 1000* 9% / 2= 45
(A). Type N= 40, FV= 1000, PV= -940, PMT= 45 into a financial calculator. Click the I / Yr key= 4.84% Maturity equivalent to bond yield= 4.84%* 2= 9.68%.
Effective annual maturity yield= (1.0484)2-1 = 9.91 per cent
(B). Type N= 40, FV= 1000, PV= -1000, PMT= 45 also into a financial calculator. Click the I / Yr key= 4.50 percent Maturity Bond equivalent yield= 4.50 percent* 2= 9 percent equal to the yearly coupon rate.
Average annual maturity yield= (1.045)2-1= 9.20 per cent
(C). Type N= 40, FV= 1000, PV= -1060, PMT= 45 into a financial calculator.
Click the I / Yr key = 4.19% Bond comparable yields to maturity = 4.19% * 2 = 8.38%
Total yearly yield to maturity = (1.0419)2-1 = 8.55%
Answer:
Part a: For the bond price of $950, the bond equivalent yield is 10.63% while that of effective annual yield is 10.9%.
Part b:For the bond price of $1000, the bond equivalent yield is 10% while that of effective annual yield is 10.25%.
Part c:For the bond price of $1050, the bond equivalent yield is 9.42% while that of effective annual yield is 9.64%.
Explanation:
As the data here is not complete, by finding the complete question online which is attached herewith.
Part a: $950
As per the given data,
- The bond price is $950.
- The coupon rate is 10% of 1000 which is given as $100 annually.
- As the coupon is semi-annual this indicates that each payment is of $50.
- Number of total years is 20.
- The par value is $1000.
So the price for semi-annual coupons is given as
[tex]Price=[\sum_{i=1}^{2n-1} \frac{CFi}{(1+YTM)^i}]+ \frac{CF+Par}{(1+YTM)^{2n}}[/tex]
Here
- CF_i is the value of per coupon which is $50 in this case
- Price is $950.
- Par value is $1000.
- n is number of years which is 20.
By applying this formula in
[tex]950=[\sum_{i=1}^{39} \frac{50}{(1+YTM)^i}]+ \frac{1050}{(1+YTM)^{40}}[/tex]
Solving this with the help of a financial calculator yields
[tex]YTM\approx 0.053036 \approx 5.31\%[/tex]
Now
Bond Equivalent yield is given as
[tex]Bond \, Equivalent \, Yield=2\times YTM\\Bond \, Equivalent \, Yield=2\times5.31\%\\Bond \, Equivalent \, Yield=10.63\%[/tex]
So the bond equivalent yield is 10.63%.
The effective annual yield is given as
[tex]Effective\, Annual\, Yeild=(1+YTM)^2-1\\Effective\, Annual\, Yeild=(1+0.0531)^2-1\\Effective\, Annual\, Yeild=0.1090 =10.9\%[/tex]
So the effective annual yield is 10.9%
For the bond price of $950, the bond equivalent yield is 10.63% while that of effective annual yield is 10.9%.
Part b: $1000
As per the given data,
- The bond price is $1000.
- The coupon rate is 10% of 1000 which is given as $100 annually.
- As the coupon is semi-annual this indicates that each payment is of $50.
- Number of total years is 20.
- The par value is $1000.
So the price for semi-annual coupons is given as
[tex]Price=[\sum_{i=1}^{2n-1} \frac{CFi}{(1+YTM)^i}]+ \frac{CF+Par}{(1+YTM)^{2n}}[/tex]
Here
- CF_i is the value of per coupon which is $50 in this case
- Price is $1000.
- Par value is $1000.
- n is number of years which is 20.
By applying this formula in
[tex]1000=[\sum_{i=1}^{39} \frac{50}{(1+YTM)^i}]+ \frac{1050}{(1+YTM)^{40}}[/tex]
Solving this with the help of a financial calculator yields
[tex]YTM\approx 0.05 \approx 5\%[/tex]
Now
Bond Equivalent yield is given as
[tex]Bond \, Equivalent \, Yield=2\times YTM\\Bond \, Equivalent \, Yield=2\times5\%\\Bond \, Equivalent \, Yield=10\%[/tex]
So the bond equivalent yield is 10%.
The effective annual yield is given as
[tex]Effective\, Annual\, Yeild=(1+YTM)^2-1\\Effective\, Annual\, Yeild=(1+0.05)^2-1\\Effective\, Annual\, Yeild=0.1025 =10.25\%[/tex]
So the effective annual yield is 10.25%
For the bond price of $1000, the bond equivalent yield is 10% while that of effective annual yield is 10.25%.
Part c: $1050
As per the given data,
- The bond price is $1050.
- The coupon rate is 10% of 1000 which is given as $100 annually.
- As the coupon is semi-annual this indicates that each payment is of $50.
- Number of total years is 20.
- The par value is $1000.
So the price for semi-annual coupons is given as
[tex]Price=[\sum_{i=1}^{2n-1} \frac{CFi}{(1+YTM)^i}]+ \frac{CF+Par}{(1+YTM)^{2n}}[/tex]
Here
- CF_i is the value of per coupon which is $50 in this case
- Price is $1050.
- Par value is $1000.
- n is number of years which is 20.
By applying this formula in
[tex]1050=[\sum_{i=1}^{39} \frac{50}{(1+YTM)^i}]+ \frac{1050}{(1+YTM)^{40}}[/tex]
Solving this with the help of a financial calculator yields
[tex]YTM\approx 0.0471 \approx 4.71\%[/tex]
Now
Bond Equivalent yield is given as
[tex]Bond \, Equivalent \, Yield=2\times YTM\\Bond \, Equivalent \, Yield=2\times4.71\%\\Bond \, Equivalent \, Yield=9.42\%[/tex]
So the bond equivalent yield is 9.42%.
The effective annual yield is given as
[tex]Effective\, Annual\, Yeild=(1+YTM)^2-1\\Effective\, Annual\, Yeild=(1+0.0471)^2-1\\Effective\, Annual\, Yeild=0.09641 =9.64\%[/tex]
So the effective annual yield is 9.64%
For the bond price of $1050, the bond equivalent yield is 9.42% while that of effective annual yield is 9.64%.
