Question

A 20-year maturity bond with par value of $1,000 makes semiannual coupon payments at a coupon rate of 10%. Find the bond equivalent and effective annual yield to maturity of the bond for the following bond prices. (Round your answers to 2 decimal places.)

Answer 1

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 2

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

$Price=[\sum_{i=1}^{2n-1} \frac{CFi}{(1+YTM)^i}]+ \frac{CF+Par}{(1+YTM)^{2n}}$

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

$950=[\sum_{i=1}^{39} \frac{50}{(1+YTM)^i}]+ \frac{1050}{(1+YTM)^{40}}$

Solving this with the help of a financial calculator yields

$YTM\approx 0.053036 \approx 5.31\%$

Now

Bond Equivalent yield is given as

$Bond \, Equivalent \, Yield=2\times YTM\\Bond \, Equivalent \, Yield=2\times5.31\%\\Bond \, Equivalent \, Yield=10.63\%$

So the bond equivalent yield is 10.63%.

The effective annual yield is given as

$Effective\, Annual\, Yeild=(1+YTM)^2-1\\Effective\, Annual\, Yeild=(1+0.0531)^2-1\\Effective\, Annual\, Yeild=0.1090 =10.9\%$

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

$Price=[\sum_{i=1}^{2n-1} \frac{CFi}{(1+YTM)^i}]+ \frac{CF+Par}{(1+YTM)^{2n}}$

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

$1000=[\sum_{i=1}^{39} \frac{50}{(1+YTM)^i}]+ \frac{1050}{(1+YTM)^{40}}$

Solving this with the help of a financial calculator yields

$YTM\approx 0.05 \approx 5\%$

Now

Bond Equivalent yield is given as

$Bond \, Equivalent \, Yield=2\times YTM\\Bond \, Equivalent \, Yield=2\times5\%\\Bond \, Equivalent \, Yield=10\%$

So the bond equivalent yield is 10%.

The effective annual yield is given as

$Effective\, Annual\, Yeild=(1+YTM)^2-1\\Effective\, Annual\, Yeild=(1+0.05)^2-1\\Effective\, Annual\, Yeild=0.1025 =10.25\%$

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

$Price=[\sum_{i=1}^{2n-1} \frac{CFi}{(1+YTM)^i}]+ \frac{CF+Par}{(1+YTM)^{2n}}$

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

$1050=[\sum_{i=1}^{39} \frac{50}{(1+YTM)^i}]+ \frac{1050}{(1+YTM)^{40}}$

Solving this with the help of a financial calculator yields

$YTM\approx 0.0471 \approx 4.71\%$

Now

Bond Equivalent yield is given as

$Bond \, Equivalent \, Yield=2\times YTM\\Bond \, Equivalent \, Yield=2\times4.71\%\\Bond \, Equivalent \, Yield=9.42\%$

So the bond equivalent yield is 9.42%.

The effective annual yield is given as

$Effective\, Annual\, Yeild=(1+YTM)^2-1\\Effective\, Annual\, Yeild=(1+0.0471)^2-1\\Effective\, Annual\, Yeild=0.09641 =9.64\%$

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%.