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Homework answers / question archive / Consider a $1,000 par value bond with a 12% semiannual coupon and an 8

Consider a $1,000 par value bond with a 12% semiannual coupon and an 8

Finance

Consider a $1,000 par value bond with a 12% semiannual coupon and an 8.5% required rate of return (YTM).a. What is the value of this bond if it matures 8 years from today?b. What is the value of this bond if it matures 4 years from today?c. What is the value of this bond if it matures 1 year from today?d. Holding the required rate of return constant, what happens to the value of a bond selling at a premium as it approaches maturity?

 

An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 10% annual coupon. Bond S matures in 1 year, while Bond L matures in 30 years.a. Compute the value of Bond S at required rates of return of 5%, 10%, and 15%.b. Compute the value of Bond L at required rates of return of 5%, 10%, and 15%.c. Define interest rate risk for a bond. Which bond, S or L, has more interest rate risk?

 

Acumenix Corp has 10.25% semiannual-pay bonds outstanding that have a $1,000 par value and 25 years remaining until maturity that are currently selling for $865.50.a. What is the yield to maturity (YTM) for these bonds?b. What is the current yield for these bonds?c. Does the current yield represent the rate of return an investor should expect to earn on a bond if she holds the bond until maturity? Why or why not?

 

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1)

a) Computation of Value of Bond if Bond matures 8 Years from Today using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,

PV = Value of Bond = ?

Rate = 8.5%/2 = 4.25%

Nper = 8 years*2 = 16 Periods 

PMT = $1,000*12%/2 = $60

FV = $1,000

Substituting the values in formula:

=-pv(4.25%,16,60,1000)

PV or Value of Bond = $1,200.21

 

b) Computation of Value of Bond if Bond matures 4 Years from Today using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,

PV = Value of Bond = ?

Rate = 8.5%/2 = 4.25%

Nper = 4 years*2 = 8 Periods 

PMT = $1,000*12%/2 = $60

FV = $1,000

Substituting the values in formula:

=-pv(4.25%,8,60,1000)

PV or Value of Bond = $1,116.62

 

c) Computation of Value of Bond if Bond matures 1 Years from Today using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,

PV = Value of Bond = ?

Rate = 8.5%/2 = 4.25%

Nper = 1 year*2 = 2 Periods 

PMT = $1,000*12%/2 = $60

FV = $1,000

Substituting the values in formula:

=-pv(4.25%,2,60,1000)

PV or Value of Bond = $1,032.89

 

d) The value of bond decrease as it approaches maturity if the required rate of return is constant.

 

 

 

2)

a) Computation of Value of Bond S using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

 

Required Rate of Return is 5%:

Here,

PV = Value of Bond = ?

Rate = 5%

Nper = 1 Year 

PMT = $1,000*10% = $100

FV = $1,000

Substituting the values in formula:

=-pv(5%,1,100,1000)

PV or Value of Bond = $1,047.62

 

Required Rate of Return is 10%:

Here,

PV = Value of Bond = ?

Rate = 10%

Nper = 1 Year 

PMT = $1,000*10% = $100

FV = $1,000

Substituting the values in formula:

=-pv(10%,1,100,1000)

PV or Value of Bond = $1,000

 

Required Rate of Return is 15%:

Here,

PV = Value of Bond = ?

Rate = 15%

Nper = 1 Year 

PMT = $1,000*10% = $100

FV = $1,000

Substituting the values in formula:

=-pv(15%,1,100,1000)

PV or Value of Bond = $956.52

 

b) Computation of Value of Bond L using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

 

Required Rate of Return is 5%:

Here,

PV = Value of Bond = ?

Rate = 5%

Nper = 30 Year 

PMT = $1,000*10% = $100

FV = $1,000

Substituting the values in formula:

=-pv(5%,30,100,1000)

PV or Value of Bond = $1,768.62

 

Required Rate of Return is 10%:

Here,

PV = Value of Bond = ?

Rate = 10%

Nper = 30 Year 

PMT = $1,000*10% = $100

FV = $1,000

Substituting the values in formula:

=-pv(10%,30,100,1000)

PV or Value of Bond = $1,000

 

Required Rate of Return is 15%:

Here,

PV = Value of Bond = ?

Rate = 15%

Nper = 1 Year 

PMT = $1,000*10% = $100

FV = $1,000

Substituting the values in formula:

=-pv(15%,1,100,1000)

PV or Value of Bond = $671.70

 

c) Long-term bonds are subject to greater interest rate risk than short-term bonds. Here is why,

From the above it is clear that the value of a bond is a present value of coupons and maturity value. That means coupons coupons and maturity value discounted at interest rate. So, Longer life of a bond will result in more time to discounted at interest rate. So, they become more sensitive than bond with shorter life. So, Bond L has more interest risk as it is more sensitive.

 

 

3) 

a) Computation of Yield to Maturity (YTM) using Rate Function in Excel:

=rate(nper,pmt-pv,fv)*2

Here,

Rate = Yield to Maturity = ?

Nper = 25 years * 2 = 50 periods

PMT = $1,000*10.25%/2 = $51.25

PV = $865.50

FV = $1,000

Substituting the values in formula:

=rate(50,51.25,-865.50,1000)*2

Rate or Yield to Maturity = 11.95%

 

b) Computation of Current Yield:

Current Yield = Annual Coupon Payment/Current Bond Price

= ($1,000*10.25%)/$865.50

= $102.50/$865.50

Current Yield = 11.84% 

 

c) No current yield is not the rate if bond is held till maturity. It is merely the coupon to price over 1 year period. Infact YTM is the rate at which bond is held till maturity.

 

 

 

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