If a bond\'s yield to maturity does not change, the return on the bond each year
ID: 2811452 • Letter: I
Question
If a bond's yield to maturity does not change, the return on the bond each year will be equal to the yield to maturity. Confirm this for both a premium and a discount bond using a 4-year 3.5 percent coupon bond with annual coupon payments and a face value of $1,000 a. Assume the yield to maturity is 2.5 percent What is the current value of the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Bond price today What will the bond value be in one year? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Bond price in one year What is the rate of return for the first year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.) Rate of return b. Assume the yield to maturity is 4.5 percent. What is the current value of the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Bond price today What will the bond value be in one year? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Bond price in one year What is the rate of return for the first year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.) Rate of returnExplanation / Answer
a.
Bond price today:
Using financial calculator BA II Plus - Input details:
#
I/Y = R = Rate or yield / frequency of coupon in a year =
2.500000
PMT = Coupon rate x FV / frequency =
-$35.00
N = Number of years remaining x frequency =
4
FV = Future Value =
-$1,000.00
CPT > PV = Present value of bond =
$1,037.62
Formula for bond value = |PMT| x ((1-((1+R%)^-N)) / R%) + (|FV|/(1+R%)^N)
$1,037.62
Bond price in one year:
Using financial calculator BA II Plus - Input details:
#
I/Y = R = Rate or yield / frequency of coupon in a year =
2.500000
PMT = Coupon rate x FV / frequency =
-$35.00
N = Number of years remaining x frequency =
3
FV = Future Value =
-$1,000.00
CPT > PV = Value of bond after 1 year =
$1,028.56
Formula for bond value = |PMT| x ((1-((1+R%)^-N)) / R%) + (|FV|/(1+R%)^N)
$1,028.56
Rate of return:
Rate of return = (Bond value in one year - Bond price today + Coupon)/ Bond price today
Rate of return = (1028.56 - 1037.62 + 35)/ 1037.62
Rate of return = 2.5%
b.
Bond price today
Using financial calculator BA II Plus - Input details:
#
I/Y = R = Rate or yield / frequency of coupon in a year =
4.500000
PMT = Coupon rate x FV / frequency =
-$35.00
N = Number of years remaining x frequency =
4
FV = Future Value =
-$1,000.00
CPT > PV = Present value of bond =
$964.12
Formula for bond value = |PMT| x ((1-((1+R%)^-N)) / R%) + (|FV|/(1+R%)^N)
$964.12
Bond value in one year
Using financial calculator BA II Plus - Input details:
#
I/Y = R = Rate or yield / frequency of coupon in a year =
4.500000
PMT = Coupon rate x FV / frequency =
-$35.00
N = Number of years remaining x frequency =
3
FV = Future Value =
-$1,000.00
CPT > PV = Value of bond after 1 year =
$972.51
Formula for bond value = |PMT| x ((1-((1+R%)^-N)) / R%) + (|FV|/(1+R%)^N)
$972.51
Rate of return:
Rate of return = ($972.51 - $964.12 + $35)/ $964.12
Rate of return = 4.5%
Using financial calculator BA II Plus - Input details:
#
I/Y = R = Rate or yield / frequency of coupon in a year =
2.500000
PMT = Coupon rate x FV / frequency =
-$35.00
N = Number of years remaining x frequency =
4
FV = Future Value =
-$1,000.00
CPT > PV = Present value of bond =
$1,037.62
Formula for bond value = |PMT| x ((1-((1+R%)^-N)) / R%) + (|FV|/(1+R%)^N)
$1,037.62
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