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Homework answers / question archive / Question 33 A nine-year, 6
Question 33 A nine-year, 6.5-percent coupon bond is selling for 106.2 percent of par. What is the bond's market yield if it makes semi-annual coupon payments?
Question 35
For each of the following VIM figures, calculate the price and current yield for a 10-year, 5-percent, semi-annual-pay bond with a face value of 51,000. a VIM = 4 percent b VIM = 5 percent c VIM = 6 percent
Question 39 a What is the value of a 10-year, zero coupon bond with a face value of 51,000 when the market rate is 8 percent? b Calculate the VIM of the above zero coupon bond if the current price is 5760.
Question 42 A bond has a yield to maturity of 8 percent and a current yield of 6 percent. Is the bond trading at par, at a premium, or at a discount? What can you say about the coupon rate?
Question 44
The present value of a dollar to be received one year from today is 50.927644. The present value of a dollar to be received two years from today is 50.854172. What is the price of a bond that pays an annual coupon of 7 percent and matures in two years? Find its yield to maturity.
33) Computation of Bond's Market Yield (YTM):
We can find the YTM by solving for I/Y.
N = 9*2 = 18
PMT = 1000*6.5%/2 = 32.50
PV = 1000*106.2% = 1062
FV = 1000
Now, press CPT I/Y and you should find that the YTM is 2.81%. Since the YTM is always stated as an annual rate, we need to double this answer. In this case, then, the YTM is 5.61% per year.
35) Computation of Price and Current Yield of Bond:
a) We can find the Price of Bond by solving for PV.
I/Y = 4%/2 = 2%
N = 10*2 = 20
PMT = 1000*5%/2 = 25
FV = 1000
Now, press CPT PV and you should find that the PV is $1,081.76
Current Yield of Bond = Annual Coupon Payment/Current Price of Bond
= $1000*5%/$1,081.76
= $50/$1,081.76
Current Yield of Bond = 4.62%
b) We can find the Price of Bond by solving for PV.
I/Y = 5%/2 = 2.5%
N = 10*2 = 20
PMT = 1000*5%/2 = 25
FV = 1000
Now, press CPT PV and you should find that the PV is $1,000
Current Yield of Bond = Annual Coupon Payment/Current Price of Bond
= $1000*5%/$1,000
= $50/$1,000
Current Yield of Bond = 5%
c) We can find the Price of Bond by solving for PV.
I/Y = 6%/2 = 3%
N = 10*2 = 20
PMT = 1000*5%/2 = 25
FV = 1000
Now, press CPT PV and you should find that the PV is $925.61
Current Yield of Bond = Annual Coupon Payment/Current Price of Bond
= $1000*5%/$925.61
= $50/$1,081.76
Current Yield of Bond = 5.40%
39) a) We can find the Price of Bond by solving for PV.
I/Y = 8%
N = 10
PMT = 0
FV = 1000
Now, press CPT PV and you should find that the PV is $463.19
b)We can find the YTM by solving for I/Y.
N = 10
PMT = 0
PV = 760
FV = 1000
Now, press CPT I/Y and you should find that the YTM is 2.78%.
42) a) The bonds are issued at premium as Coupon rate is greater than Market Current Yield. Coupon Rate is rate on which company pay discount to shareholders, bondholders. Coupon Rate is fixed over the life of bond. It helps to understand the cost.
44) Computation of Price of Bond:
|
Years |
Coupons (1000*7%) (A) |
Par Value (B) |
Total Cash Flow (C = A+B) |
Present Value Factors (D) |
Present Values (E = C * D) |
|
1 |
70 |
0 |
70 |
0.927644 |
64.94 |
|
2 |
70 |
1000 |
1070 |
0.854172 |
913.96 |
Total Present Value of Bonds = $64.94+$913.96 = 978.90
So, Price of Bond is $978.90
Computation of YTM of Bond:
We can find the YTM by solving for I/Y.
N = 2
PMT = 70
PV = 978.90
FV = 1000
Now, press CPT I/Y and you should find that the YTM is 8.19%.
