FIN3010 - WA 6
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Feb 20, 2024
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Christopher Cauble
TESU-FIN3010
Dr. Frank DeCaro
Written Assignment 06
1.
A $1,000 bond has a coupon of 6 percent and matures after ten years.
a. What would be the bond’s price if comparable debt yields 8 percent?
P
b
= Coupon*PVAIF X Principle*PVIF
Coupon
60
(Coupon*PVAIF)=
402.6
PVAIF
6.71
(Principle*PVIF)=
463
Principle
1000
Pb=
$865.60
PVIF
0.463
Price Value $865.60
b. What would be the price if comparable debt yields 8 percent and the bond matures after five years?
P
b
= Coupon*PVAIF X Principle*PVIF
Coupon
60
(Coupon*PVAIF)=
239.58
PVAIF
3.993
(Principle*PVIF)=
681
Principle
1000
Pb=
$920.58
PVIF
0.681
Price Value $920.58
c. Why are the prices different in a and b? Because of the 10 year yield, the payments are smaller and collected over a longer period of time. Additionally, this exposes the bond to interest rate risk for a longer period of time than the 5 year bond. It is worth noting that interest rates inversely affect bonds. d. What are the current yields and the yields to maturity in a and b?
5 year bond
Y2M PV
-920.58
FV
1000
PMT
60
N
5
I
8%
8% 10 year bond
Y2M PV
-$865.60
FV
1000
PMT
60
N
10
I
8%
8%
Christopher Cauble
TESU-FIN3010
Dr. Frank DeCaro
Current Yields:
Current Yield= Annual Interest Payment
Selling Price of Bond
Annual Interest Payment= 60
Selling Price of Bond=
865.6
Current Yield = 6.93%
Current Yield= Annual Interest Payment
Selling Price of Bond
Annual Interest Payment= 60
Selling Price of Bond=
920.58
Current Yield = 6.52%
2.
a $1,000 bond has a 7.5 percent coupon and matures after ten years. If current interest rates are 10 percent, what should be the price of the bond?
P
b
= Coupon*PVAIF X Principle*PVIF
Coupon
75
(Coupon*PVAIF)=
460.875
PVAIF
6.145
(Principle*PVIF)=
386
Principle
1000
Pb=
$846.88
PVIF
0.386
Price Value $846.88
b. If after six years interest rates are still 10 percent, what should be the price of the bond?
P
b
= Coupon*PVAIF X Principle*PVIF
Coupon
75
(Coupon*PVAIF)=
237.75
PVAIF
3.17
(Principle*PVIF)=
683
Principle
1000
Pb=
$920.75
PVIF
0.683
Price Value $920.75
c. Even though interest rates did not change in a and b, why did the price of the bond change?
The bond is being sold at a discount to begin with. But as the bond reaches closer to maturity the price of the bond will increase. Mathematically you can see that there is less periods (n) until maturity. Logically, a shorter investment period would net you less, so a steeper discount would make no sense. The less of an investment, the closer to the par value you should be.
Christopher Cauble
TESU-FIN3010
Dr. Frank DeCaro
d. Change the interest rate in a and b to 6 percent and rework your answers. Even though the interest rate is 6 percent in both calculations, why are the bond prices different?
P
b
= Coupon*PVAIF X Principle*PVIF
Coupon
75
(Coupon*PVAIF)=
552
PVAIF
7.36
(Principle*PVIF)=
564
Principle
1000
Pb=
$1,116.00
PVIF
0.564
Price Value $1,116.00
P
b
= Coupon*PVAIF X Principle*PVIF
Coupon
75
(Coupon*PVAIF)=
259.875
PVAIF
3.465
(Principle*PVIF)=
792
Principle
1000
Pb=
$1,051.88
PVIF
0.792
Price Value $1,051.88
Just as stated before, the price on the bond is going to be affected by the remaining time until maturity or periods (n). While in this case, because bonds are affected inversely by interest rates, the price has risen and is now being sold at a premium. 3.
Carrie’s Clothes, Inc. has a five-year bond outstanding that pays $60 annually. The face value of each bond is $1,000, and the bond sells for $890.
a.
What is the bond’s coupon rate? Annual Coupon= 60
Par value= 1000
Coupon Rate = Annual Coupon payment
Par value of bond
Coupon Rate = 6.00%
b.
What is the current yield? Current Yield= Annual Interest Payment
Selling Price of Bond
Annual Interest Payment= 60
Selling Price of Bond=
890
Current Yield = 6.74%
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Christopher Cauble
TESU-FIN3010
Dr. Frank DeCaro
c.
What is the yield to maturity?
Y2M PV
-$890.00
FV
1000
PMT
60
N
5
I
8.81%
Y2M = 8.81
4.
A bond has the following features: • Coupon rate of interest: 5 percent •Principal: $1,000 •Term to maturity: 10 years
a. What will the holder receive when the bond matures?
When the bond matures, the holder will receive the principle value of $1,000. Additionally, the bond holder would receive annual coupon payments of $50 up until maturity. b. If the current rate of interest on comparable debt is 8 percent, what should be the price of this
bond? Would you expect the firm to call this bond? Why?
P
b
= Coupon*PVAIF X Principle*PVIF
Coupon
50
(Coupon*PVAIF)=
335.50
PVAIF
6.71
(Principle*PVIF)=
463
Principle
1000
Pb=
$798.50
PVIF
0.463
Price Value $798.50
No the firm would not call the bond. Currently the firm is paying less interest on their debts than
current market conditions. If the firm were to call the bond and reissue, rates would be at 8% rather than the low 5% originally issued. c. If the bond has a sinking fund that requires the firm to set aside annually with a trustee sufficient funds to retire the entire issue at maturity, how much must the firm remit each year for ten years if the funds earn 8 percent annually and there is $100 million outstanding?
Christopher Cauble
TESU-FIN3010
Dr. Frank DeCaro
Annual payment=
100,000,000 x [(1+08)^10-1]
[0.08]
Annual Payment=
100,000,000 x
0.069029489
Annual Payment=
$6,902,948.86
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