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Lycan, Inc., has 7.9 percent coupon bonds on the market that have 6 years left to maturity.
The bonds make annual payments and have a par value of $1,000.
If the YTM on these bonds is 9.9 percent, what is the current bond price?
(Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
 
Current bond price            $ 912.64
 
https://www.buyupside.com/calculators/bondpresentvalue.htm
 
The calculator, uses the following formulas to compute the present value of a bond:
Present Value Paid at Maturity = Face Value / (Market Rate/ 100) ^ Number Payments
Present Value of Interest Payments = Payment Value * (1 - (Market Rate / 100) ^ -Number Payments) / Number Payments)
Present Value of Bond = Present Value Paid at Maturity + Present Value of Interest Payments
  Say you own an asset that had a total return last year of 16 percent.
Assume the inflation rate last year was 5 percent.
 
What was your real return?
(Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
 
 
Real return             %
 
real return = (1+nominal return) / (1+inflation) -1
1.16 / 1.05 – 1 = 10.476 or 10.48%
 
https://www.miniwebtool.com/real-rate-of-return-calculator/?n1=16&n2=5
   
Both Bond Bill and Bond Ted have 9.4 percent coupons, make semiannual payments, and are priced at par value.
Bond Bill has 5 years to maturity, whereas Bond Ted has 22 years to maturity. Both bonds have a par value of 1,000.
 
If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds?
(A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your
answers as a percent rounded to 2 decimal places, e.g., 32.16.)
   

 
1. If the YTM is to rise by 2%, i.e to 11.4% : Semiannual rate = 11.4 % / 2 = 5.7 %
Price of Bond Bill = Semiannual coupon x PVIFA _{5.7%, 10 terms} + Par Value x PVIF _{5.7%, 10th term}
= $ 47 x 7.4658 + $ 1,000 x 0.5744 = $ 925.30
Percentage change in price = $ ( 925.30 - 1,000) / $ 1,000 x 100 = - 7.47%
Price of Bond Ted = Semiannual coupon x PVIFA _{5.7%, 44 terms} + Par Value x PVIF _{5.7%, 44th term} =
$ 47 x 16.0134 + $ 1,000 x 0.0872 = $ 839.83
Perecentage change in price = $ ( 839.83 - 1,000) / $ 1,000 x 100 = - 16.02 %
 
If rates were to suddenly fall by 2 percent instead, what would be the percentage change in the price of these bonds?
(Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
 
 
2. If the rates were to fall by 2%, new YTM = 7.4%, semiannual interest rate = 7.4 % / 2 = 3.7%
New price of Bond Bill = Semiannual Coupon x PVIFA _{3.7%, 10 terms} + Par Value x PVIF _{3.7%, 44 terms} =
$ 47 x 8.2334 + $ 1,000 x 0.6954 = $ 1,082.37
Percentage change in price of Bond Bill = $ ( 1,082.37 - 1,000) / $ 1,000 x 100 = 8.24 %
New price of Bond Ted = $ 47 x 21.5627+ $ 1,000 x 0.2022 = $ 1,215.65
Percentage change in price of Bond Ted = $ ( 1,215.65 - 1,000) / 1,000 x 100 = 21.56 %
  PK Software has 9.2 percent coupon bonds on the market with 23 years to maturity.
The bonds make semiannual payments and currently sell for 112.25 percent of par.
 
What is the current yield on PK's bonds?
(Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

What is the YTM?
(Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

What is the effective annual yield?
(Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
 

 
$92 / 1122 = .0819 = 8.20%
 
(1 + YTM / 2)² - 1
https://goodcalculators.com/bond-yield-to-maturity-calculator/
   
You find the following corporate bond quotes.
To calculate the number of years until maturity, assume that it is currently January 15, 2016. The bonds have a par value of $2,000.
 

Company (Ticker)	Coupon	Maturity	Last Price	Last Yield	EST $ Vol (000’s)
Xenon, Inc. (XIC)	7.300	Jan 15, 2039	94.373	??	57,381
Kenny Corp. (KCC)	7.310	Jan 15, 2036	??	6.40	48,960
Williams Co. (WICO)	??	Jan 15, 2042	96.925	6.65	43,821

What is the coupon rate for the Williams Co. bond?
(Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
 

 
Here, we need to find the coupon rate of the bond. The dollar price of the bond is:
Dollar price = 96.925 * $1,000
Dollar price = $969.25
 
Now, what we need to do is to set up the bond pricing equation and solve for the coupon payment as follows:
P = $969.25 = C(PVIFA3.325%,52) + $1,000(PVIF3.325%,52)
969.25 = C*25.25898 + 1000* 0.160139  
Solving for the coupon payment, we get : C= $32
Since this is the semiannual payment, the annual coupon payment is:
2 * $32.0 = $64.
 
And the coupon rate is the coupon rate divided by par value, so:
Coupon rate = $64 / $1,000
Coupon rate = 0.064 or 6.4%
   
You find the following corporate bond quotes. To calculate the number of years until maturity, assume that it is currently January 15, 2022. The bonds have a par value of $2,000 and semiannual coupons.
 
6.53%
   
What is the interest rate on an 8-year, BB-rated, Subordinated bond issued by a large company?
a) 9.1%
b) 9.9%
c) 10.1%
d) 10.55%
 

10.55 = 2 + (4 + 4 + 3 + 3 + 3 + 3 + 3 +3 ) / 8 + .1 x 8 + 2.5 + 1 + 1
   
Which of the following is likely to result in a lower nominal risk-free rate?

a) More good investment opportunities
b) Higher time preference for consumption
c) An increase in the supply of money
d) An increase in the demand for money
   
A(n) ___________ yield curve is often taken as a sign of a possible future recession.

a) Backward
b) Normal
c) Upward
d) Inverted
   
Investors do not have to pay federal income taxes on interest earned on ______________ securities.
a) Corporate
b) Foreign
c) Municipal
d) Treasury
c) Municipal
   
Which type of security is likely to have the lowest required return?

a) Treasury Bills
b) Common Stock
c) High-Yield (Junk) Bonds
d) Preferred Stock
   
If a bond is selling at a discount, then it's current yield will be _______ than it's yield to maturity and _________than it's coupon rate.

a) Higher; Higher
b) Higher; Lower
c) Lower; Higher
d) Lower; Lower
c) Lower; Higher
   
What is the coupon payment of a 25-year $1000 bond with a 4.5% coupon rate with quarterly payments?
A) $3.75
B) $11.25
C) $22.50
D) $45.00

1000 × 0.045 / 4 = $11.25
   
What is the coupon payment of a 15-year $10,000 bond with a 9% coupon rate with semiannual payments?
A) $150.00
B) $450
C) $900.00
D) $1800.00
 
$10,000 × 0.09/2 = $450
   
A corporate bond makes payments of $9.67 every month for ten years with a final payment of $2009.67.
Which of the following best describes this bond?


A) a 10-year bond with a face value of $2,000 and a coupon rate of 4.8% with monthly payments
B) a 10-year bond with a face value of $2,000 and a coupon rate of 5.8% with monthly payments
C) a 10-year bond with a face value of $2,009.67 and a coupon rate of 4.8% with monthly payments
D) a 10-year bond with a face value of $2,009.67 and a coupon rate of 5.8% with monthly payments
 
9.67 × 12 / (2,009.67 - 9.67) = 5.802
   
An investor holds a Ford bond with a face value of $5000, a coupon rate of 8.5%, and semiannual payments that matures on January 15, 2029.
How much will the investor receive on January 15, 2029?

A) $2606.25
B) $5000.00
C) $5212.50
D) $5425.00
 
$5000 + $5000 × 0.085 / 2 = $5212.5
   
What is the coupon payment of a 25-year $1000 bond with a 4.5% coupon rate with quarterly payments?

$11.25

(1000 x 0.045 / 4 = 11.25)
   
What is the coupon payment of a 15-year $10,000 bond with a 9% coupon rate with semiannual payments?
 
$450

(10,000 × 0.09 / 2 = 450)
   
An investor holds a Ford bond with a face value of $5000, a coupon rate of 8.5%, and semiannual payments that matures on January 15, 2029.
How much will the investor receive on January 15, 2029?
 
$5212.50

(5000 + 5000 x 0.085 / 2 = 5212.5)
   
A university issues a bond with a face value of $5000 and a coupon rate of 4.41% that matures on July 15, 2018. The holder of such a bond receives coupon payments of $110.25 . How frequently are coupon payments made in this case?
 
Semiannually
   
The Sisyphean Company has a bond outstanding with a face value of $5000 that matures in 10 years. The bond certificate indicates that the stated coupon rate for this bond is 8.9% and that the coupon payments are to be made semiannually. How much will each semiannual coupon payment be?
 
$222.5

0.089 × 5000 / 2 = 222.5
   
The following table summarizes prices of various default-free zero-coupon bonds (expressed as a percentage of face value):

   Maturity (years)            price

1                             94.52
2                              89.68
3                              85.40
4                              81.65
5                             78.35

a. The yield to maturity for the three -year zero-coupon bond is closest to ________.
b. Based upon the information provided in the table above, you can conclude ________.
 
5.40%

 (100 / 85.40)^(1/3) - 1  = 0.054 or 5.40%
 
that the yield curve is downward sloping
   
The Sisyphean Company has a bond outstanding with a face value of $1000 that reaches maturity in 15 years.
The bond certificate indicates that the stated coupon rate for this bond is 8% and that the coupon payments
are to be made semiannually.
How much are each of the semiannual coupon payments?
Assuming the appropriate YTM on the Sisyphean bond is 8.8%, then at what price should this bond trade for?
 
$934.07
 
(.08 × 1,000) / 2 = 40
FV = 1,000
.044 (8.8 / 2)
40 (80 / 2)
30 (15 × 2)
$934.07
   
A risk-free, zero-coupon bond has 15 years to maturity. Which of the following is closest to the
price per $1000 of face value that the bond will trade at if the YTM is 6.1%?
 
$553.15

(1000 ) / (1 + 6.1%)10 = 553.15
  A U.S. Treasury bond pays 3.05 percent interest. You are in the 28 percent marginal tax bracket.
What is your after tax yield on this bond?
 
.0220 or 2.20 percent
 
After tax yield = .0305 ×(1 -.28) = 0.0220, or 2.20 percent
   
Arts and Crafts Warehouse wants to issue 15-year, zero-coupon bonds that yield 7.5 percent.
What price should it charge for these bonds if the face value is $1,000?
Assume semiannual compounding.
 
$331.40
 
PV = $1,000 / [1 + (.075 / 2)]30
PV = $331.40
   
Deltona Motors just issued 230,000 zero-coupon bonds. These bonds mature in 18 years, have a par value of $1,000,
and have a yield to maturity of 5.9 percent.
What is the approximate total amount of money the company raised from issuing these bonds?
Assume semiannual compounding.
 
$80,756,819
 
Total amount raised = 230,000 × {$1,000 / [1 + (.059 / 2)]36}
Total amount raised = $80,756,819  
A bond has a $1,000 face value, a market price of $1,045, and pays interest payments of $74.50 every year.
What is the coupon rate?
 
0.0745, or 7.45 percent
 
Coupon rate = $74.50 / $1,000 = 0.0745
   
A $1,000 face value bond is currently quoted at 100.8.
The bond pays semiannual payments of $22.50 each and matures in six years.
What is the coupon rate?
 
0.0450, or 4.50 percent
 
Coupon rate = ($22.50 ×2)/$1,000 = .0450
   
The 6.5 percent bond of ABCO has a yield to maturity of 6.82 percent.
The bond matures in seven years, has a face value of $1,000, and pays semiannual interest payments.
What is the amount of each coupon payment?
 
$32.50
 
Coupon payment = ($1,000 ×.065)/2 = $32.50
   
A bond has a par value of $1,000, a current yield of 6.25 percent, and semiannual interest payments.
The bond quote is 100.8. What is the amount of each coupon payment?
 
$31.50
 
Coupon payment = [.0625 × (1.008 × $1,000)] / 2 = $31.50
   
The 4.5 percent bond of JL Motors has a face value of $1,000, a maturity of 7 years,
semiannual interest payments, and a yield to maturity of 6.23 percent.
What is the current market price of the bond?
 
$903.05
 
PV = [(.045 × $1,000)/ 2] × {(1 - {1 / [1 + (.0623 / 2)]14}) / (.0623 / 2)} + $1,000 / [1 + ( .0623 / 2)]14
PV = $903.05
   
A $1,000 face value bond currently has a yield to maturity of 8.22 percent.
The bond matures in five years and pays interest semiannually. The coupon rate is7.5 percent.
What is the current price of this bond?
 
$970.96
 
PV = [(.075 × $1,000)/ 2] ×{(1 - {1 / [1 + (.0822/ 2)]10}) / (.0822 / 2)} + $1,000 / [1 + ( .0822/ 2)]10
PV= $970.96
   
A six-year, semiannual coupon bond is selling for $991.38.
The bond has a face value of $1,000 and a yield to maturity of 9.19 percent.
What is the coupon rate?
 
0.0900, or 9.00 percent
 
PV = $991.38 = PMT ×{(1 - {1 / [1 + (.0919/ 2)]12}) / (.0919 / 2)} + $1,000 / [1 + ( .0919/ 2)]12
PMT = $45.00
Coupon rate = (2 ×$45.00) / $1,000 = 0.0900
   
A 12-year, annual coupon bond is priced at $1,102.60.
The bond has a $1,000 face value and a yield to maturity of 5.33 percent.
What is the coupon rate?
 
0.0651, or 6.51 percent
 
PV = $1,102.60 = PMT ×{1 - [1 / (1 + .0533)12]} / .0533 + $1,000 / (1 + .0533)12
PMT = $65.09
Coupon rate = $65.09 / $1,000 = 0.0651
   
AB Builders has 15-year bonds outstanding with a face value of $1,000 and a market price of $974.
The bonds pay interest annually and have a yield to maturity of 4.03 percent.
What is the coupon rate?
 
0.0380, or 3.80 percent
 
PV = $974 = PMT ×{1 - [1 / (1 + .0403)15]} / .0403 + $1,000 / (1 + .0403)15
PMT = $37.96
Coupon rate = $37.96 / $1,000 = 0.0380
   
New Markets has $1,000 face value bonds outstanding that pay interest semiannually, mature
in 14.5 years, and have a 4.5 percent coupon.
The current price is quoted at 97.6. What is the yield to maturity?
 
0.0473, or 4.73 percent
 
PV = $976 = [(.045 × $1,000) / 2] × {(1 - {1 / [1 + (r / 2)]29}) / (r / 2)} + $1,000 / [1 + (r/ 2)]29
r = .0473, or 4.73 percent
   
The $1,000 face value bonds of Galaxies International have coupon of 6.45 percent and pay interest semiannually.
Currently, the bonds are quoted at 103.4 and mature in 4 years.
What is the yield to maturity?
 
0.0549, or 5.49 percent
 
PV = $1,034 = [(.0645 × $1,000) / 2] ×{(1 - {1 / [1 + (r / 2)]8}) / (r / 2)} + $1,000 / [1 + (r/ 2)]8
r = .0549, or 5.49 percent
   
The 8 percent, $1,000 face value bonds of Sweet Sue Foods are currently selling at $1,057.
These bonds have 16 years left until maturity. What is the current yield?
 
0.0757 or 7.57 percent
 
Current yield = (.08 ×$1,000)/$1,057
Current yield = .0757
   
A bond has a yield to maturity of 9.38 percent, a coupon of 7.5 percent paid semiannually, a $1,000 face value,
and a maturity date 21 years from today. What is the current yield?
 
0.0905, or 9.05 percent
 
PV = [(.075 × $1,000) / 2] × {(1 - {1 / [1 + (.0938 / 2)]42}) / (.0938/ 2)} + $1,000 / [1 + (.0938/ 2)]42
PV = $828.81
Current yield = (.075 × $1,000) / $828.81
Current yield = .0905, or 9.05 percent