Question

a) You are considering investing in bonds and have collected the following information about the prices of a 1-year zero-coupon bond and a 2-year coupon bond.

- The 1-year discount bond pays $1,000 in one year and sells for a current price of $950.

- The 2-year coupon bond has a face value of $1,000 and an annual coupon of $60. The bond currently sells for a price of $1,050.

i) What are the implied yields to maturity on one- and two-year discount bonds?

ii) What is the implied forward rate between years 1 and 2?

iii) Consider a 2-year annuity with annual coupon payments of $800. What is the most that you would be willing to pay for this annuity?

b) A 5%, $1,000 bond makes coupon payments on June 15 and December 15 and is trading with a YTM of 4% (APR). The bond is purchased and will settle on August 21 when there will be four coupons remaining until maturity. Calculate the full price of the bond using actual days.

Answer #1

a)

i) Let the rate today for one year and 2 year be y1 and y2

y1 is the implied YTM of the one year discount bond and y2 is the YTM of the 2 year discount bond

950= 1000/(1+y1)

=> y1 = 0.052632 or **5.26% which is the implied YTM of
the one year bond**

From 2 year coupon bond

60/(1+y1) +1060/(1+y2)^2 = 1050

.=> 57+1060/(1+y2)^2 = 1050

=> (1+y2)^2 =1.067472

=> y2 =0.033186 or **3.32%**

**So, implied ytm of the 2 year discount bond is
3.32%**

ii) implied forward rate between year 1 and year 2=
(1+y2)^2/(1+y1) -1 = 0.014099 or **1.41%**

iii) Price of annuity = 800/(1+y1) +800/(1+y2)^2 =
800/1.052632+800/1.067472 = **$1509.43**

**For the 2 year annuity , I will pay an amount of
$1509.43 at the most.**

iv)

Coupon amount = $1000*5%/2 = $25

Semiannual YTM = 4%/2 =2%

So, clean price of the bond with 4 payments remaining

= 25/1.02+25/1.02^2+25/1.02^3+25/1.02^4+1000/1.02^4

=$1019.04

So full price of the bond = dirty price = Clean price + accrued interest

Accrued Interest (from June15 to August 21 i.e. 67 days) = 67/365*$1000*5% = $9.18

So, Full price = $1019.04+$9.18 = **$1028.22**

7)
The prices of several bonds with face values of $1,000 are
summarized in the following table:
Bond
A
B
C
D
Price
$905.72
$057.48
$1,179.66
$1,000.00
For each bond, provide an answer for whether it trades at a
discount, at par, or at a premium. Bond A trades at
(a).----------------?
Is it Discount, Par Or Premium?
(Select from the drop-down menu.)
5)
Suppose a 10-year, $1,000 bond with a 12% coupon rate and
semiannual coupons are trading for a...

1. The following is a list of
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yields to maturity of each bond and the implied sequence of forward
rates.
maturity years: Price of bond
1 943.40
2 898.47
3 847.62
4 792.16
2. [Chapter 15] The current yield curve
for default-free zero-coupon bonds is as follows:
Maturity (Years): YTM%
1 10%
2 11%
3 12%
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b. Assume that the pure
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A 5%, $1,000 bond makes coupon payments on June 15 and December
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The following is a list of prices for zero-coupon bonds of
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and the implied sequence of forward rates. (Do not round
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Omit the "%" sign in your response.
Maturity (Years)
Price of Bond
YTM
Forward Rate
1
$980.90
___%
2
$914.97
___%
____%
3
$843.12
___%
____%
4
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___%
____%

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Given the purchase prices, coupons and maturities of four bonds,
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zero but calculate its yield with a semi-annual equivalency.
Provide your answers to 4 significant digits (example: 6.1234%)
Bond A Price 984.00, annual coupon 3%, maturing in 2 years Bond B
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Lynn Parsons is considering investing in either of two
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a. Calculate the present value of bond A if
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b. Calculate the present value of bond B if
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1.
What is the price of a bond with the following features?
Face Value = $1,000
Coupon Rate = 7% (stated as an ANNUAL rate)
Semiannual coupon payments
Maturity = 7 years
YTM = 6.34% (Stated as an APR)
State your answer to the nearest penny (e.g., 984.25)
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Coupon Rate = 5%
Face Value = $1,000
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When you buy the bond the market interest rate...

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Bond 2: Coupon rate 10% per year, price $133.34
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