Question

**Basic Discounting**

1. A. What is the price of a 10-year, $1,000 face value zero-coupon bond using a 4% rate of discount?

B. What price results if the rate of discount is 5%?

. c.What is the YTM if this bond could be purchased for $600?

Answer #1

Answer 1

(A)

Price of this zero coupon bond will be the present Value of this Bond.

Present value of zero coupon bond or Price of the coupon Bond is given by :

PV = FV/(1 + r)^{n}

where PV = Price of the Bond or present value of the bond, FV = Face Value = 1,000 , n = time period= 10 and r = discount rate = 4% = 0.04.

Hence Using above formula we get :

Price of this Bond = PV = FV/(1 + r)^{n} = 1,000/(1 +
0.04)^{10} = $675.56

Hence, the price of a 10-year, $1,000 face value zero-coupon bond using a 4% rate of discount is $675.56

(B)

Price of this zero coupon bond will be the present Value of this Bond.

Present value of zero coupon bond or Price of the coupon Bond is given by :

PV = FV/(1 + r)^{n}

where PV = Price of the Bond or present value of the bond, FV = Face Value = 1,000 , n = time period= 10 and r = discount rate = 5% = 0.05.

Hence Using above formula we get :

Price of this Bond = PV = FV/(1 + r)^{n} = 1,000/(1 +
0.05)^{10} = $613.91

Hence, the price of a 10-year, $1,000 face value zero-coupon bond using a 5% rate of discount is $613.91

(C)

As Discussed above Present value of zero coupon Bond is given by :

PV = FV/(1 + r)^{n}

where PV = Price of the Bond or present value of the bond, FV = Face Value, n = time period and r = discount rate ot YTM i.e. Yield to Maturity.

=> (1 + r)^{n} = (FV/PV)

=> r = (FV/PV)^{1/n} - 1

Here FV = Future value or face value of this bond = 1,000 , PV = Present Value or Price of the bond = 600 , n = time = 10 and r = YTM = Discount rate that we have to calculate

Hence, r = (FV/PV)^{1/n} - 1 => r =
(1,000/600)^{1/10} - 1

=> R = 0.0524 = 5.24%.

Hence, the YTM if this bond could be purchased for $600 is 5.24%.

A 5-year zero coupon bond pays 10% annual coupons, and has a
face value of $1,000. Zero coupon bonds with 1-5 years to maturity,
each with a face value of $100, have the following prices:
Price of 1-year zero = $99.14
Price of 2-year zero = $97.88
Price of 3-year zero = $96.32
Price of 4-year zero = $89.44
Price of 5-year zero = $87.76
What is the price of the 5-year coupon bond?

PRICING ZERO COUPON BONDS -
(a) Calculate the price of a zero coupon, $1,000 face value,
5-year bond if the appropriate annual discount rate is 12 percent.
Calculate your total return if you hold this bond for three years
and the discount rate does not change. (INCLUDE FORMULAS USED TO
SOLVE PROBLEM IN EXCEL).
EXPECTED RETURN ON T-BILLS -
(b) What is the actual expected return on a US government
12-month, T-bill that is priced at $990, assuming its face...

You bought a 10-year zero-coupon bond with a face value of
$1,000 and a yield to maturity of 2.7% (EAR). You keep the bond for
5 years before selling it. The price of the bond today is P 0 = F (
1 + r ) T = 1,000 1.027 10 = 766.12
If the yield to maturity is still 2.7% when you sell the bond at
the end of year-5, what is your personal ANNUAL rate of return?

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)
2.
Assume you buy a bond with the following features
Bond maturity = 4
Coupon Rate = 5%
Face Value = $1,000
Annual Coupons
When you buy the bond the market interest rate...

Suppose the price of a 1-year 5%-coupon bond is $1,000 and the
price of a 2-year 5%-coupon bond is $1027.81. Using bootstrapping,
what is the two-year zero-coupon spot rate? Each bond has a face
value of $1,000 and makes annual coupon payments.

You bought a 10-year
zero-coupon bond with a face value of $1,000 and a yield to
maturity of 3.4% (EAR). You keep the bond for 5 years before
selling it.
The price of the bond
today is P0=F(1+r)T=1,0001.03410=P0=F(1+r)T=1,0001.03410= 715.8
If the yield to
maturity is still 3.4% when you sell the bond at the end of year-5,
what is your personal annual rate of return?

What is the price of a bond with the following features? Face
Value = $1,000 Coupon Rate = 4% (stated as an ANNUAL rate)
Semiannual coupon payments Maturity = 5 years YTM = 4.48% (Stated
as an APR) State your answer to the nearest penny (e.g.,
984.25)

1. A 12-year semiannual bond with a coupon rate of 6% has a face
value of $1,000 and a YTM of 7%. The price of the bond is
A. 912.85. B. 914.25. C. 916.36. D. 919.71 E. 920.57
2. A 4-year discount bond with a face value of $1,000 sells at
$915. The YTM of the bond is
A. 2.24%. B. 2.52% C. 2.83% D. 3.21% E. 3.48%
3. A 7-year semiannual bond with a face value of $1,000 and...

1. Maturity (years) = 5 Face Value = $1,000 Coupon Rate = 3.00%
Price = $900 Coupon (Annual)
What is the YTM (annual) of the above bond?
A 5.38%
B 5.30%
C 5.33%
D 4.80%
E 5.36%
2. Consider a bond with the following features: Maturity = 7
years Face value = $1,000 Coupon rate = 4% Semiannual coupons Price
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What is this bond's YTM stated as an annual rate?
A 3.2500%
B 4.1161%
C 2.0581%
D 6.500%

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Face Value = $1,000
Coupon Rate = 2% (stated as an ANNUAL rate)
Semiannual coupon payments
Maturity = 5 years
YTM = 4.8% (Stated as an APR)
State your answer to
the nearest penny (e.g., 984.25)

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