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Solutions To Practice Problem Set #5: Bonds: (A) The YTM of 9% Is An APR Rate, With Coupons Occurring Semi-Annually. So

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raymond

1. This document provides solutions to practice problems involving calculations of bond prices, yields to maturity, and realized rates of return. It includes step-by-step workings for four bond valuation problems. 2. The problems calculate bond prices using the present value of cash flows formula given the yield to maturity. They also determine the realized rate of return for bonds sold before maturity by including the value of reinvested coupons. 3. The document demonstrates how to value bonds and calculate yields and returns under different scenarios such as varying holding periods, reinvestment rates, and coupon payment frequencies.

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Solutions To Practice Problem Set #5: Bonds: (A) The YTM of 9% Is An APR Rate, With Coupons Occurring Semi-Annually. So

Uploaded by

raymond
41 views2 pages
1. This document provides solutions to practice problems involving calculations of bond prices, yields to maturity, and realized rates of return. It includes step-by-step workings for four bond valuation problems. 2. The problems calculate bond prices using the present value of cash flows formula given the yield to maturity. They also determine the realized rate of return for bonds sold before maturity by including the value of reinvested coupons. 3. The document demonstrates how to value bonds and calculate yields and returns under different scenarios such as varying holding periods, reinvestment rates, and coupon payment frequencies.

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Bonds II - solutions

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1. This document provides solutions to practice problems involving calculations of bond prices, yields to maturity, and realized rates of return. It includes step-by-step workings for four bond valuation problems. 2. The problems calculate bond prices using the present value of cash flows formula given the yield to maturity. They also determine the realized rate of return for bonds sold before maturity by including the value of reinvested coupons. 3. The document demonstrates how to value bonds and calculate yields and returns under different scenarios such as varying holding periods, reinvestment rates, and coupon payment frequencies.

Copyright:

© All Rights Reserved
Download as PDF, TXT or read online from Scribd
Download as pdf or txt
41 views2 pages

Solutions To Practice Problem Set #5: Bonds: (A) The YTM of 9% Is An APR Rate, With Coupons Occurring Semi-Annually. So

Uploaded by

raymond
1. This document provides solutions to practice problems involving calculations of bond prices, yields to maturity, and realized rates of return. It includes step-by-step workings for four bond valuation problems. 2. The problems calculate bond prices using the present value of cash flows formula given the yield to maturity. They also determine the realized rate of return for bonds sold before maturity by including the value of reinvested coupons. 3. The document demonstrates how to value bonds and calculate yields and returns under different scenarios such as varying holding periods, reinvestment rates, and coupon payment frequencies.

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Solutions to Practice Problem Set #5: Bonds

1. (a) The YTM of 9% is an APR rate, with coupons occurring semi-annually.


.09
So, rsa = = .045
2
1 − (1.045 )−40  − 40
P0 = 40   + 1,000(1.045 ) = $907.99
 .045 

(b) If you require a YTM of 9% and if the YTM on the bond were 7%, you would not
buy the bond. If you require 9%, you would not be willing to settle for a bond
yielding only 7%.

At 9%YTM, the price of the bond is $907.99. This is the most that you would be
willing to pay in order to earn the YTM you require. However, at 7% YTM, the price
of the bond would be much greater than $907.99. This would be too high a price
for you to pay, and so you would not buy the bond.

2. (a) The equation to be solved for the effective periodic yield, rannual , is:
1 − (1 + rannual )−28  − 28
P7 = 1,151.74 = 105   + 1,000(1 + rannual )
 rannual 
Using the trial and error method, rannual = 0.09 = 9%. Since the bond has
annual coupons, YTM = rannual × 1= 9%.

(b)
1 − (1.12)−25  − 25
P10 = 105   + 1,000(1.12) = $882.35
 .12 

At date 10, the value of the 3 reinvested coupons is:

 (1.03)3 − 1
FVRC10 = 105   = $324.54
 .03 

Therefore, the realized rate of return, ROR, is:


1
 ($882.35 + $324.54 ) 3
ROR = 
$1,151.74  − 1 = .01571 or 1.571% per year
 
(c) The bond was not held to maturity and coupons were not reinvested at the yield to
maturity.
3. (a) The assumed YTM at sale date is 11.5%, with coupons occurring semi-annually.
.115
So, rsa = = .0575
2
1 − (1.0575)−10  −10
P5 = 60   + 1,000(1.0575) = $1,018.62
 .0575 

At year 5, the value of the 10 reinvested coupons is:


 (1.07)10 − 1
FVRC5 = 60   = $828.99
 .07 

Therefore, the realized rate of return, ROR, is:


1
 ($1,018.62 + $828.99 ) 5
ROR =   − 1 = .13063 or 13.063% per year
 $1,000 

(b) The purchase price was $1,000, because the bond was trading at par. This also
means that the yield was 12%, or equal to the coupon rate. The ROR is higher than
the original YTM, due to the reinvestment rate that was higher than the YTM at
purchase. The bond was also not held to maturity.

1 − (1.08)−19  −19
4. P1 = 70   + 1,000(1.08) = $903.96
 . 08 
1
 70 + 903.96 
ROR =   − 1 = −.0260 = −2.60%
 1,000 

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