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# Week 8

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Simon Fraser University

Business Administration

BUS 315

George Blazenko

Fall

Description

Business 312: Assignment #8
Cutting, pasting, and printing the suggested solution is not sufficient effort for a mark on this
assignment.
1. Consider a 10 year bond that makes annual coupon payments. The bond has just made a
coupon payment. The next and upcoming coupon is in exactly one year. The coupon rate on the
bond is 7% per annum (compounded once per year). The yield on the bond is 8% per annum
(compounded once per year). The par-value is $10,000. Find the current yield. Explain why the
current yield is greater or lesser than the yield to maturity.
700 1 10,000
The value of the bond is: 1− 10+ 10 = $9,328.99. The current yield is
0.08 1.08 1.08
700/9,328.99 = 7.5%.
The current yield (7.5%) is less than the yield (8%) because this is a discount bond. The return on
a discount bond has a relativelylow income component, and therefore, the current yield is low
relative to the expected rate of return on the bond, the yield, (8%). The low current yield is offset
with a “natural” capital gain so that the expected rate of return on this bond is equal to the yield
of 8%.
2. You have just purchased a newly issued $1000 par-value five year ABC Company bond
at par. The fixed coupon rate is 7% paid semi-annually (the next coupon is exactly six months
from today). You are considering buying another ABC company bond (another issue with
possibly different features and terms). This second bond has been outstanding for some time
now and it trades in the secondary market. The second bond has 5.5 years remaining to maturity,
has a fixed coupon rate of 6% paid annually (next receivable coupon in six months), and has a
par value of $1000.
(a) What is the yield to maturity on the five year bond?
(b) Employ the rate you calculated in (a) (in an appropriate manner) to value the 5.5 year bond.
(a) Yield on the five year bond is 7 per cent per annum compounded semi-annually(because the
bond trades at par, yield is the same as the coupon rate).
(b) The effective rate of interest is 7.1225% per annum (using the above). Use this rate as the
discount rate for the second bond. Note that the second bond pays coupons annually. There
are six remaining coupons on the bond and the next coupon is in six months. (Notice that
there is no such thing as 5.5 coupons on a bond!)
60 1 1000
1− 6÷+ 6
The value of the second bond is: 0.071225 (1.071225) (1.071225) = $979.83.
1.071225 1/2−1
3. Consider a bond that offers a 10% coupon rate, paid semi-annually, and has a par value of
$10,000. There are 20 remaining coupon payments on the bond. The next and upcoming coupon is in exactly 4 months. The yield to maturity on the bond is 9 percent per annum compounded
semi-annually. You buy the bond today and sell it in exactly three years. The yield on the bond at
that time is 10% per annum compounded semi-annually. Over the interim, you receive and
reinvest coupons at a rate of 10.5 per cent per annum compounded daily(360 days in a year).
For the purpose of calculations with this rate, you can presume that there are 30 days in a month.
(a) What is your annualized holding period rate of return on your three year investment?
(b) What is the quoted price of the bond and accrued interest when you purchase it?
(c) What is the quoted price of the bond and accrued interest when you sell it?
(a) The value of the bond today is $10,807.81.
500 1 10000
1− 20+ 20
0.045 (1.045) (1.045) =10,807.81
PP = (1.045)4/6−1
The value of the bond in 3 years if the yield at that time is 10% is $10,163.96.
10,000 2/6
SP = 4/6−110,000*1.05 =10,163.96
(1.05)
180
The coupon reinvestment rate is: 1+ 0.105 ÷ −1= 5.3894493% . The FV of reinvested
360
coupons at the time of the last coupon is $3,434.45. The value two months hence, and therefore,
the value exactly three years from today is $3,495.07.
FV RP = 500 1.05389 −1 *(1.05389) 2/6=3,495.08
0.05389
The 3 year holding period rate of return is 26.381%.
[0,163.96+3,495.08−10,807.81 ]
HPRR = 10,807.81 = 0.2638
The annualized holding period rate of return (compounded once per year) is 8.117%.
EAR = (1.26381) −1=8.117%
(b) At the purchase, 2 months have past since a coupon payment. Therefore, accrued interest is
500*(2/6) = $166.67. The quoted price of the bond is $10,807.81-$166.66 = $10,641.14.
(c) At the sale, two months have past since a coupon payment, therefore, accrued interest is
500/3 = $166.67. The quoted price of the bond is 10,163.96 -166.67 = $9,997.29.
4. Consider a bond which offers an 8.0% coupon rate, paid semi-annually, and has a par
value of $10,000. There are 30 remaining coupon payments on the bond. The next and
upcoming coupon is in exactly 5 months. The yield to maturity on the bond is 8 percent per
annum compounded semi-annually. You buy the bond today and sell it in exactly three years and seven months. The yield on the bond at that time is 8% per annum compounded semi-annually.
Over the interim, you receive and reinvest coupons at a rate of 7.5 per cent per annum
compounded monthly.
Required: What is the annualized holding period rate of return on your three year -- seven
month investment, compounded quarterly?
1/6
The value of the bond today is (1.04) *10,000 = $10,065.58.
The value of the bond in three years is (1.04) *10,000 = $10,131.59.
The effective reinvestment rate over a six month period is: (1+0.075/12) -1 = 3.8090%
The future value of reinvested coupons at the time of the last coupon

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