Please can someone help me with this : Minicase 1 Interest Rates, Bond Yields, a
ID: 2653366 • Letter: P
Question
Please can someone help me with this :
Minicase 1
Interest Rates, Bond Yields, and Duration
CONCEPTS IN THIS CASE
simple loans
fixed-payment loans
coupon bonds
present value
yield-to-maturity
current yield
nominal and real interest rates
rate of return
capital gain
interest-rate and reinvestment risk
duration
You have been hired to analyze the debt securities of your organization. The firm has outstanding loans and bonds. A quick review of the balance sheet shows the following:
Liability
Amount ($)
Nominal
Interest
(coupon)
Rate
Years to
Maturity
Selected Liabilities of the firm
Simple Loans
800
5%
1
Fixed-Payment Loans
5,000
12%
19
Long-term Bonds #1
500,000
10%
4
Long-term Bonds #2
1,080,000
10%
10
Liabilities Total
1,585,800
Market Price for Bond #1
930.50
Market Price for Bond #2
859.50
Face Value of Each Bond
1,000.00
Selected Current Assets of the firm
Marketable Securities:
Treasury Bills
100,000
Note: Treasury Bills have a $10,000 face value, which matures in one year. Each Treasury Bill has a cost of $9,580.00
How much interest would the firm pay each year on the simple-interest loan?
How much would you write a cheque for to pay off the loan in one year?
What is the monthly payment needed to pay off the fixed-payment loans?
What is the current yield for each bond if the current price is:
$930.50 for Bond #1?
$859.50 for Bond #2?
What is the expected yield to maturity for each bond?
Bond #1 selling for $930.50?
Bond #2 selling for $859.50
What is the rate of capital gain if both bonds sell for $900.00 in one year?
Bond #1 selling for $930.50 today?
Bond #2 selling for $859.50 today?
If the Yield to Maturity expected by investors changes to 11%:
What will be the market price of Bond #1?
What will be the market price for Bond #2?
What will be the dollar change in price for Bond #1?
What will be the dollar change in price for Bond #2?
What will be the percent change in price for Bond #1?
What will be the percent change in price for Bond #2?
Since the change in expected yield to maturity is the same, why is the amount of change different between the bonds?
If investors holding our 4-year bonds (Bond #1) receive interest income annually for four years, plus the face value of the bonds at maturity,
What will be the total interest earned on the bond over the next four years?
What will be the face value received at maturity?
Given the following projected income stream for Bond #1:
Projected Reinvestment Rates
Year
Coupon
Interest ($)
Face
Value ($)
10%
5%
1
100
2
100
10.00
5.00
3
100
21.00
10.25
4
100
1000
33.10
15.76
Total Income
400
1000
64.10
31.01
What is the total cash available over the next four years to the bond holder earning
10%
15%
What is the average annual rate of return for the bond holder earning
10%
15%
Why does the reinvestment rate affect the annual rate of return for the same bond?
If the expected rate of return on our bonds is 10%, what is the duration of Bond #1?
What is the yield to maturity on the Treasury Bills (a discount bond)?
What is the real rate of interest if the nominal rate is 10% and the inflation rate is 3%?
Copyright © 2000–2001 Addison Wesley Longman, a division of Pearson Education
Adaptation copyright © 2002 Pearson Education Canada
Liability
Amount ($)
Nominal
Interest
(coupon)
Rate
Years to
Maturity
Selected Liabilities of the firm
Simple Loans
800
5%
1
Fixed-Payment Loans
5,000
12%
19
Long-term Bonds #1
500,000
10%
4
Long-term Bonds #2
1,080,000
10%
10
Liabilities Total
1,585,800
Market Price for Bond #1
930.50
Market Price for Bond #2
859.50
Face Value of Each Bond
1,000.00
Selected Current Assets of the firm
Marketable Securities:
Treasury Bills
100,000
Explanation / Answer
Interest paid on the simple interest loan:
Principal amount = $800
Interest rate=5%.
Interest payment =$800*5%
=$40.
Cheque to be written for:
To clear the loan of $800, the cheque to be written is for principal amount and interest amount i.e., $800+$40=$840.
Monthly payments needed to payoff the fixed period loan:
Principal amount=$5000 =PV
Interest rate=12% =Rate= 12%/12 as montly interest rate needs to be applied.
Number of years to maturity=19 years.
Number of months for which monthly payment needs to be made=19*12 =228 months.=nper
Formula to be used=PMT(rate,nper,pv)
Substituting the values in the above formula=PMT(12%/12,228,5000)
=$55.77 this appears as a negative amount as this is a payment that needs to be made.
Current Yield:
Formula for current yield = Annual return earned/Current market price.
For Bond 1 coupon rate=10%. Interest earned per annum =$100 per bond and current market price =930.50
Current yield for Long term bond #1=$100/$930.50
=10.75%.
Current market price of long term bond #2=$859.50
Coupon earned per bond @10%=$1000*10%=$100.
Current yield =$100/$859.50
=11.63%.
Yield to maturity for Long term bond#1:
Simple formula for calculation of YTM=C+[(F-P)/n]/(f+P)/2
For Bond #1 C=$100, F=$1000, P=$930.50
n= years to maturity =4.
Substituting the values in the above formula gives approximate YTM=$100+[($1000-$930.50)/4]/($1000+$930.50)/2
=12.16%
Expected YTM of Long term bond #2:
Simple formula for calculation of YTM=C+[(F-P)/n]/(f+P)/2
For Bond #2 C=$100, F=$1000, P=$859.50
n= years to maturity =10
Substituting the values in the above formula gives approximate YTM=$100+[($1000-$859.50)/10]/($1000+$859.50)/2
=12.27%.
Yield to maturity of treasury bill:
=(Face value - Purchase price/Face value)*360/365
=[($10,000-$9,580)/$10,000]*360/365
={$420/$10000*360/365}*100
=0.04142 *100
=4.14%.
Real rate of interest:
Real rate of interest = 1+interest rate/1+inflation rate - 1
Nominal Interest rate=10%
Inflation rate=3%
Real rate of interest =1+.10/1+.03 -1
=1.10/1.03 -1
=1.0679611 -1
=0.06796*100
=6.80% rounded to two digits.