You have been hired to analyze the debt securities of your organization. The fir
ID: 2653572 • Letter: Y
Question
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
1-How much interest would the firm pay each year on the simple-interest loan?
2-How much would you write a cheque for to pay off the loan in one year?
3-What is the monthly payment needed to pay off the fixed-payment loans?
4-What is the current yield for each bond if the current price is:
a-$930.50 for Bond #1?
b-$859.50 for Bond #2?
5-What is the expected yield to maturity for each bond?
a-Bond #1 selling for $930.50?
b-Bond #2 selling for $859.50
6-What is the rate of capital gain if both bonds sell for $900.00 in one year?
a-Bond #1 selling for $930.50 today?
b-Bond #2 selling for $859.50 today?
7-If the Yield to Maturity expected by investors changes to 11%:
a-What will be the market price of Bond #1?
b-What will be the market price for Bond #2?
c-What will be the dollar change in price for Bond #1?
d-What will be the dollar change in price for Bond #2?
e-What will be the percent change in price for Bond #1?
f-What will be the percent change in price for Bond #2?
g-Since the change in expected yield to maturity is the same, why is the amount of change different between the bonds?
8-If investors holding our 4-year bonds (Bond #1) receive interest income annually for four years, plus the face value of the bonds at maturity,
a-What will be the total interest earned on the bond over the next four years?
b-What will be the face value received at maturity?
Given the following projected income stream for Bond #1:
Projected Reinvestment Rates
Year
Coupon
Interest ($)
Face
Value ($)
10%
5%
1
100
2
100
10.00
5.00
3
100
21.00
10.25
4
100
1000
33.10
15.76
Total Income
400
1000
64.10
31.01
c-What is the total cash available over the next four years to the bond holder earning
ii-10%
iii-15%
d-What is the average annual rate of return for the bond holder earning
ii-10%
iii-15%
e-Why does the reinvestment rate affect the annual rate of return for the same bond?
f-If the expected rate of return on our bonds is 10%, what is the duration of Bond #1?
Liability
Amount ($)
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.
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