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# Fixed Income Homework Essay

1493 words - 6 pages

FINE 7650 Fall 2015
Homework 1
Chapters 1-3

Directions: Homework 1 is to be done in your groups. Please submit this homework to the gmail account that is consistent with your section. In order to receive full credit, you must show all work. If you use a financial calculator, please remember to show all of the calculations that you use.
Time Value of Money and Bond Basics
1. ABC Corp bonds have four years to maturity and yield 7%. The bond pays a coupon rate of 5.8%. What happens to the price of the bond one year from today if yields (i) remain same, and (ii) drop to 6.2%?
(i) P=1000, N=3, PMT= 58, I/Y =7, pv =968.51
(ii) p=1000,n=3,pmt=58,i/y= 6.2, pv =989.35

If interest rates are greater than zero, it is possible for a zero-coupon bond to sell at a premium (i.e. for more than par value)
c. If a bond’s yield to maturity is greater than its coupon rate, the bond will sell at a premium
d. If market rates do not change, the price of a bond selling at a discount increases over time
e. All of the above statements are false

6. You want to borrow \$2 million now. You are being offered two different
loans:
a. A short term loan would give you \$2 million now at 8% for one year.
b. A longer term loan would give you \$2 million today at 7.5% for 2 years.
Interest on this loan would accrue and be paid at the end of the second

You receive a payment one year from now that would be exactly sufficient
to repay the short-term loan. If you take the long-term loan, you have to
invest this money for one more year. You have an opportunity to lock in the
interest rate now and invest this cash flow one year from now at a 1-year
interest rate of 7%. Which loan should you take?

Option 1: 2*1.08= 2.19 million
We will receive sufficien to pay short-term loan.
Option 2: 2*(1.075)^2 = 2.31125 million
Cash inflow: 2.16*1.07 =2.3112 million
So it is not enough to cover two year loan, so we choose option 1.

7. You have a choice between receiving your salary of \$120,000 in equal monthly
installments of \$10,000 or in a single lump sum at the end of each year. If
your required return is 12%. Assume monthly interest compounding. What year-end salary would you demand?

Monthly Installment: pmt=10,000, i/y=12/12=1, n=12, fv=126,825.03
Single lump sum: 120,000, so choose monthly installment.

8. (a) You have a \$1000 par 5% coupon (nominal rate) US Treasury bond with
7 years remaining in its life. Coupons are paid semiannually and the next
coupon payment is exactly six months away. The market interest rate is 6%
(assume semiannual compounding). What is the current price of
this bond?

Fv=1000, n=14, pmt=25, i/y=3, pv= 943.52

(b) What is the effective annual rate that corresponds to a nominal interest rate
of 6% with semi-annual compounding?

(1+0.03)^2-1=6.09%

(c) Price a zero coupon bond with a face amount of \$1000 maturing in 7 years.
Assume that the nominal interest rate is 6% and interest is compounded
semiannually.

Fv=1000,i/y=3,n=14,pv=661.12

(d) Assume now that interest rates have instantaneously increased by 1% to 7%.
What are the bonds in parts (a) and (c) worth now?

Fv=1000, i/y=3.5, pmt= 25, n=14, pv=890.79
Fv=1000,i/y=3.5, n=14, pv= 617.78

Total return and yield measures

1. Assume a bondholder purchased at par an initial issue of bonds and held them to maturity. Over the maturity, the interest rates rose at which the coupons income was invested. Compare the realized return to the yield to maturity of bond at the time of...

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