Question

Sam Strother and Shawna Tibbs are vice presidents of Mutual of Seattle Insurance
Company and co-directors of the company’s pension fund management division. An
important new client, the North-Western Municipal Alliance, has requested that Mutual
of Seattle present an investment seminar to the mayors of the represented cities, and
Strother and Tibbs, who will make the actual presentation, have asked you to help them
by answering the following questions.
a. What are the key features of a bond?
b. What are call provisions and sinking fund provisions? Do these provisions make
bonds more or less risky?
c. How does one determine the value of any asset whose value is based on expected
future cash flows?
d. How is the value of a bond determined? What is the value of a 10-year, $1,000 par
value bond with a 10% annual coupon if its required rate of return is 10%?
e. (1) What would be the value of the bond described in Part d if, just after it had been
issued, the expected inflation rate rose by 3 percentage points, causing investors
to require a 13% return? Would we now have a discount or a premium bond?
(2) What would happen to the bond’s value if inflation fell and rd declined to 7%?
Would we now have a premium or a discount bond?
(3) What would happen to the value of the 10-year bond over time if the required
rate of return remained at 13%? If it remained at 7%? (Hint: With a financial
calculator, enter PMT, I/YR, FV, and N, and then change N to see what happens
to the PV as the bond approaches maturity.)
f. (1) What is the yield to maturity on a 10-year, 9% annual coupon, $1,000 par value
bond that sells for $887.00? That sells for $1,134.20? What does the fact that a
bond sells at a discount or at a premium tell you about the relationship between
rd and the bond’s coupon rate?
(2) What are the total return, the current yield, and the capital gains yield for the
discount bond? (Assume the bond is held to maturity and the company does not
default on the bond.)

Answer 1

a) The basic features of Bond

1- Maturity - Maturity is the time at which the bond matures and the holder receives the final payment of principal and interest. The term to maturity is the amount of time until the bond actually matures. Basically, there are 3 basic classes of maturity, these are - 1) Short term maturity (1 to 5 years), 2) Intermediate term maturity (5 to 12 years), 3) Long term maturity (12 years or more).

Maturity is important because it indicates the length of time in which an investor will receive interest as well as when he or she will receive principal payments. It affects the yield on the bond, longer maturities tend to yield higher rates. The price volatility of a bond is a function of its maturity and a longer maturity typically indicates higher volatility.

2- Par value - It is the dollar amount the holder will receive at the bond's maturity. It can be any amount but is typically $1,000 per bond. Par value is also known as principle, face, maturity or redemption value. Bond prices are quoted as a percentage of par.

3. Coupon Rate - A coupon rate states the interest rate the bond will pay the holders each year. To find the coupon's dollar value, simply multiply the coupon rate by the par value. The rate is for one year and payments are usually made on a semi-annual basis. Some asset-backed securities pay monthly, while many international securities pay only annually. The coupon rate also affects a bond's price. Typically, the higher the rate, the less price sensitivity for the bond price because of interest rate movements.

4. Currency Denomination - Currency denomination indicates what currency the interest and principle will be paid in. There are two main types, 1) Dollar Denominated - refers to bonds with payment in USD, 2) Non dollar-Denominated - denotes bonds in which the payments are in another currency besides USD.

​

b) A call provision in a bond indenture allows the bond issuer to call in the bonds after stated years. The provision provides advantage for bond issuer when interest rate turns lower than the bond’s coupon rate. Bond holder can call in the bond when the interest rate went down, and then reissue new bond to retire the higher rate bond in order to save interest expense. Forbond holders, the provision can be harmful. When the bond is called, bond holders face reinvestment rate risk as the current interest rate is lower than the bond’s yield. Call provisionmakes the bond less risky for the issuer, but is more risky for the bond holders.Sinking fund provision allows the issuer to retire certain portion of the bond every year. The issuer can either call in buy back the portion of the bond. The retired portion of the bond is deposited in a sinking fund and will be used to repay the bond on the maturity date. A bond that has sinking fund provision is consider safer for bond holders and usually has lower yield.

c) Cash flow method can be used to determine the value of an asset when there are a series of expecting future cash flows. The information needed for the cash flow method includes the asset’s required rate of return, the time period for the expected cash flows, the interest payment frequency, and the future value of the asset. Each cash flow is then discounted back to current period using the required rate of return as the discount rate. The asset’s value is the sum of the present value of each cash flow.

d) A bond value is calculated based on the bond’s required rate of return, the bond’s coupon rate, the frequency of the coupon payments, and the maturity date of the bond. The value of a bond is determined by discounting the expected future cash flows using the bond's required rate of return. The required rate of return for a bond can be determined by summing of risk-free rate, the bond’s default risk premium, liquidity premium and maturity risk premium. By using the required rate of return as discount rate, each bond coupon payment is discounted to current period. The bond’s value is the sum of discounted interest payments plus the discounted par value of the bond.

e)