Question

1.) 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.)

g. How does the equation for valuing a bond change if semiannual payments are made? Find the value of a 10-year, semiannual payment, 10% coupon bond if the nominal rd 13%.

h. Suppose a 10-year, 10% semiannual coupon bond with a par value of $1,000 is currently selling for $1,135.90, producing a nominal yield to maturity of 8%. However, the bond can be called after 5 years for a price of $1,050.

(1) What is the bond’s nominal yield to call (YTC)?

(2) If you bought this bond, do you think you would be more likely to earn the YTM
or the YTC? Why?

i. Write a general expression for the yield on any debt security rd and define these terms: real risk-free rate of interest (r ), inflation premium (IP), default risk premium (DRP), liquidity premium (LP), and maturity risk premium (MRP).

j. Define the real risk-free rate (r ). What security can be used as an estimate of r ? What is the nominal risk-free rate rRF ? What securities can be used as estimates of rRF?

k. Describe a way to estimate the inflation premium (IP) for a t-year bond.

l. What is a bond spread and how is it related to the default risk premium? How are bond ratings related to default risk? What factors affect a company’s bond rating?

m. What is interest rate (or price) risk? Which bond has more interest rate risk: an annual payment 1-year bond or a 10-year bond? Why?

n. What is reinvestment rate risk? Which has more reinvestment rate risk: a 1-year bond or a 10-year bond?

o. How are interest rate risk and reinvestment rate risk related to the maturity risk premium?

p. What is the term structure of interest rates? What is a yield curve?

q. Briefly describe bankruptcy law. If a firm were to default on its bonds, would the company be liquidated immediately? Would the bondholders be assured of receiving all of their promised payments?

Answer 1

As per rules I will answer the first sub parts of the question

a. The key features of a bond are

They have a specific maturity date which is the time at which the investor receives the face value amount of the bond.

The bonds come with a specific face value which is also known as the par value. This is the principal amount of a bond.

Bonds have a specific coupon rate which is the interest that the bond will pay to the investors every period. This could be paid quarterly semi annually or annually.

Bonds also specify the currency in which the interest and the principal will be paid. Hence they could be dollar denominated or non dollar denominated bonds.

b: Call provision refers to a provision on a bond which allows the issuer to repurchase the bond at the call period. When bonds come with the call provision, the yield will be higher since the provisions are for the benefit of the issuer. Bonds with call provisions have added risk since the issuer can retire the bond when the market interest rates are lower and issue fresh bonds at lower interest.

A sinking fund provision refers to the means of repaying funds which were borrowed through a bond issue. The issuer of the bonds makes payments to a Trustee who thereafter retires a part of the bonds by purchasing them in the open market. This is equivalent to receiving the par value at periodic intervals and hence it reduces the risk faced by the investor.

c: The value of an asset whose value is based on expected future cash flows is determined by discounting the value of the future cash flows to its present value. The future cash flows are discounted at a particular rate of interest to arrive at the present value of the asset.

d:

N=10

FV=1000

Coupon= 10%*1000 = $100

R=10%

Price of the bond= C*(1-1/(1+r)^n)/ r + FV/(1+r)^n

=100*(1-1/1.1^10)/0.1 + 1000/1.1^10

=$1000

Hence price of bond is same as its par vale since the coupon rate is equal to the required rate of return.