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 salient features of any bond comprise the followwing:

1. Par value- This is considered to be the face value or principal amount of bonds. Bonds are generally issued having a value of $1,000 or in multiples of the same.

2. Coupons- Bonds are considered to have a stated rate of interest which is provided with respect to its face value. It reflects the payments of interests to the bond holders by the issuer of the bonds. Such payments are usually made on a semi-annual or annual mode. Zero coupon bonds do not fall under this category as they have no coupon payments and hence the name zero.

3. Maturity- Bonds are considered to have a stated maturity date on which the principal or face value of the bonds would be repaid to bond holders.

4. Yield to maturity- It is considered to be the effective rate of interest of the bond which equates the present values of all the future cash inflows expected to be received from the bond to that with the price of the bond.

b. Call provisions are generally quoted as a percentage of face value and that it allows the issuer of bonds to buy back the bonds before its maturity at a certain call price. Sinking fund provisions allow the issuer of the bond to set aside a pool of money such as to facilitate part purchase of the bonds issued before its maturity date. The provisions of sinking fund normally require its issuer to repurchase its bonds on a periodic basis and at the agreed sinking fund price (usually the nominal value of the bonds) or at the prevailing market price. As a result, businesses usually use funds accumulated in their sinking fund to repurchase bonds when there is fall in the rate of interest (which implies that existing bonds have risen in value) and as such they can facilitate bonds repurchase at the agreed sinking fund price, which is cheaper than the market price. There is a cap with respect to the size of the bond issue that the issuer can repurchase at the agreed sinking fund price (whereas the call provisions usually allow its issuers to repurchase the entire issue of bonds at their sole discretion). Nevertheless, the established prices of sinking fund set out in bond indentures are typically lower than that of the prices of call, and even though bonds issued are less likely to be repurchased under the sinking fund clause than that of the call clause, the holders of bonds with sinking fund provisions are likely to lose more money if such bonds are repurchased under the sinking fund provision.

c. The value of any asset which is dependent on its anticipated future cash inflows is measured by finding the sum of its present values of all such future inflows of cash. Such discounting is mainly done through a discounting factor generally known as the cost of capital or required rate of return.

d. As stated above, the value of any asset which is dependent on the anticipated future cash inflows is measured by finding the sum of its present values of all such future inflows of cash. Bond is considered to be forming part of such asset class.

As the stated rate of interest for the bond is 10% which is equal to its YTM or required rate of return of also 10%, the price of the bond can be calculated with performing any calculations because it would be equal to its par value i.e. $1,000.