Chapter $5-$ Mini Case

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 $r_d$ 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 $$887\mathrm{.}00?$ That sells for $$1,134\mathrm{.}20?$ What does the fact that a bond sells at a

discount or at a premium tell you about the relationship between $r_d$ 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 $r_d=13\%.$

h$.$ Suppose a $10-$year, $10\%$ semiannual coupon bond with a par value of $$1,000$ is currently selling

for $$1,135\mathrm{.}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 $(r_d)$ 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 nominal risk$-$free rate $(r_{RF}).$ What security can be used as an estimate of $r_{RF}?$