Question

How Would I answer Question "D" "E 3" and "F" . I need to enter into excel and display graphs if applicable.

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

Solution:

D.i)Value of the bond is the present value of expected future coupon paymets and its maturity value.Required rate of return is used to determine the present value.

ii)Calculation of value of bond

Annual coupon payment(A)=$1000*10%=$100

Maturity value(M)=$1000

Maturity period(n)=10 years

required rate of return=10% or 0.10

Price of bond

=$100/(1+0.10)^1+$100/(1+0.10)^2+$100/(1+0.10)^3+$100/(1+0.10)^4+$100/(1+0.10)^5+$100/(1+0.10)^6+$100/(1+0.10)^7+$100/(1+0.10)^8+$100/(1+0.10)^9+($100+$1000)/(1+0.10)^10

=$1000

Thus value of bond is $1000.(You should note that,when require rate of return is equal to coupon rate,then the value of bond is equal to its par value)

E3.Value of bond increases over the period and will be equal to its apr value at maturity,if the required rate is remained at 13%

ii)When the required rate is higher than the coupon rate,bond is issued traded at premium.In the given case,required rate is 7% and coupon rate is 10%,hence bond would have been issued at premium.The value of bond would decrease over the time and shall be equal to its par value at maturity.

F.Calculation of YTM(Yield to maturity)

YTM=[Annual coupon+(Par value-Current price)/years to maturity]/(Par value+Current price)/2

YTM of bond that sells for $887.00

=[$90+($1000-$887)/10]/($1000+$887)/2

=$101.30/943.50=0.1074 or 10.74%

YTM of bond that sells for $1,134.20

=[$90+($1000-$1134.20)/10]/($1000+$1134.20)/2

=$76.58/$1067.10=0.0718 or 7.18%

It shows that when rd is higher than coupon rate,bond is sale at discount and vice versa