Question

1. Robert Campbell and Carol Morris are senior vice-presidents of the Mutual of Chicago Insurance Company. They are co-directors of the company’s pension fund management division, with Campbell having responsibility for fixed income securities (primarily bonds) and Morris being responsible for equity investments. A major new client, the California League of Cities, has requested that Mutual of Chicago present an investment seminar to the mayors of the represented cities. Campbell and Morris, who will make the actual presentation, have asked you to help them by an­swering the following questions.

   What is the yield to maturity on a 10-year, 8% annual coupon, $1,000 par value bond that sells for $880.00? That sells for $1,130.50? 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?What would happen to the value of the 10-year bond over time if the required rate of return remained at (i) 12% or (ii) remained at 8%?

Answer 1

1: Using financial calculator

Input: FV= 1000,

PMT = 8%*1000=80

N= 10

PV=-880

Solve for I/Y as 9.95

Hence the YTM is 9.95%

2: Using financial calculator

Input: FV= 1000,

PMT = 8%*1000=80

N= 10

PV=-1130.5

Solve for I/Y as 6.21

Hence the YTM is 6.21%

3: When the rate is higher than the coupon rate, the bond sells at a discount.However if the rate is lower than the coupon rate, the bond sells at a premium.

4: If the required rate is 12%, which is higher than the coupon rate of the bond, the bond’s price will decline since the investors will not be adequately compensated for the investment. However if the return is 8% which is same as the coupon rate, the bond price will stay at par.