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.

1. What is the value of a 1-year, $1,000 par value bond with a 8% annual coupon if its required rate of return is 12%? What is the value of a similar 10-year bond?
2.             What would be the value of the bond described in part (a) if, just after it had been issued, the expected inflation rate rose by three percentage points, caus­ing investors to require a 15% return? Is the security now a discount bond or a premium bond?
3.             What would happen to the bond’s value if inflation fell, and r_d declined to 8%? Would it now be a premium bond or a discount bond?
4.             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

As per rules I am answering the first 4 subparts of the question

1: Using financial calculator

Input: Fv = 1000

N = 1

PMT= 8%*1000= 80

I/Y = 12

Solve for PV as -964.29

Value of the bond is $964.29

2: Using financial calculator

Input: Fv = 1000

N = 10

PMT= 8%*1000= 80

I/Y = 12

Solve for PV as -773.99

Value of the bond is $773.99

3: For a 1 year Bond, after increase in inflation

Using financial calculator

Input: FV = 1000

N = 1

PMT= 8%*1000= 80

I/Y = 15

Solve for PV as -939.13

Value of the bond is $939.13

It is now a discount bond

4: If required rate is 8%, this is the same as the coupon rate and so the bond isa par value bond.