Question

Robert Campbell and Carol Morris are senior vice-presidents of the Mutual Chicago Insurance Company. They are co- directors of the company’s pension fund management division, with Campbell having responsibility for fixed income securities (primarily bods) and Morris being responsible for equity investment. 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. A. What are the key features of a bond? B. How do you determine the value of a bond? C. What is the value of a 1-year, $1,000 par value bond with a 10% annual coupon if its required rate of return is 10%? What is the value of a similar 10- year bond? D. (1) What would be the value of the bond described in part (c) if, just after it had been issued, the expected inflation rate rose by three percentage/points, causing investors to require a 13% return? Is the security now a discount bond or a premium bond? (2) What would happen to the bond’s value if inflation fell, declined to 7%? Would it now be a premium bond 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 (i) 13% or (iI) remained at 7%? E. (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 ata discount or at a premium tell you about the relationship between rd and the bond’s coupon rate? (2) What is the current yield, the capital gains yield, and the total return in each case in the preceding question?

Answer 1

A. Key features of a bond:

• Par value - face amount paid at maturity.
• Coupon interest rate - stated interest rate,
• Maturity - years until bonds must be repaid
• Issue date - date when bond was issued.
• Default risk - risk of issuer fails to make payment of interest or principal.

B. Value of a bond

Value of a bond is present value of future cash flows via interest and principle.

C.

Value of a bond	= Coupon amount (PVIFA r%,n yrs)+ maturity amount (PVIF r%,nth year)
Value of 1 year bond	=(10*(0.909))+(1000*(0.909))
	=918.09
Value of 10 year old bond	=(10*6.145)+(1000*0.386)
	=447.45

D.

Value of a bond	= Coupon amount (PVIFA 13%,n yrs)+ maturity amount (PVIF 13%,nth year)
Value of 1 year bond	=(10*(0.885))+(1000*(0.885))
	=893.85
Value of 10 year old bond	=(10*5.426)+(1000*0.295)
	=349.26

Value of a bond	= Coupon amount (PVIFA 7%,n yrs)+ maturity amount (PVIF 7%,nth year)
Value of 1 year bond	=(10*(0.935))+(1000*(0.935))
	=944.35
Value of 10 year old bond	=(10*7.024)+(1000*0.508)
	=578.24

E. (1)

YIELD TO MATURITY (YTM)	=COUPON AMOUNT + (REDEMPTION VALUE - ISSUE PRICE)/N
	(REDEMPTION VALUE + ISSUE PRICE )/2
sells for $887.00
YTM	=90+(1000-887)/10
	(1000+887)/2
	=7.02%
That sells for$1,134.20
YTM	=90+(1000-1134.2)/10
	(1000+1134.2)/2
	=9.69%
WHEN SELLING AT DISOUNT YTM IS LESS THAN COUPON RATE AND WHEN SELLING AT PREMIUM, YTM IS GREATER THAN YTM.

(2)

CURRENT YIELD	=ANNUAL CASH INFLOW
	MARKET PRICE PER SHARE
sells for $887.00
CURRENT YIELD	90	*100
	887
	=10.15%
That sells for$1,134.20
CURRENT YIELD	90
	1134.2
	=7.94%

CAPITAL GAIN YIELD	=FACE VALUE- MARKET PRICE
	MARKET PRICE PER SHARE
sells for $887.00
CAPITAL GAIN YIELD	=1000-887	*100
	887
	=12.74%
That sells for$1,134.20
CAPITAL GAIN YIELD	(1000-1134.2)
	1134.2
	=-11.83%

TOTAL RETURN = CURRENT YIELD + CAPITAL GAIN YIELD.

sells for $887.00
TOTAL RETURN	=10.15%+12.74%
	=22.89%
That sells for$1,134.20
TOTAL RETURN	=7.94%-11.83%
	=-3.89%