Clean Price and Dirty Price

FIN36058 Financial System

Instructor: Aiwu Zhao

Chapter 6

In-class Exercise

Clean price and dirty price

1. On September 1, 2000 an investor purchases a $10,000 par T-Bond that matures in 15.67 years. The coupon rate is 6% and the investor buys the bond 60 days after the last coupon payment (120 days before the next). The ask yield is 7%. What is the dirty price of the bond?

Clean price: 300PVIFA*(3.5%,31.34) + 10,000PVIF*(3.5%,31.34) = 9057.47 ;

Dirty: 300*(60/180) = 100; 9057.47 + 100 = 9157.47

TIPS

2. An investor buys a $10,000 par, 3% coupon TIPS security with 2 years to maturity. If inflation every six months over the investor's holding period is 2%, what is the final payment the TIPS investor will receive?

($10,000 * 1.024) *(1 + (0.03/2))= $10,986.69

Convertible Bond

3. A firm issues annual payment 6% convertible bonds at par. Each bond can be converted into 250 shares of common stock and the firm’s common stock is trading at $3.20. What percentage increase in share price is needed to justify conversion? If the bondholder gave up 30 basis points in coupon and yield rate in order to get the conversion feature, and was not able to profitably convert the bonds for three years, how did the investor do relative to a stockholder and an investor who bought an equivalent nonconvertible bond?

1000/250=$4, (4-3.2)/3.2=25% increase in share price to justify conversion.

Callable Bond

4. An investor buys a corporate callable bond at par that has a 6-year maturity. The bond is called after three years at a call price of $1045.12. You reinvested your money for the remaining three years in the same risk level of investment. Which one of the following is true?

I.Over the full six years you earned less than the yield rate you were promised when you originally purchased the bond.

II.At the end of the first three years, interest rates were probably higher than when you bought the bond.

III.Over the full six years you earned more than the yield rate you were promised when you originally purchased the bond.

IV.You were able to reinvest the coupons at a higher rate of interest in the last three years than the reinvestment rate you earned in the first three years.

Definitions

STRIPS; TIPS; Revenue Bonds; General Obligation Bonds

Concepts

1. Interest income from Treasury securities is _____, and interest income from municipal bonds is always _____.

A)Exempt from federal taxes; exempt from all taxes

B)Taxable at the state level only; exempt from state taxes only

C)Taxable at federal level only; exempt from federal taxes

D)Taxable at the state level; taxed at the federal level

2. With respect to private placements of bonds, which of the following is correct?

I.Issuers of privately placed bonds tend to be less well known than public bond issues

II.Interest rates on privately placed debt tend to be higher than for similar public issues

III.Purchasers of privately placed debt have assets of at least $100 million

IV.Once bonds have been privately placed, the original buyers must hold the bonds until maturity

A)I only

B)I and III only

C)I, II and III only

D)I, III and IV only

E)I, II, III and IV

3. Which one of the following bonds is likely to have the highest required rate of return, ceteris paribus?

A)AAA rated noncallable corporate bond with a sinking fund.

B)AA rated callable corporate bond with a sinking fund

C)AAA rated callable corporate bond with a sinking fund

D)High quality municipal bond

E)AA rated callable corporate bond without a sinking fund