FIN 3010 Written Assignment 4

docx

School

Thomas Edison State College *

*We aren’t endorsed by this school

Course

FIN-301-OL

Subject

Finance

Date

Feb 20, 2024

Type

docx

Pages

Uploaded by ElderDove3906

Written Assignment 4 Chapter 13 Exercises —Exercises 1, 2, 4, and 9 1. A $1,000 bond has a coupon of 6 percent and matures after 10 years. a. What would be the bond’s price if comparable debt yields 8 percent? i. Price of bonds (annual payments) =60/(1+.08)+…+60/(1+.08)^10+1000/(1+.08)^10 =$60(6.710)+$1,000(0.463) =$403+$463=$866 IIII b. What would be the price if comparable debt yields 8 percent and the bond matures after five years? i. =60/(1+.08)+…+60/(1+.08)^5+1000/(1.08)^5 =60(3.993)+1000(.681) =$920 c. Why are the prices different in questions (a) and (b)? i. In both cases the bond’s price is less than the face amount (principal) because the current rate of interest is greater than the rate paid on these bonds (that is, 8% versus 6%). However, the amount of price decline is affected by the term of the bond, and the bond with the longer term experiences the larger price decline because the investors will collect the smaller interest payment for a longer period of time. d. What are the current yields and the yields to maturity in questions (a) and (b)? i. $60/866= 6.92% and $60/920= 6.53% e. If interest rates increase 100 basis points (that is, from 8 percent to 9 percent), what are the new prices of both bonds assuming annual compounding? i. Bond A: (PMT = 60; FV = 1,000; N = 10; I = 9; and PV = ? = −807.) Bond B: (PMT = 60; FV = 1,000; N = 5; I = 9; and PV = ? = −883.) f. Calculate the percentage change in the price of each bond and, based on this information, identify which has the higher duration. i. Bond A was $866 when the YTM was 8% and decreased to $807 when interest rates rose 1 percentage point. $807/$866 − 1 = a 6.8% decrease. Bond B was $920 when the YTM was 8% and decreased to $883 when interest rates rose 1 percentage point. $883/$920 − 1 = a 4.0% decrease. Bond A has higher duration because the majority of the cash flows come later for a bond that matures in 10 years than a bond that matures in five years. The interest payments that come before maturity cause the durations to be less than the 10-year and five-year maturities, but the 10-year bond is more

sensitive to changes in interest rates because the future cash flows are discounted for more periods than an otherwise identical five-year bond. 2. A $1,000 bond has a 7.5 percent coupon and matures after 10 years. If current interest rates are 10 percent, what should the price of the bond be? a. =$75/(1+.1)+…+$75/(1+.1)^10 + 1000/(1+.1)^10 =$75(6.145)+$1000(.836) =$847 b. If after six years, interest rates are still 10 percent, what should be the price of the bond? i. The term to maturity has diminished which increases the value of the bond (that is, the investor gets the principal back in only four instead of 10 years). c. Even though interest rates did not change in questions (a) and (b), why did the price of the bond change? i. The term to maturity is less; the value of the bond declines. Before, the bond sold for a discount. Now, it sells for a premium, which declines as the bond approaches maturity. The investor earns the higher coupon interest for a shorter time period, which decreases the attractiveness of the bond. d. Change the interest rate in questions (a) and (b) to 6 percent and rework your answers. Even though the interest rate is 6 percent in both calculations, why are the bond prices different? a. 10 yrs to maturity Pb=$75/(1+.06)+…+75/(1+.06)^10+1000/(1+.06)^10 =$75(7.360)+1000(.558)= $1,110 4 yrs to maturity; Pb=$75/(1+.06)+…+75/(1+.06)^4 + 1000/(1 +.06)^4 = $75(5.242) + 1000(.792)= $1052 The term to maturity is but the value of the bond declines. The investor will earn the higher coupon interest for a shorter time period, which decreased the attractiveness of the bond. 4. Carrie’s Clothes, Inc. has a five-year bond outstanding that pays $60 annually. The face value of each bond is $1,000, and the bond sells for $890. a. What is the bond’s coupon rate? i. The coupon rate: 6% ($60/$1,000) b. What is the current yield? i. The current yield: $60/$890 = 6.7%

c. What is the YTM? i. $890= 60/(1+r) +…+60/(1+r)^5 + 1000/(1+r)^5 8% interest rate: $60(3.993)+1000(.681= $921 9% interest rate: $60(3.890) + 1000(.650) = $883 PV = −890; PMT = 60; FV = 1,000; N = 5; and I = ? = 8.81% 9. A bond has the following features: Coupon rate of interest: 5 percent Principal: $1,000 Term to maturity: 10 years a. What will the holder receive when the bond matures? i. The investor receives the principal at maturity (that is, $1,000). b. If the current rate of interest on comparable debt is 8 percent, what should be the price of this bond? Would you expect the firm to call this bond? Why? i. Pb= $50/(1+.08)+…+$50/(1+.08)^10+1000/(1+.08)^10 = $50(6.710)+1000(.463)= $799 Since the bond is selling for a discount, there is no reason to expect the firm to call the bond. c. If the bond has a sinking fund that requires the firm to set aside annually with a trustee sufficient funds to retire the entire issue at maturity, how much must the firm remit each year for 10 years if the funds earn 8 percent annually and there is $100 million outstanding? i. The amount the firm must set aside annually (X) is X(15.193) = $10,000,000 X = $10,000,000/15.193 = $658,198 15.193 is the interest factor for the future value of an annuity of $1 at 9% for 10 years. (PV = 0; FV = 10,000,000; N = 10; I = 9; and PMT = ? = −658,201.)

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version