Question

Kaufman Enterprises has bonds outstanding with a $1,000 face value and 10 years left until maturity. They have an 12% annual coupon payment, and their current price is $1,180. The bonds may be called in 5 years at 109% of face value (Call price = $1,090).

1. What is the yield to maturity? Round your answer to two decimal places.
   %
   
2. What is the yield to call if they are called in 5 years? Round your answer to two decimal places.
   %
   
3. Which yield might investors expect to earn on these bonds? Why?
   
   1. Investors would not expect the bonds to be called and to earn the YTM because the YTM is less than the YTC.
   2. Investors would expect the bonds to be called and to earn the YTC because the YTC is less than the YTM.
   3. Investors would expect the bonds to be called and to earn the YTC because the YTM is less than the YTC.
   4. Investors would expect the bonds to be called and to earn the YTC because the YTC is greater than the YTM.
   5. Investors would not expect the bonds to be called and to earn the YTM because the YTM is greater than the YTC.
   
   -Select I-V
   
4. The bond's indenture indicates that the call provision gives the firm the right to call the bonds at the end of each year beginning in Year 5. In Year 5, the bonds may be called at 109% of face value; but in each of the next 4 years, the call percentage will decline by 1%. Thus, in Year 6, they may be called at 108% of face value; in Year 7, they may be called at 107% of face value; and so forth. If the yield curve is horizontal and interest rates remain at their current level, when is the latest that investors might expect the firm to call the bonds?
   
   In Year (5,6,7,8,9)?

Answer 1

a. Yield to Maturity is 9.17%

Calculating YTM:

• Face value = $1,000
• Coupon payment = 12% of $1,000 = $120
• Number of periods, n = 10
• Current price = $1,180
• Let YTM be r

Current price of bond =$1,180 =120(1+r)1+120(1+r)2+......+1,120(1+r)10

r = 9.17%

b. Investor will expect 8.89% (yield to call) on these bonds.

Calculating Yield to Call:

• Face value = $1,000
• Coupon payment = 12% of $1,000 = $120
• Number of periods, n = 5
• Current price = $1,180
• Call price = $1,090
• Let Yield to call be r

Current price of bond =$1,180 =120(1+r)1+120(1+r)2+......+1,210(1+r)5

r = 8.89%

Investors expect the lower of yield to maturity and yield to call as a return. So, they will expect 8.89% yield on the bonds.

c. (iii) Investors would expect the bonds to be called and to earn the YTC because the YTC is less than the YTM
  

d. In Year 6

YTC can be found, if called in each subsequent year.  

  If called in Year 6:  

N = 6, PV = -1,180, PMT = 120, FV = 1,080   

I/YR = YTC = 9.04%.  

   If called in Year 7:  

N = 7, PV = -1,180, PMT = 120, FV = 1,070   

I/YR = YTC = 9.16%.  

  If called in Year 8:  

N = 8, PV = -1,180, PMT = 120, FV = 1,060  

I/YR = YTC = 9.26%.  

  If called in Year 9:  

N = 9, PV = -1,180, PMT = 120, FV = 1,050  

I/YR = YTC = 9.34%.  

According to these calculations, the latest investors might expect a call of the bonds is in Year 6.
This is the last year that the expected YTC will be less than the expected YTM. At this time, the
firm still finds an advantage to calling the bonds, rather than seeing them to maturity.