Question

YIELD TO MATURITY

A firm's bonds have a maturity of 8 years with a $1,000 face value, have an 11% semiannual coupon, are callable in 4 years at $1,144, and currently sell at a price of $1,265.82.

1. What is their nominal yield to maturity? Do not round intermediate calculations. Round your answer to two decimal places.
   
   %
   
2. What is their nominal yield to call? Do not round intermediate calculations. Round your answer to two decimal places.
   
   %
   
3. What return should investors expect to earn on these bonds?
   
   1. Investors would expect the bonds to be called and to earn the YTC because the YTC is greater than the YTM.
   2. Investors would not expect the bonds to be called and to earn the YTM because the YTM is greater than the YTC.
   3. Investors would not expect the bonds to be called and to earn the YTM 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 less than the YTM.
   5. Investors would expect the bonds to be called and to earn the YTC because the YTM is less than the YTC.

Answer 1

Answer to Part a.

Face Value = $1,000
Current Price = $1,265.82

Annual Coupon Rate = 11%
Semiannual Coupon Rate = 5.50%
Semiannual Coupon = 5.50% * $1,000 = $55

Time to Maturity = 8 years
Semiannual Period to Maturity = 16

Let semiannual YTM be i%

$1,265.82 = $55 * PVIFA(i%, 16) + $1,000 * PVIF(i%, 16)

Using financial calculator:
N = 16
PV = -1265.82
PMT = 55
FV = 1000

I = 3.33%

Semiannual YTM = 3.33%
Annual YTM = 2 * 3.33%
Annual YTM = 6.66%

Answer to Part b.

Face Value = $1,144
Current Price = $1,265.82

Annual Coupon Rate = 11%
Semiannual Coupon Rate = 5.50%
Semiannual Coupon = 5.50% * $1,000 = $55

Time to Call = 4 years
Semiannual Period to Call = 8

Let semiannual YTC be i%

$1,265.82 = $55 * PVIFA(i%, 8) + $1,144 * PVIF(i%, 8)

Using financial calculator:
N = 8
PV = -1265.82
PMT = 55
FV = 1144

I = 3.273%

Semiannual YTC = 3.273%
Annual YTC = 2 * 3.273%
Annual YTC = 6.55%

Answer to Part c.

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