Question

"Consider the following bond: Coupon rate = 11% Maturity = 18 years Par value = $1,000 First par call in 13 years Only put date in five years and putable at par value Suppose that the market price for this bond is $1,169.

Show that the yield to maturity for this bond is 9.077%.

Show that the yield to first par call is 8.793%.

Show that the yield to put is 6.942%.

Suppose that the call schedule for this bond is as follows: Can be called in eight years at $1,055 Can be called in 13 years at $1,000

And suppose this bond can only be put in five years and assume that the yield to first par call is 8.535%. What is the yield to worst for this bond?"

Answer 1

No of periods = 18 years

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (11% / 2) * $1000

Coupon per period = $55

a)

Bond Price = Coupon / (1 + YTM / Compounding frequency )^period + Face value / (1 + YTM / Compounding frequency )^period

$1169 = $55 / (1 + YTM / 2)¹ + $55 / (1 + YTM / 2)² + ...+ $110 / (1 + YTM / 2)³⁶ + $1000 / (1 + YTM / 2)³⁶

Using Texas Instruments BA 2 Plus Calculator

SET N = 36, FV = 1000, PMT = 55, PV = -1169

CPT --> I/Y = 4.5384%

YTM / 2 = I/Y

YTM = 2 * 4.538%

Yield to Maturity (YTM) = 9.077%

b)

Bond Price = Coupon / (1 + YTM / Compounding frequency )^period + Face value / (1 + YTM / Compounding frequency )^period

$1169 = $55 / (1 + YTC / 2)¹ + $55 / (1 + YTC / 2)² + ...+ $110 / (1 + YTC / 2)²⁶ + $1000 / (1 + YTC / 2)²⁶

Using Texas Instruments BA 2 Plus Calculator

SET N = 26, FV = 1000, PMT = 55, PV = -1169

CPT --> I/Y = 4.396%

YTC / 2 = I/Y

YTC = 2 * 4.396%

Yield to First par Call (YTC) = 8.793%

c)

Bond Price = Coupon / (1 + YTM / Compounding frequency )^period + Face value / (1 + YTM / Compounding frequency )^period

$1169 = $55 / (1 + YTP / 2)¹ + $55 / (1 + YTP / 2)² + ...+ $110 / (1 + YTP / 2)¹⁰ + $1000 / (1 + YTP / 2)¹⁰

Using Texas Instruments BA 2 Plus Calculator

SET N = 10, FV = 1000, PMT = 55, PV = -1169

CPT --> I/Y = 3.4709%

YTP / 2 = I/Y

YTP = 2 * 3.4709%

Yield to Put (YTP) = 6.942%

d)

Yield to Worst is the lowest of the various Yield to Call & Yield to Maturity

Yield to first call = 8.535% (Since the Bond will be called at $1055 & not at Par value)

Yield to first par call = 8.793% (Since the Bond will be called at Par value)

Yield to Maturity = 9.077%

Yield to Worst = 8.535%