Question

"Company A has just issued a callable (at par) 8 year, 12% coupon bond with annual coupon payments. The bond can be called at par in one year or anytime thereafter on a coupon payment date. It has a price of $107 per $100 face value. What is the bond's yield to call?

Answer 1

No of periods = 20 years

Yield to call on 1^st coupon date

Bond Price = Coupon / (1 + YTC)^period + Face value / (1 + YTC)^period

$107 = $12 / (1 + YTC)¹ + $100 / (1 + YTC)¹

Using Texas Instruments BA 2 Plus Calculator

SET N = 1, FV = 100, PMT = 12, PV = -107

CPT I/Y = 4.67

Yield to Call (YTC) = I/Y = 4.67%

Yield to call on 2^nd coupon date

Bond Price = Coupon / (1 + YTC)^period + Face value / (1 + YTC)^period

$107 = $12 / (1 + YTC)¹ + $12 / (1 + YTC)² + $100 / (1 + YTC)²

Using Texas Instruments BA 2 Plus Calculator

SET N = 2, FV = 100, PMT = 12, PV = -107

CPT I/Y = 8.07

Yield to Call (YTC) = I/Y = 8.07%

Yield to call on 3^rd coupon date

Bond Price = Coupon / (1 + YTC)^period + Face value / (1 + YTC)^period

$107 = $12 / (1 + YTC)¹ + $12 / (1 + YTC)² + $12 / (1 + YTC)³ + $100 / (1 + YTC)³

Using Texas Instruments BA 2 Plus Calculator

SET N = 3, FV = 100, PMT = 12, PV = -107

CPT I/Y = 9.22

Yield to Call (YTC) = I/Y = 9.22%

Yield to call on 4^th coupon date

Bond Price = Coupon / (1 + YTC)^period + Face value / (1 + YTC)^period

$107 = $12 / (1 + YTC)¹ + $12 / (1 + YTC)² + ,,,+$12 / (1 + YTC)⁴ + $100 / (1 + YTC)⁴

Using Texas Instruments BA 2 Plus Calculator

SET N = 4, FV = 100, PMT = 12, PV = -107

CPT I/Y = 9.80

Yield to Call (YTC) = I/Y = 9.80%

Yield to call on 5^th coupon date

Bond Price = Coupon / (1 + YTC)^period + Face value / (1 + YTC)^period

$107 = $12 / (1 + YTC)¹ + $12 / (1 + YTC)² + ,,,+$12 / (1 + YTC)⁵ + $100 / (1 + YTC)⁵

Using Texas Instruments BA 2 Plus Calculator

SET N = 5, FV = 100, PMT = 12, PV = -107

CPT I/Y = 10.15

Yield to Call (YTC) = I/Y = 10.15%

Yield to call on 6^th coupon date

Bond Price = Coupon / (1 + YTC)^period + Face value / (1 + YTC)^period

$107 = $12 / (1 + YTC)¹ + $12 / (1 + YTC)² + ,,,+$12 / (1 + YTC)⁶ + $100 / (1 + YTC)⁶

Using Texas Instruments BA 2 Plus Calculator

SET N = 6, FV = 100, PMT = 12, PV = -107

CPT I/Y = 10.38

Yield to Call (YTC) = I/Y = 10.38%

Yield to call on 7^th coupon date

Bond Price = Coupon / (1 + YTC)^period + Face value / (1 + YTC)^period

$107 = $12 / (1 + YTC)¹ + $12 / (1 + YTC)² + ,,,+$12 / (1 + YTC)⁷ + $100 / (1 + YTC)⁷

Using Texas Instruments BA 2 Plus Calculator

SET N = 7, FV = 100, PMT = 12, PV = -107

CPT I/Y = 10.54

Yield to Call (YTC) = I/Y = 10.54%

Yield to call/maturity on 8^th coupon date

Bond Price = Coupon / (1 + YTC)^period + Face value / (1 + YTC)^period

$107 = $12 / (1 + YTM)¹ + $12 / (1 + YTM)² + ,,,+$12 / (1 + YTM)⁸ + $100 / (1 + YTM)⁸

Using Texas Instruments BA 2 Plus Calculator

SET N = 8, FV = 100, PMT = 12, PV = -107

CPT I/Y = 10.66

Yield to Maturity (YTM) = I/Y = 10.66%