Question

UF Issued a 20-year bond that pays a semi-annual coupon of $32.00, ha a par value of $1,000 and a nominal annual yield-to-maturity- of 7.508 percent. This bond can be called in 5 years, and the nominal annual yield-to-call is 10.15 percent. Determine the call premium for this bond.

Answers:

A) $30 B) $40 C) $50 D) $60 E) $70

Please do not use excel to explain this to me. I would like to see the actual work. thank you

Answer 1

Calculation of current price:

Par Value = $1,000
Semiannual Coupon = $32

Annual YTM = 7.508%
Semiannual YTM = 3.754%

Time to Maturity = 20 years
Semiannual Period = 40

Current Price = $32 * PVIFA(3.754%, 40) + $1,000 * PVIF(3.754%, 40)
Current Price = $32 * (1 - (1/1.03754)^40) / 0.03754 + $1,000 / 1.03754^40
Current Price = $886.22

Calculation of Call Premium:

Annual YTC = 10.15%
Semiannual YTC = 5.075%

Time to Call = 5 years
Semiannual Period to Call = 10

$886.22 = $32 * PVIFA(5.075%, 10) + Call Price * PVIF(5.075%, 10)
$886.22 = $32 * (1 - (1/1.05075)^10) / 0.05075 + Call Price * (1/1.05075)^10
$886.22 = $246.1980 + Call Price * 0.60955
$640.0220 = Call Price * 0.60955
Call Price = $1,050

Call Premium = Call Price - Par Value
Call Premium = $1,050 - $1,000
Call Premium = $50