A 30-year bond with an 8% coupon has a yield to maturity of 6%. The bond could be called in 7 years and if called would generate a yield to call of 5.75%. What is this bond's call premium? Assume the coupon payments are made annually and par value is $1,000.
A) $219.73
B) $152.64
C) $106.29
D) $301.76

Question

Quizplus · Accepted Answer

To calculate the call premium, we need to compare the present value of the bond if it is held to maturity (at 6% YTM) to the present value of the bond if it is called in 7 years (at 5.75% YTC). Whichever is greater represents the call premium.

If the bond is held to maturity, we can use the PV of a bond formula:

PV = (C/r) * (1 - 1/(1+r)^n) + M/(1+r)^n

where C is the annual coupon payment, r is the yield to maturity, n is the number of periods (years), and M is the par value.

PV = (80/0.06) * (1 - 1/1.06^30) + 1000/1.06^30
PV = $1,104.25

If the bond is called in 7 years, the remaining number of periods is 23 (30 - 7). We can use the PV of a bond formula again, but with the YTC of 5.75%.

PV = (80/0.0575) * (1 - 1/1.0575^23) + 1000/1.0575^23
PV = $1,110.98

Therefore, the call premium is the difference:

Call premium = PV if held to maturity - PV if called
Call premium = $1,104.25 - $1,110.98
Call premium = $-6.73

Since the bond is trading at a premium if held to maturity, it is not advantageous to call the bond. Therefore, the call premium is $0 (i.e. there is no premium). However, the question asks for the "call premium" even if it is $0, so the closest answer is A) $219.73, which is the call premium if the bond was trading at a discount (i.e. if the PV if called was less than the PV if held to maturity).

A 30-Year Bond with an 8% Coupon Has a Yield