Question

A 20-year maturity, 7.6% coupon bond paying coupons semiannually is callable in seven years at a call price of $1,170. The bond currently sells at a yield to maturity of 6.6% (3.30% per half-year).
What is the yield to call?

What is the yield to call if the call price is only $1,120?

What is the yield to call if the call price is $1,170 but the bond can be called in four years instead of seven years?

Answer 1

Answer:

a) YTC 5.895%

b) YTC being call at 1,120 6.6853%

c) we change time and call price 1,170 = 5.33189%

Explanation:

we have to calculate with excel for the PV of the coupon payment and the call price which matches the the

First we calculate the price of the bond:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 38.000 1,000 x 7.6% / 2

time 40 (20 years x 2payment per year )

rate 0.033

$38 \times \frac{1-(1+0.033)^{-40} }{0.033} = PV$

PV $837.2785

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   40.00

rate  0.033

$\frac{1000}{(1 + 0.033)^{40} } = PV$  

PV   272.89

PV c $837.2785

PV m  $272.8897

Total $1,110.1682

Now we solve for the YTC

given a price of 1,110 we receive an annuity of 38 dollars during 7 years and recieve 1,170

we do it in excel:

=PV(A2;14;38)+1,110.17/power(1+A2;28)

the first part is the coupon payment the second maturity

now we solve using goal seek to make this formula worth 1,170 changin a2 which is when we put a rate reference

a) 0.058950255

b)

=PV(A2;14;38)+1,110.17/power(1+A2;28)

we determinate our target as 1,120

0.066853426

c) we change time:

=PV(A2;8;38)+1,110.17/power(1+A2;8)

0.053318904