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
<em><u>First we calculate the price of the bond:</u></em>
C 38.000 1,000 x 7.6% / 2
time 40 (20 years x 2payment per year )
rate 0.033
PV $837.2785
Maturity 1,000.00
time 40.00
rate 0.033
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