Question

A bond that settles on June 7, 2016, matures on July 1, 2036, and may be called at any time after July 1, 2026, at a price of 161. The coupon rate on the bond is 7.4 percent and the price is 173.50. What are the yield to maturity and yield to call on this bond? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Answer 1

YTM: 2.64%

YTC: 3.66%

Step-by-step explanation:

The market price is the discounted price of the maturity and coupon payment at market rate:

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 3.700

time 40

rate 0.013221404

`3.7 * (1-(1+0.0132214040405666)^(-40) )/(0.0132214040405666) = PV\\`

PV $114.3676

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 100.00

time 40.00

rate 0.013221404

`(100)/((1 + 0.0132214040405666)^(40) ) = PV`

PV 59.13

PV c $114.3676

PV m $59.1324

Total $173.5000

Then we do the same calcaulation with the 161 call price being the maturity and adjusting time for 10 years (20 payment)

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 3.700

time 20

rate 0.018309924

`3.7 * (1-(1+0.0183099243918235)^(-20) )/(0.0183099243918235) = PV\\`

PV $61.4988

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 161.00

time 20.00

rate 0.018309924

`(161)/((1 + 0.0183099243918235)^(20) ) = PV`

PV 112.00

PV c $61.4988

PV m $112.0021

Total $173.5009

Now we got the semiannual rate we simply multiply by two to convert into annual rates.

YTM:

0.013221404 X 2 = 0,026442808‬ = 2.64%

YTC:

0.0183099243918235 X 2 = 0,036619848783647‬ = 0.0366 = 3.66%