Question

SHOW WORK PLEASE!!!!!!!

1. Complete problem: Yield to Maturity for Annual Payments XYZ Corporation’s bonds have 14 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 10%. The bonds sell at a price of $950. What is their yield to maturity? Show your work.

Answer 1

Approximate YTM = ((I+(RV-MV)/n))/((RV+MV)/2))
where
I = Annual interest
RV = Redemption value
MV = Market value
n = number of years
Substituting values
Approximate YTM = ((100+(1000-950)/14))/((1000+950)/2)) =	10.62%
YTM by trial and error:
YTM is that discount rate which equates the PV of the
expected cash flows form the bond [if it is held till maturity]
with the price.
The expected cash flows are:
*the periodic interest of $100 for 14 years, which is an annuity
and
*the redemption value of $1000 receivable at EOY 14.
Such a discount rate has to be found out by trial and error by
varying the interest rates to get PV of cash flows equal to $950.
Discounting with 10%:
As the coupon rate is also 10%, the PV of cash flows will be
$1,000
Discounting with 11%:
PV of cash flows = 1000/1.11^14+100*(1.11^14-1)/(0.11*1.11^14) =	$              930
PV of 950 will be got between 10% and 11%.
By simple interpolation, the discount rate [YTM] = 10%+1%*(1000-950)/(1000-930) =	10.71%
YTM = 10.71%