Question

What is the yield-to-maturity of a $1,000, 7% semi-annual coupon bond that matures in 20 years and currently sells for $990?

7.7%

7.1%

3.55%

14.15%

Answer 1

YTM is that discount rate which equates the PV of the
expected cash flows from the bond with its current price.
The expected cash flows are:
*The maturity value of the bond of $1000 at EOY20, and
*The semiannual interest payments of $35 receivable for
40 half years. It is an annuity.
Such a discount rate is to be found out by trial and error.
But to start with, the YTM can be found out by using the
approximation formula:
YTM = ((I+(FV-P)/n)/((FV+P)/2)
where
FV face value, P = Current price and n = number of years
YTM = ((70+(1000-990)/20)/((1000+990)/2) =	7.09%
For the exact YTM, the trial and error approach is required.
Discounting with 8%--Half year 4%:
Price = 1000/1.04^40+35*(1.04^40-1)/(0.04*1.04^40) =	$          901.04
Discounting with 7%--Half year 3.5%, the price = Face value =	$ 1,000.00
Helf yearly discount rate, by simple interpolation = 3.5%+0.5%*(1000-990)/(1000-901.04) =	3.55%
YTM = 3.55%*2 =	7.10%