Question

The Sisyphean Company has a bond outstanding with a face value of $5,000 that reaches maturity in nine years. The bond certificate indicates that the stated coupon rate for this bond is 8% and that the coupon payments are to be made semiannually Assuming that this bond trades for $5,466, then the YTM for this bond is closest to O A 53% OB. 6.615 OC. 7.93% OD. 9.25% line

Answer 1

YTM based on approximate formula = ((400+(5000-5466)/9))/((5000+5466)/2)) =	6.65%
YTM based on trial and error method:
YTM is that discount rate for which the
PV of the expected cash flows from the
bond will equal its price [here $5466]
The expected cash flows are:
*maturity value of $5000 receivable at
EOY 9.
*the semiannual interest of $200 [18 half years]
which is an annuity.
Such a discount rate [half yearly] is to be found
out by trial and error.
Discounting with 3% half yearly:
PV = 5000/1.03^18+200*(1.03^18-1)/(0.03*1.03^18) =	$      5,687.68
Discounting with 3.5% half yearly:
PV = 5000/1.035^18+200*(1.035^18-1)/(0.035*1.035^18) =	$      5,329.74
So the halfyearly discounting rate lies between 3% and
3.5%.
The required half yearly rate = 3%+0.5%*(5687.68-5000)/(5687.68-5329.74) =	3.31%
YTM = 3.31*2 = 6.62%
Answer: Option [C] 6.61%
Difference in calculation and option [C] is due to
approximation.