Question

A firm raises capital by selling ​ $18,000 worth of debt with flotation costs equal to 1% of its par value. If the debt matures in 10 years and has an annual coupon onterest rate of 12%, what is th ebond's YTM?

The bond's YTM is _______%/

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Answer 1

The bonds proceeds = 18000*99% =	$        17,820
YTM is that discount rate which equates the PV of
expected cash proceeds from the bonds if it is held
till maturity.
The expected cash flows are:
1) The maturity value of the bond of $18000
receivable at EOU 10, and
2) The annual interest payment of $2160 [18000*12%] which is a ten year annuity
The discount rate which the equates PV of the
above cash flows with $17820, is the YTM.
It has to be found out by trial and error by trying
different discount rates.
Discounting with 13%:
PV of the cash flows = 18000/1.13^10+2160*(1.13^10-1)/(0.13*1.13^10) =	$ 17,023.28
PV with 12% would be the face value =	$ 18,000.00
YTM lies between 12% and 13%.
By simple interpolation YTN = 12%+1%*(18000-17820)/(18000-17023.28) =	12.18%