Question

Alice bought a bond selling at 1030 that had an 8% coupon rate. At that time market rates were 5%. The bond matures in 8 years. Its yield to maturity is

Answer 1

Answer: YTM = 7.50%

Calculation & Explanation:

YTM of a bond is that discount rate which equates the PV of the
cash flows from the bond with its current price.
The cash flows are:
*The maturity value of $1000 payable after 8 years, and
*The annual interest of $80 for 8 years, which is an annuity
Such a discount rate has to be found out by trial and error
till the PV of cash flows equals $1030.
Discounting at 7%:
PV of cash flows = 1000/1.07^8+80*(1.07^8-1)/(0.07*1.07^8) =	$              1,059.71
When discounted at 8% [same as coupon rate] the PV of cash flows =	$              1,000.00
So YTM, which gives PV = $1030 lies between 7% and 8%
YTM = 7%+1%*(1059.71-1030)/(1059.71-1000) =	7.50%