Question

eddie bauer’s 5 year annual coupon bond is priced at $984.56. The bond has a $1000 face value and a yield to maturity of 6.5 percent. What is the coupon rate?

6.74%

6.34%

2.50%

3.17%

Answer 1

YTM :

YTM is the rate at which PV of Cash inflows are equal to Bond price when the bond is held till maturity. Yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until it matures. Yield to maturity is considered a long-term bond yield but is expressed as an annual rate

Let X be the coupon amount.

at YTM PV of CFs will be equal to Bond Price.

Year	CF	PVF @6.5%	PV of CFs
1	X	0.9390	0.9390X
2	X	0.8817	0.8817X
3	X	0.8278	0.8278X
4	X	0.7773	0.7773X
5	X	0.7299	0.7299X
5	$ 1,000.00	0.7299	$ 729.88
Price of Bond			4.1557X + 729.88

Thus 4.1557X + 729.88 = 984.56

4.1557X = 984.56 - 729.88

= 254.68

X = 254.68 / 4.1557

= $ 61.28

Thus Coupon rate = Coupon Amount / Face Value

= $ 61.28 / $ 1000

= 0.06128 I.e 6.1

Proof:

At YTM, PV of CFs will be equal to Bond Price.

Year	CF	PVF @6.5%	PV of CFs
1	61.28	0.9390	57.54
2	61.28	0.8817	54.03
3	61.28	0.8278	50.73
4	61.28	0.7773	47.63
5	61.28	0.7299	44.73
5	$ 1,000.00	0.7299	729.88
Price of Bond			984.54