Question

Digital Empire has 5 percent coupon bonds on the market with 15 years to maturity, and the par value of $1,000. At what price should the bonds be selling for if YTM is 7%? (note: coupons are paid semi-annually) Had the bond been selling at $1,022.50, what would be the YTM (assuming the same coupon, maturity and par value)? Based on your answers above, what is the relationship between YTM and bond price

Answer 1

Maturity	15 years
Par value of bond	$1,000
Coupen rate annually	5%
Semi annually coupen rate	2.5%
Total period =	30
Coupen Amount	1000* 2.5%
	$        25.00
YTM is per year =	7.0%
YTM for the period =	3.50%
PVAF ( 3.5% , 30)    =	1/(1.035)^1 + 1/1.35)^2 + 1/(1.35)^3……………. 1/(1.035)^30
	18.3920
PVF ( 3.5%, 30)	1/1.035^30
	0.3562
Price of bond   =	25* 18.3920 +1000*1/(1.05)^30
	$     459.80	+1000*.3563
	$     816.00
If the bond is selling 1022.50 then YTM should have been lower than coupen rate because if coupen rate and YTM becomes same then price of bond will be its facevalue
hence let YTM be 4%
YTM for the period =	2%
PVAF ( 2% , 30)    =	22.3964
PVF ( 2%, 30)	0.5521
Price of bond   =	25* 22.3964 +1000*1/(1.05)^30
	$ 1,112.01
Price of bond at 2% Ytm is	1112.01
Price of bond at 3.5% Ytm is	816
Hence currect YTM =	2% + {( 1112.01 -1022.50) / (1112.01 - 1022.50) + (1022.50 - 816)} *(3.5 %-2 %)
	2% +   (89.51/ 89.51+206.5)*1.5
	2% + .302388 * 1.5
	2 % + 0.4535
	2.45%
YTM for the year =	4.90%

Relation ship of YTM and Price is If ytm Increases Price wil decrease and vice versa