Question

F 1What is the yield to maturity on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887.00? That sells for $1,134.20? What does the fact that a bond sells at a discount or at a premium tell you about the relationship between and the bond’s coupon rate?

Answer 1

Answer:

When the bond is sale at premium, it means the market rate is lower than coupon rate. So investor purchase the bond a higher price until the bond yield equal the market rate

If sold at discount, the market rate is higher than coupon rate. This means it's sold below face value to increase the bond yield to market rate.

YTM if market price is 887 =  10.7366190%

YTM if market price is 1,134.2= 7.1764596%

Explanation:

For the YTM we can calculate an estimated using the following formula:

$YTM = \frac{C + \frac{F-P}{n }}{\frac{F+P}{2}}$

Where:

C= coupon payment 1,000 x 9% = 90

F= face value of the bonds = 1000

P= market price = 887

n= years to maturity = 10

YTM =  10.7366190%

$YTM = \frac{C + \frac{F-P}{n }}{\frac{F+P}{2}}$

C= 90

F= 1000

P= 1134.2

n= 10

YTM = 7.1764596%

A more precise answer can be achieve using excle or a financial calculator.