Question

Use the financial calculator to estimate the Yield to maturity on a 10% coupon Rate Bond maturing in 30 years to be paid annually if the bond is selling at the following prices:

Price of Bond ($)	YTM (%)
1,100
1000
900

a. Describe the relationship of the YTM, the coupon rate and the price of a bond.

Answer 1

Sol :

Face value (F) = 1,000

Bond price (P) = 1,100, 1000 and 900

Maturity time (n) = 30 years

Coupon rate (C) = 10%

Coupon payment, 10% of 1,000 = 100

Yield to maturity (YTM) = [C + (F-P)/ n] / (F +P)/2] x 100 (1)

i) P = 1,100

YTM = [100 + (1,000 - 1,100)/ 30]/ (1,000 +1,100)/2] x 100

YTM = 96.67/ 1,050 x 100

YTM  = 9.21%

ii) P = 1,000

YTM = [100 + (1,000- 1,000)/30]/ (1.000 +1,000)/2] x 100

YTM = 100/ 1,000 x 100

YTM = 10%

iii) P = 900

YTM = [100 + (1,000 - 900)/ 30]/ (900 +1,000)/2] x 100

YTM = 103.333/ 950 *100

YTM = 10.88%

Relationship between YTM, coupon rate and price of a bond.

When YTM is less than coupon rate, the bond sells at a premium, that is, the price of the bond would be higher than its face value.

When YTM equals to coupon rate, the bond sells at par. That is, the price of the bond would be equal to its face value.

When YTM is greater than coupon rate, the bond sells at a discount. That is, the price of the bond would be less than its face value.