Question

8. Croft Inc, bonds have a par value of $1,000. The bonds have a 4% coupon rate and will mature in 10 years. Assume the bond is semi-annual a. Calculate the price if the yield to maturity on the bonds is 7, 8, and 9 percent, respectively. b. Explain the impact on price if the required rate of return decreases. c. How does the relationship between the coupon rate and the yield to maturity determine how a bond's price will compare to it par value?

Answer 1

a. We can use financial calculator for calculation of price with below key strokes:

Coupon is semi-annual. so maturity will be double and coupon and yield to maturity will be half.

N = maturity = 10*2 = 20; I/Y = yield to maturity = 7%/2 = 3.5%; PMT = coupon = $1,000*4%/2 = $20; FV = par value = $1,000 > CPT = compute > PV = price = $786.81

Price at yield to maturity of 8%

N = maturity = 10*2 = 20; I/Y = yield to maturity = 8%/2 = 4%; PMT = coupon = $1,000*4%/2 = $20; FV = par value = $1,000 > CPT = compute > PV = price = $728.19

Price at yield to maturity of 9%

N = maturity = 10*2 = 20; I/Y = yield to maturity = 9%/2 = 4.5%; PMT = coupon = $1,000*4%/2 = $20; FV = par value = $1,000 > CPT = compute > PV = price = $674.80

b. If the required rate of return decreases then price will increase. From the calculations in part (a), we can see that as yield to maturity increases from 7% to 9%, price decreases from $786.81 to $674.80.

Price at 6% yield to maturity will higher then 7% yield to maturity.

N = maturity = 10*2 = 20; I/Y = yield to maturity = 6%/2 = 3%; PMT = coupon = $1,000*4%/2 = $20; FV = par value = $1,000 > CPT = compute > PV = price = $851.23

c. If the yield to maturity is lower than the coupon value then bond's price will be higher than its par value and bond will trade at premium. this is because yield to maturity is the return required by the investor. if yield to maturity is 7% and bond is paying coupon of 9% then price will be higher than par value of $1,000 because investor is getting coupon of 9% higher than required return of 7%.

If the yield to maturity is higher than the coupon value then bond's price will be lower than its par value and bond will trade at discount. this is because yield to maturity is the return required by the investor. if yield to maturity is 7% and bond is paying coupon of 5% then price will be lower than par value of $1,000 because investor is getting coupon of 5% lower than required return of 7%.