Question

Suppose you buy a bond for $1230 with an 11.3% coupon maturing in 7 years.

Required:
a. Calculate the maturity.
b. What is the yield to maturity if the bond pays quarterly.
c. Explain why the yield to maturity is higher or lower than the coupon.

Answer 1

a. 7.03%

b. 7.10%

c. Yield to maturity is lower than the coupon because the price is more than the face value.

Step-by-step explanation:

a. Coupon amount = 11.3% * 1000 = 113

FV = 1000

PV = -1230,

PMT = 113

N = 7

Yield to maturity = I/Y(FV, -PV, PMT, N) using a financial calculator

Yield to maturity = I/Y(1000, -1230, 113, 7)

Yield to maturity = 0.070280

Yield to maturity = 7.03%

b. Coupon amount = 11.3% * 1000 = 113 /4 = 28.25

FV = 1000

PV = -1230,

PMT = 28.25

N = 7*4 = 28

Yield to maturity = I/Y(FV, -PV, PMT, N) using a financial calculator

Yield to maturity = I/Y(1000, -1230, 28.35, 28)*4

Yield to maturity = 0.01775426*4

Yield to maturity = 0.07101704

Yield to maturity = 7.10%

c. Yield to maturity is lower than the coupon because the price is more than the face value. The bond will sell at premium when YTM is greater than coupon rate. This happens because the bond is paying a return more than the market is offering.