Question

2. Answer the following questions regarding bond valuation.
   1. What is the price of a $1,000 par value bond with a 6% coupon rate paid semiannually, if the bond is priced to yield 4% and it has five years to maturity?
   2. Following a, what would be the price of the bond if the coupon is paid quarterly?
   3. Explain how the calculation changes, given semi-annual coupons in (a) versus quarterly coupons in (b).

Answer 1

a. We can use financial calculator for calculation of price of bond with below keystrokes.

coupons are paid semi-annually. so, maturity and yield will also be semi-annual.

N = semi-annual maturity = 5*2 = 10; I/Y = yield = 4%/2 = 2%; PMT = semi-annual coupon = $1,000*6%/2 = $30; FV = par value = $1,000 > CPT = compute > PV = price of the bond = $1,089.83

calculator will display PV as negative value because it's a cash outflow.

the price of the bond is $1,089.83.

b. N = maturity in quarters = 5*4 = 20; I/Y = yield = 4%/4 = 1%; PMT = semi-annual coupon = $1,000*6%/4 = $15; FV = par value = $1,000 > CPT = compute > PV = price of the bond = $1,090.23

there are 4 quarters in a year.

the price of the bond if the coupon is paid quarterly would be $1,090.23.

c. due to more compounding frequency, 4 in case of quarterly and 2 in case of semi-annually, maturity of the quarterly bond increases but yield and coupon decrease. with more no.of coupons in a year in quarterly compounding, coupons can again be reinvested which increases price of the bond.