Question

Heather Smith is considering a bond investment in Locklear Airlines. The $1,000 par value bonds have a quoted annual interest rate of 8 percent and the interest is paid semiannually. The yield to maturity on the bonds is 10 percent annual interest. There are 15 years to maturity. Compute the price of the bonds based on semiannual analysis. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Bond Price $ __________

Answer 1

Formula

Price of a bond is the present value of its cash flows, the cash flows being the coupon payments and face value repaid at maturity.

PV of annuity = P * [1 - (1 + r)^-n] / r,

where P = periodic payment.  Semiannual coupon payment = face value * coupon rate / 2 = $1,000 * 8% / 2 = $40

r = interest rate per period. This is 10%/2 = 5%. We divide by 2 to convert the annual YTM into semiannual YTM.

n = number of periods. This is 15*2 = 30. Total number of semiannual coupon payments = years to maturity * 2.

PV of coupon payments = $40 * [1 - (1 + 5%)^-30] / 5%

PV of coupon payments = $614.90

PV of lump sum = future value / (1 + (r/n))^n*t)

where r = annual rate, n = number of compounding periods per year, t = number of years

PV of face value repaid at maturity = $1,000 / (1 + (10%/2))^2*15

PV of face value repaid at maturity = $231.38

Price of bond = PV of coupon payments +  PV of face value repaid at maturity

Price of bond = $614.90 + $231.38

Price of bond = $846.28

Calculator

Price of bond is calculated using these inputs :

N = 30  

I/Y = 5

PMT = -40

FV = -1000

CPT --> PV

PV is calculated to be $846.28

Bond price is $846.28