Question

What is the price for a $1,000 par, 20 year, 8% coupon bond with semiannual payments and a 10% yield to maturity? (express your answer in dollars and cents. Do not include the $ symbol)

Answer 1

Face value of the bond = $1000

Coupon rate = 8% pa, paid semi-annually

Semi-annual coupon rate = 4%, Semi-annual coupon payment = 4%*1000 = 40

Time to maturity = 20 years

Since, the bond pays coupon semi-annually, therefore, no. of periods = 2*20 = 40

Annual YTM = 10%, Semi-annual YTM = r = 10%/2 = 5%

Following are the cash flows for this bond:

C₁ = C₂ = ....... = C₃₉ = 40; C₄₀ = 40+1000 = 1040

Present value of the bond is calculated using the below equation:

PV = 680.6816269 + 147.7275096 = 828.4091365

Answer -> 828.41

Method 2: Using BA ii plus calculator

N = 40, I/Y = 5, PMT = -40, FV = -1000; CPT -> PV

We get PV = 828.4091365

Answer -> 828.41

Method 3: Usinf Excel

Using the PV Function in Excel where, rate = 5%, nper = 40, pmt = -40, fv = -1000

=PV(5%, 40, -40, -1000) = 828.409136460056

Answer -> 828.41