Question

Roadside Markets has a 6.75 percent coupon bond outstanding that matures in 10.5 years. The bond pays interest semiannually. What is the market price per bond if the face value is $1,000 and the yield to maturity is 7.2 percent

Answer 1

Step-by-step explanation:

Answer:

The market price per bond is $967.24

Step-by-step explanation:

Data Given;

present value = $1,000

Yield to maturity = 7.2%

number of years (t) = 10.5

semiannual (n) = 2

The present value is calculated using an excel sheet.

The manual calculation is given as

PV = Fv/(1+i/n)^nt

where i is the interest rate, t is the number of years and n is the period of interest

Subsituting into the formula, we have

PV = 1000/(1+0.072/2)^2*10.5

= 1000/1.0338

= $967.24

Answer 2

$967.24

Step-by-step explanation:

In order to determine the price of the bond we must determine its present value:

• future value = $1,000
• discount rate = 7.2% / 2 = 3.6%
• n = 10.5 years x 2 = 21 periods
• 20 cash flows of $67.50 / 2 = $33.75
• 1 final cash flow of $1,033.75

I like to use an excel spreadsheet because it generally is more exact that annuity tables, so I'll use the NPV function:

=NPV(3.6%, 33.75 ⇔ 20 times ... 1033.75) = $967.24

The current market price of the bond sis $967.24