Question

Microhard has issued a bond with the following characteristics:

Par: $1,000
Time to maturity: 8 years
Coupon rate: 11 percent
Semiannual payments

Calculate the price of this bond if the YTM is (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.):

Answer 1

At Yield to maturity = 11%

Price = $1,000

Step-by-step explanation:

As for the provided information we have:

Par value = $1,000

Interest each year = $1,000
`*` 11% = $110

Effective interest rate semiannually = 11%/2 = 5.5% = 0.055

Since it is paid semiannually, interest for each single payment = $110
`*` 0.5 = $55 for each payment.

Time = 8 years, again for this since payments are semi annual, effective duration = 16

Price of the bond =
`C * ((1 - (1)/((1+i^n))) )/(i) + (M)/((1 + i)^n)`

Here, C = Coupon payment = $55

i = 0.055

n = Time period = 16

M = Maturity value = Par value = $1,000

Therefore, if yield to maturity = 11% then,

P =
`55 * (1 - (1)/((1 + 0.055)^1^6) )/(0.55) + (1,000)/((1 + 0.55)^1^6)`

= $1,000