Question

Harrison co. issued 17-year bonds one year ago at a coupon rate of 6.8 percent. the bonds make semiannual payments. if the ytm on these bonds is 5.4 percent, what is the current dollar price assuming a $1,000 par value? (do not round intermediate calculations and round your answer to 2 decimal places,

e.g., 32.16.) current bond price $ 1,148.73 correct

Answer 1

To find the current price of the 17-year bond with a 6.8 percent coupon rate and a YTM of 5.4 percent, one needs to calculate the present value of all the remaining coupon payments plus the par value at maturity, discounted at the current YTM. The calculation considers semiannual payments and the inverse relationship between interest rates and bond prices.

Step-by-step explanation:

The question asks for the current dollar price of 17-year bonds that were issued one year ago with a 6.8 percent coupon rate and now have a yield to maturity (YTM) of 5.4 percent. We need to calculate the present value of the remaining semiannual payments, including the principal repayment at maturity, discounted at the new YTM. This involves summing the present value of all future cash flows, which include semiannual interest payments and the final par value payment. The formula for the present value of an annuity is used for the interest payments, and a present value of a lump sum formula is used for the final par value payment.

When calculating bond prices, there are a few factors that one must consider. Firstly, bonds make payments in the form of interest, known as coupon payments, which represent a series of cash flows over time. The par value is the amount that will be returned to the bondholder upon maturity, which is typically $1,000 for corporate bonds. The present value of these cash flows is calculated using the YTM, which reflects the total return expected on a bond if it is held to maturity. Interest rates affect the bond prices inversely; when they rise, existing bonds with lower coupon rates are worth less and when they fall, these bonds are worth more.

For the provided bond, assuming semiannual payments, the formula for the present value of the annuity would take the coupon rate divided by two (for semiannual payments), multiplied by the par value, and then discounted by the YTM divided by two, over the number of periods left until maturity. The present value of the lump sum would be calculated by taking the par value and discounting it by the same YTM over the period until maturity.

Answer 2

Answer: The current market price of the bond is $1148.73.

We have:

Face Value (FV) 1000

Coupon rate 6.80%

YTM 5.40%

No. of years 16

Compounding Semi-Annual

We take 16 as the number of years since the bonds were issued a year ago.

We calculate ytm per period, coupon rate, number of periods as follows:

Coupon interest per period (C)
`34 = (1000*0.068)/(2)`

YTM per period (r)
`2.70% = (0.054)/(2) *100`

Number of periods (n)
`32 =16*2`

The bond's current market price is calculated as :

`\mathbf{CMP_(bond) = C*\left ( (1-(1+r)^(n))/(r) \right )}+(FV)/((1+r)^n)`

Substituting the values we get,

CMP_{bond} = 34*\left ( \frac{1-(1.027)^{32}}{0.027}\right )}+\frac{1000}{(1.027)^32}[/tex]

CMP_{bond} = 34*21.247040283 +\frac{1000}{2.345601308 }[/tex]

`CMP_(bond) = 722.3993696+426.3299124`

mathbf{CMP_{bond} = 1,148.73}