Question

lincoln park company has a bond outstanding with a coupon rate of 5.88 percent and semiannual payments. the yield to maturity is 4.5 percent and the bond matures in 23 years. what is the market price if the bond has a par value of $2,000?

Answer 1

The market price of the bond can be calculated using the present value formula. The bond has a coupon rate of 5.88 percent, semiannual payments, and a yield to maturity of 4.5 percent.

Step-by-step explanation:

The market price of the bond can be calculated using the present value formula. The bond has a coupon rate of 5.88 percent, semiannual payments, and a yield to maturity of 4.5 percent. First, calculate the number of periods, which is the product of the number of years (23) and the number of periods per year (2). In this case, there are 46 periods. Next, calculate the coupon payment per period by multiplying the coupon rate by the par value and dividing by the number of periods per year (2). In this case, each coupon payment is $58.80. Finally, calculate the present value of the bond by discounting each coupon payment and the final principal payment to the present. The market price of the bond is the sum of the present values of all these cash flows. The present value formula used is:

Market Price = (Coupon Payment / (1+Yield)^Period) + (Coupon Payment / (1+Yield)^(Period-1)) + ... + (Coupon Payment / (1+Yield)) + (Final Principal / (1+Yield)^Period)

Substituting the values, the market price of the bond is:

Market Price = ($58.80 / (1+0.045)^1) + ($58.80 / (1+0.045)^2) + ... + ($58.80 / (1+0.045)^46) + ($2000 / (1+0.045)^46)

Answer 2

The market price of the bond is $1,852.41.

Step-by-step explanation:

The market price of a bond can be calculated using the present value formula. In this case, we have a bond with a par value of $2,000, a coupon rate of 5.88%, semiannual payments, a yield to maturity of 4.5%, and a maturity period of 23 years.

To calculate the market price, we need to discount the semiannual coupon payments and the final par value using the yield to maturity. Each semiannual coupon payment can be calculated as $2,000×5.88% / 2 = $58.80.

The number of semiannual periods remaining until maturity is 23 × 2 = 46. The present value of the coupon payments can be calculated as

`\[ 58.80 * (1 - \left(1 + (4.5\%)/(2)\right)^(-46))/((4.5\%)/(2)) = 1,067.02 \]`

The present value of the final par value can be calculated as

`\[ (2,000)/(\left(1 + (4.5\%)/(2)\right)^(46)) = 785.39 \]`

Therefore, the market price of the bond is $1,067.02 + $785.39 = $1,852.41.