Question

Regatta Ltd has six-year bonds outstanding that pay an 8.25 percent coupon rate. The par value of the bond is $1000. Investors buying the bond today can expect to earn a yield to maturity of 6 percent. What should the company's bonds be priced at today? Assume annual coupon payments. (Round to the nearest dollar.)

A. $923
B. $1,110
C. $1,014
D. $972

Answer 1

The price of Regatta Ltd's bonds with a coupon rate of 8.25 percent, a par value of $1,000, and a yield to maturity of 6 percent, is calculated using present value formulas and is approximately $1,014.

Step-by-step explanation:

The question is asking to determine the current price of Regatta Ltd's bonds that have a coupon rate of 8.25 percent, a par value of $1,000, and a yield to maturity of 6 percent, with the assumption of annual coupon payments. To find the bond price, we need to discount the future cash flows (annual interest payments and the principal amount at maturity) back to the present value at the current yield to maturity of 6 percent. The bond's annual interest payment can be calculated as 8.25 percent of the par value, which is $82.50. Since the coupon rate is higher than the current yield to maturity, the bond will sell for more than its face value.

The process of pricing a bond involves using the formula for the present value of an annuity to calculate the present value of the interest payments, and the present value of a lump sum to calculate the present value of the final principal repayment.

Using a financial calculator or a bond pricing formula, we can determine that the price of the bond today, rounded to the nearest dollar, should be Option C, $1,014.

Answer 2

Regatta Ltd's bonds should be priced at $1,110.63 today. The Option B is correct.

`Price = (C * (1 - (1 + r)^(-n)) / r) + (FV / (1 + r)^n)`. We will use this to calculate the price of Regatta Ltd's six-year bonds with an 8.25 percent coupon rate and a yield to maturity of 6 percent.

C = Annual coupon payment = $1000 * 8.25% = $82.50

r = Yield to maturity = 0.06

n = 6 and FV = $1000

`Price = ($82.50 * (1 - (1 + 0.06)^(-6)) / 0.06) + ($1000 / (1 + 0.06)^6)`

= ($82.50 * (1 - 0.704961) / 0.06) + $704.96054

= $24.3407175 / 0.06

= $405.678625 + $704.96054

= $1,110.63917

= $1,110.63

Therefore, the bonds should be priced at $1,110.63 today.