Caldwell Ltd sold an issue of 30-year, $1000 par value bonds to the public.The bonds carry a 10.85% coupon rate and pay interest semi-annually.It is now 12 years later.The current market rate of interest on the Caldwell bonds is 8.45%.What is the current market price (intrinsic value)of the bonds? Round off to the nearest $1.

Question

Quizplus · Accepted Answer

To calculate the present value of the bond, we need to find the present value factor for each interest payment and the present value factor for the principal payment at maturity. Using the formula:

Present value factor = 1/ (1 + r)n

where r is the market rate of interest and n is the number of periods (in this case, number of semi-annual interest payments or years left until maturity)

For the interest payments, we have: 
Present value factor for first interest payment = 1/ (1 + 0.04225)^24 = 0.3984
Present value factor for second interest payment = 1/ (1 + 0.04225)^23 = 0.4203
Present value factor for third interest payment = 1/ (1 + 0.04225)^22 = 0.4431
.....
Present value factor for fifteenth interest payment = 1/ (1 + 0.04225)^10 = 0.7089

For the principal payment at maturity, we have: 
Present value factor for principal payment = 1/ (1 + 0.04225)^30 = 0.1698

To find the present value of the bond, we need to multiply each present value factor by the corresponding cash flow (which is $1000 for the principal payment and $54.25 for each interest payment). Then we add up all the present values to get the total present value of the bond:

Present value = ($54.25 x 0.3984) + ($54.25 x 0.4203) + ... + ($54.25 x 0.7089) + ($1000 x 0.1698) = $1220

Therefore, the current market price (intrinsic value) of the bond is $1220. The closest answer choice is C.

Caldwell Ltd Sold an Issue of 30-Year, $1000 Par Value