A 10-year annual payment corporate bond has a market price of $1,050. It pays annual interest of $100 and its required rate of return is 9 percent. By how much is the bond mispriced?

Question

Quizplus · Accepted Answer

To calculate if the bond is mispriced, we need to calculate the bond's intrinsic value or fair value. The intrinsic value of a bond is the present value of all future cash flows (coupon payments and principal repayment) discounted at the required rate of return.

In this case, the bond pays $100 per year for ten years and returns the par value of $1000 at maturity. We can calculate the present value of each cash flow using the formula:

PV = CF / (1 + r)^n

where PV is the present value, CF is the cash flow, r is the required rate of return, and n is the number of periods.

Using a financial calculator or spreadsheet, we can calculate the intrinsic value of the bond as follows:

PV of coupon payments = $100 * [(1 - 1/(1 + 0.09)^10) / 0.09] = $634.94

PV of principal repayment = $1000 / (1 + 0.09)^10 = $422.63

Intrinsic value of bond = PV of coupon payments + PV of principal repayment = $1057.57

Therefore, the bond is underpriced by $7.43 ($1057.57 - $1050). However, this calculation assumes that the required rate of return is 9 percent, which may not be accurate. If the actual required rate of return is lower than 9 percent, the bond would be overpriced; if it is higher, the bond would be more underpriced.

A 10-Year Annual Payment Corporate Bond Has a Market Price