Final answer:
To determine the cash a company will receive when they issue bonds, the present discounted value (PDV) must be calculated. This involves discounting future bond payments to their present value using the current discount rate. Changes in interest rates affect the bond's PDV, reflecting the opportunity cost of capital for an investor.
Step-by-step explanation:
Calculating the Present Discounted Value of a Bond
To figure out how much discount is worth when a company issues bonds, one must calculate the bond's present discounted value (PDV). This is the present value of a stream of future payments the bond will generate, which include periodic interest payments and the repayment of the principal amount at maturity. To perform this calculation, the present value formula is applied to each future payment, discounting them at the relevant interest rate.
Example Calculation
Consider a two-year bond issued at $3,000 with an 8% interest rate. It pays $240 in interest each year and repays the $3,000 principal at the end. To find the bond's present value at an 8% discount rate, calculate the present value of each payment separately using the formula for present value: PV = Payment / (1 + r)^n, where 'r' is the discount rate and 'n' is the number of periods until the payment is received. The sum of these present values represents the total present discounted value of the bond.
If the discount rate changes to 11%, the bond's value would decrease, reflecting the investor's opportunity cost of capital being higher. That is, the investor could get 11% elsewhere, so they would pay less for a bond that pays 8%.
Factors Affecting the Discount Rate
Choosing the right discount rate to use for calculating the PDV of a bond can be complex. It must reflect the opportunity cost of capital, incorporating factors such as potential capital gains, current interest rates, and expected dividends from other investments. These factors affect the attractiveness of the bond and, consequently, the price investors are willing to pay for it.