Final answer:
The present value of a bond is calculated by discounting its future cash flows back to their current value. The example provided uses a simple two-year bond to demonstrate how changing discount rates affect the present value. Calculations show the present value of interest payments and principal based on both 8% and 11% discount rates.
Step-by-step explanation:
The question asks about calculating the present value (PV) of a semi-annual coupon bond issued by Freechoice Telecom. To find the PV, we look at the future cash flows from the bond and discount them back to their value today using a discount rate. The example given in the question illustrates the concept using a simple two-year bond with an 8% interest rate, showing how the PV changes when the discount rate is adjusted. Essentially, the value of future payments (both the interest payments and the return of principal at maturity) is determined using the present value formula, which incorporates the time value of money concept.
For the simple two-year bond issued for $3,000 with an 8% interest rate, the first year's interest is $240 (3000 × 0.08) and the second year's payment will be the same interest plus the principal amount, totaling $3,240. If the discount rate is 8%, the present value calculations are:
- First year interest PV: $240 / (1 + 0.08)¹ = $222.20
- Second year payment PV: $3,240 / (1 + 0.08)² = $2,777.80
- Total PV at 8% discount rate: $222.20 + $2,777.80 = $3,000
When the discount rate changes to 11%, these amounts will decrease due to the higher discount applied. Similarly, the $1022 trading price of the Freechoice Telecom bond is its current market value, which considers the bond's expected future payments and the market's required rate of return.