Final answer:
To purchase Iolanda's Treasury bond, Luciana must calculate the present value using the bond's future cash flows discounted at the given yield. This involves using the present value formula to discount coupon payments and the bond's face value. The calculation depends on an inverse relationship between bond prices and interest rates, with bond prices decreasing when market rates rise.
Step-by-step explanation:
The question involves calculating the present value of a Treasury bond with a coupon rate of 2.35% and a face value of $100, with a maturity date on April 15, 2029. The bond is being considered for purchase on April 11, 2018, with a yield of 3.66% per annum compounded half-yearly. To calculate the present value or price Luciana is willing to pay for Iolanda's bond, we need to discount the future cash flows of the bond to their present value on the purchase date. The technique used to perform these calculations is primarily based on the present value (PV) formula where PV = FV / (1 + r/n)nt and involves summing the present values of all future cash flows, including coupon payments and the face value of the bond at maturity.
Considering our example of a simple two-year bond issued at $3,000 with an 8% interest rate, we would calculate the bond's present value by discounting each of the annual interest payments of $240 as well as the principal amount of $3,000 at the 8% discount rate. In case the discount rate increases to 11%, the bond's present value would decrease, since the discounting factor would be larger, making the bond sell for less than its face value. Hence, if the market interest rates rise, the price of the bond decreases and if the rates fall, the price of the bond increases, which reflects a bond's sensitivity to changes in the prevailing interest rates, highlighting the inverse relationship between bond prices and interest rates.
The present value calculations are crucial in determining the price one would be willing to pay for a bond at a given yield. This involves a series of calculations, which for this Treasury bond, would require the present value of coupon payments received semiannually and the present value of the face value to be received at maturity. Without the exact calculations and Table C2 in front of us, deciding among the given choices would require actually performing the present value computations.