Final answer:
To calculate the cost, x, for a company to match obligations of $10,000 payments for two years, the present values of a one-year 4% coupon bond at a 5% yield and a two-year 6% coupon bond at an 8% yield must be determined. The given equations 10000 = 1.06y and 1.04x + 1.06y = 10000 are then solved to find x and y, representing the cost of the bonds needed.
Step-by-step explanation:
To calculate the cost, x, that a company must pay to exactly match its obligation of paying $10,000 at the end of each year for two years, we need to consider the present value of both the one-year and the two-year bonds provided.
For the one-year 4% annual coupon bond with a yield rate of 5%, we would see the present value as a function of x using the formula: PV = C / (1+y) = (0.04 * 10000) / (1 + 0.05) = 400 / 1.05, where C is the coupon payment and y is the yield. However, since the obligation payment is at the end of the year, the present value would be the full $10,000 expected at the year's end divided by (1 + 0.05) = 10000 / 1.05.
For the two-year 6% annual coupon bond with a yield rate of 8%, we can use the formula: PV = C / (1+y) + C / (1+y)^2 + P / (1+y)^2, where C is the coupon payment, P is the principal amount, and y is the yield. Therefore, the present value of the bond providing a $10,000 payment at the end of each year would be: 600 / 1.08 + (600 + 10000) / (1.08)^2.
By combining these calculations and given the two equations 10000 = 1.06y and 1.04x + 1.06y = 10000, we would solve for x and y to find the total present value that would match the company's obligation.