a. Based on a yield to maturity of \(12.5 \%\) for 10-year Treasury securities, demonstrate that the price of a \(13 \%\) coupon, 10 -year Treasury would be \(\$ 102.8102\) per \(\$ 100\) par value if all cash flows are discounted at \(12.5 \%\).

b. Based on the theoretical spot rates in Table 15-2, show that the theoretical value would be \(\$ 102.9304\) per \(\$ 100\) par value.

c. Explain why the market price for this Treasury security would trade close to its theoretical value.

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Table 15-2 Theoretical Value of a 10-Year, 14% Coupon Treasury Based on the Theoretical Spot Rate Cash Flow Required Semiannual Maturity per $100 Par Yield of 0.125 Yield Present Value 0.5 0.08000 0.04000 6.7308 1.0 0.08300 0.04150 6.4533 1.5 2.0 2.5 0.08930 0.04465 6.1402 0.09247 0.04624 5.8423 0.09468 0.04734 5.5547 3.0 0.09787 0.04894 5.2554 3.5 9.10129 0.05065 4.9534 4.0 0.10592 0.05296 4.6324 4.5 0:10850 0:05425 4.3512 5.0 0.11021 0.05511 4.0939 5.5 0,11175 0.05588 .......3.8491 6.0 0.11584 0.05792 3.5618 6.5 0.11744 0.05872 3.3338 7.0 0.11991 0.05996 3.0979 7.5 0.12405 0.06203 2.8384 8.0 0.12278 0.06139 2.6983 8.5 7 0.12546 0.06273 2.4883 9.0 7 0.13152 0.06576 2.2245 9.5 7 0.13377 0.06689 2.0458 10.0 Total 107 0.13623 0.06812 28.6433 $108.7889