Final answer:
The yield-to-maturity on a five-year, 4.50% semiannual coupon government bond priced at 98 per 100 of par value is calculated by equating the present value of future cash flows to the bond's current price, requiring iterative calculations or financial calculator functions.
Step-by-step explanation:
The yield-to-maturity (YTM) can be calculated for a five-year, 4.50% semiannual coupon payment government bond priced at 98 per 100 of par value. The bond has a face value of $1,000 and a coupon rate of 4.5%. As the coupons are paid semiannually, the annual coupon payments of $45 are split into two $22.50 payments. To find the YTM, one must solve for the discount rate that equates the present value of future cash flows (coupon payments and face value) to the current price of the bond. This typically requires a financial calculator or spreadsheet software, as the calculation involves solving for the rate in the present value of an annuity formula:
PV = C × (1 - (1 + r)^-n) / r + F / (1+r)^n
Where PV is the current bond price, C is the semiannual coupon payment, r is the discount rate (YTM), n is the number of periods, and F is the face value. In this scenario, n would be 10 as there are 10 six-month periods in five years.
Since the bond is discounted, the YTM will be higher than the coupon rate. You would iterate different discount rates in the formula until the calculated PV equals the actual bond price of $980 to find the exact YTM. Certain financial calculators and spreadsheet functions like RATE can handle these calculations more efficiently.