Final answer:
The bond's current yield is 4%. The yield to maturity is approximately 3.92%. The yield to call is approximately 5.51%. The taxable equivalent yield for an investor in the 36% marginal tax bracket is 6.12%.
Step-by-step explanation:
To compute the bond's current yield, we divide the annual coupon payment by the bond's market price. The annual coupon payment can be calculated by multiplying the coupon rate (3.90%) by the bond's par value ($5,000), which results in $195. The bond's market price is given as 97.45% of the par value, so we multiply $5,000 by 0.9745, resulting in $4,872.50. Dividing the annual coupon payment by the market price, we get 195/4,872.50 = 0.04, or 4%.
To compute the bond's yield to maturity, we need to calculate the present value of all future cash flows, including the coupon payments and the final principal payment. We can use the formula for present value of an annuity and present value of a lump sum to calculate this. The yield to maturity is the discount rate that equates the present value of the cash flows to the current market price of the bond. Using a financial calculator or spreadsheet software, we find that the yield to maturity is approximately 3.92%.
To compute the bond's yield to call, we need to calculate the present value of all future cash flows up to the call date. The yield to call is the discount rate that equates the present value of the cash flows to the current market price of the bond. Using the same formula as before, but changing the time period to the call date and adjusting the cash flows accordingly, we can calculate the yield to call, which is approximately 5.51%.
The taxable equivalent yield is the yield on a taxable investment that would be needed to match the after-tax yield on the municipal bond. To calculate this, we divide the tax-exempt yield by (1 - marginal tax rate). In this case, the tax-exempt yield is 3.92% and the marginal tax rate is 36%, so the taxable equivalent yield is 3.92%/(1 - 0.36) = 6.12%.