You are given the following expected 1-year rates for each of the next 5 years and the cash flows for Bond A (assume that it pays an annual coupon). Based on this information, determine the yield-to- maturity for Bond A. Year 1 2 3 4 5 O 7.17% 6.80% O 7.54% O6.43 % Expected 1-Year Rate 9.00% 8.00% 7.00% 6.00% 5.00% Bond A Cash Flow $ 100.00 $ 100.00 $ 100.00 $ 100.00 $1,100.00
To calculate the yield-to-maturity (YTM) for Bond A, we need to find the discount rate that makes the present value of its cash flows equal to its current price. In this case, we are given the expected 1-year rates for each of the next 5 years, which we can use to discount the future cash flows. Here are the steps to calculate the YTM:
Calculate the present value of each cash flow using the corresponding 1-year rate:
Year 1: PV(Year 1 Cash Flow) = $100 / (1 + 0.09) = $91.74
Year 2: PV(Year 2 Cash Flow) = $100 / (1 + 0.08)² = $86.08
Year 3: PV(Year 3 Cash Flow) = $100 / (1 + 0.07)³ = $80.19
Year 4: PV(Year 4 Cash Flow) = $100 / (1 + 0.06)⁴ = $74.37
Year 5: PV(Year 5 Cash Flow) = $1,100 / (1 + 0.05)⁵ = $925.69
Sum up the present values of all cash flows to find the current price of Bond A:
Current Price = $91.74 + $86.08 + $80.19 + $74.37 + $925.69 = $1,258.07
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