The total return for the bond is approximately $49.60 due to the combination of coupon payments and capital appreciation over the 4-year investment horizon.
To calculate the total return for the bond, we need to consider both the coupon payments and the capital gain or loss at the end of the investment horizon. The total return is the sum of these two components.
First, let's calculate the present value of the bond's cash flows. The bond has a 10-year maturity and a 5% coupon rate, which means it pays 5% of its face value as a coupon payment each year. Since it is selling at par, its face value is equal to its price.
Using Excel formulas, we can calculate the present value of each cash flow. Assuming the face value of the bond is $100, we have:
Year 1: Coupon payment = $100 * 5% = $5
Present value of Year 1 coupon payment = $5 / (1 + 8%)^1 = $4.63
Year 2: Coupon payment = $100 * 5% = $5
Present value of Year 2 coupon payment = $5 / (1 + 8%)^2 = $4.29
Year 3: Coupon payment = $100 * 5% = $5
Present value of Year 3 coupon payment = $5 / (1 + 8%)^3 = $3.97
Year 4: Coupon payment = $100 * 5% = $5
Present value of Year 4 coupon payment = $5 / (1 + 8%)^4 = $3.67
Year 5: Coupon payment = $100 * 5% = $5
Present value of Year 5 coupon payment = $5 / (1 + 8%)^5 = $3.39
Year 6: Coupon payment = $100 * 5% = $5
Present value of Year 6 coupon payment = $5 / (1 + 8%)^6 = $3.13
Year 7: Coupon payment = $100 * 5% = $5
Present value of Year 7 coupon payment = $5 / (1 + 8%)^7 = $2.89
Year 8: Coupon payment = $100 * 5% = $5
Present value of Year 8 coupon payment = $5 / (1 + 8%)^8 = $2.67
Year 9: Coupon payment = $100 * 5% = $5
Present value of Year 9 coupon payment = $5 / (1 + 8%)^9 = $2.47
Year 10: Coupon payment + Face value = $5 + $100 = $105
Present value of Year 10 cash flow = $105 / (1 + 8%)^10 = $68.06
Next, let's calculate the present value of the reinvested coupon payments. The investor expects to reinvest the coupon payments at an annual interest rate of 8%. Since the coupon payments are received annually, we can simply calculate the present value of each coupon payment using the same formula as above:
Present value of reinvested Year 1 coupon payment = $5 / (1 + 8%)^1 = $4.63
Present value of reinvested Year 2 coupon payment = $5 / (1 + 8%)^2 = $4.29
Present value of reinvested Year 3 coupon payment = $5 / (1 + 8%)^3 = $3.97
Present value of reinvested Year 4 coupon payment = $5 / (1 + 8%)^4 = $3.67
Present value of reinvested Year 5 coupon payment = $5 / (1 + 8%)^5 = $3.39
Present value of reinvested Year 6 coupon payment = $5 / (1 + 8%)^6 = $3.13
Present value of reinvested Year 7 coupon payment = $5 / (1 + 8%)^7 = $2.89
Present value of reinvested Year 8 coupon payment = $5 / (1 + 8%)^8 = $2.67
Present value of reinvested Year 9 coupon payment = $5 / (1 + 8%)^9 = $2.47
Now, let's calculate the capital gain or loss at the end of the investment horizon. The investor expects that 6-year bonds will be selling to offer a yield to maturity of 11%. To calculate the present value of the bond at the end of the investment horizon, we can use the same formula as above:
Present value of Year 10 cash flow at the end of the investment horizon = $105 / (1 + 11%)^6 = $57.42
Finally, we can calculate the total return by summing up the present values of all cash flows.
Total return = Present value of coupon payments + Present value of reinvested coupon payments + Present value of cash flow at the end of the investment horizon
Total return = $4.63 + $4.29 + $3.97 + $3.67 + $3.39 + $3.13 + $2.89 + $2.67 + $2.47 + $68.06 - $57.42
Total return = $49.60
Therefore, the total return for this bond is $49.60.
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