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Q1:What is the cash flow of a 8-year bond that pays coupon interest semiannually, has a coupon rate of 6%, and has a par value of $100,000?

Question

Q1: What is the cash flow of a 8-year bond that pays coupon interest semiannually, has a coupon rate of 6%, and has a par value of $100,000?

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Solution

To calculate the cash flow of an 8-year bond that pays coupon interest semiannually, we need to determine the coupon payment and the total cash flow over the life of the bond.

  1. Coupon Payment Calculation:

    • Par Value (Face Value) = $100,000
    • Coupon Rate = 6%
    • Since the bond pays interest semiannually, we divide the coupon rate by 2 and multiply the par value by this rate to find the semiannual coupon payment.

    Semiannual Coupon Payment=(6%2)×100,000=0.03×100,000=3,000 \text{Semiannual Coupon Payment} = \left(\frac{6\%}{2}\right) \times 100,000 = 0.03 \times 100,000 = 3,000

  2. Total Cash Flow Calculation:

    • The bond has a total of 8 years, and since it pays interest semiannually, there will be a total of 8×2=168 \times 2 = 16 coupon payments.
    • The total cash flow from the coupon payments over the life of the bond is:

    Total Cash Flow from Coupons=Semiannual Coupon Payment×Number of Payments=3,000×16=48,000 \text{Total Cash Flow from Coupons} = \text{Semiannual Coupon Payment} \times \text{Number of Payments} = 3,000 \times 16 = 48,000

  3. Final Cash Flow:

    • At the end of the 8 years, the bond will also pay back the par value of $100,000. Therefore, the total cash flow from the bond will be the sum of the total coupon payments and the par value.

    Total Cash Flow=Total Cash Flow from Coupons+Par Value=48,000+100,000=148,000 \text{Total Cash Flow} = \text{Total Cash Flow from Coupons} + \text{Par Value} = 48,000 + 100,000 = 148,000

In summary, the total cash flow of the bond over its 8-year life is $148,000.

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