Cinqua Terra Incorporated issued 10-year bonds three years ago with a coupon rate of 7.375% APR. The bonds pay semi-annual coupons, have a face value of $1,000.00 each and were issued at par value. What is the price of the Cinque Terra bond’s today if investors want a 6.44% APR return for bonds of similar risk and maturity?

3 answers

To calculate the current price of the Cinque Terra bond, we can use the present value formula for bonds. The price of the bond is the present value of its future cash flows, which consist of the semi-annual coupon payments and the face value at maturity.

Given:

  • Coupon Rate = 7.375% APR
  • Face Value (FV) = $1,000
  • Annual Payment (C) = \( \text{Coupon Rate} \times \text{Face Value} = 0.07375 \times 1000 = 73.75 \) (This is for a year)
  • Semi-Annual Coupon Payment = \( \frac{C}{2} = \frac{73.75}{2} = 36.875 \)
  • Total Maturity Period = 10 years
  • Time elapsed = 3 years
  • Remaining Maturity = 10 - 3 = 7 years = 14 semi-annual periods
  • Required Return (r) = 6.44% APR (or 0.0644), which needs to be converted for semi-annual periods:
    \( \text{Semi-Annual Required Return} = \frac{0.0644}{2} = 0.0322 \)

Now, we can find the present value of the future cash flows:

  1. Present Value of Coupon Payments (annuity): \[ PV_{\text{coupons}} = C \left( \frac{1 - (1 + r)^{-n}}{r} \right) \] where \( n \) is the number of periods (14) and \( r \) is the semi-annual required return (0.0322).

    Plugging in the values: \[ PV_{\text{coupons}} = 36.875 \left( \frac{1 - (1 + 0.0322)^{-14}}{0.0322} \right) \]

    Let's calculate that: \[ (1 + 0.0322)^{-14} \approx 0.636578 \quad \text{(Using a calculator)} \] So, \[ 1 - 0.636578 \approx 0.363422 \] Thus, \[ PV_{\text{coupons}} = 36.875 \left( \frac{0.363422}{0.0322} \right) \approx 36.875 \times 11.2904 \approx 416.77 \]

  2. Present Value of Face Value (lump sum): \[ PV_{\text{face}} = \frac{FV}{(1 + r)^n} = \frac{1000}{(1 + 0.0322)^{14}} \]

    Again let's calculate: \[ (1 + 0.0322)^{14} \approx 1.537679 \quad \text{(Using a calculator)} \] So, \[ PV_{\text{face}} = \frac{1000}{1.537679} \approx 651.05 \]

Finally, we add the present values of the coupon payments and the face value to find the current price of the bond:

\[ \text{Current Price} = PV_{\text{coupons}} + PV_{\text{face}} \approx 416.77 + 651.05 \approx 1067.82 \]

Therefore, the price of the Cinque Terra bond today is approximately $1067.82.

What values do I enter for N, i/y, PV, PMT, and FV to solve on a finance calculator?

To solve for the price of the bond using a finance calculator, you need to enter specific values for each parameter corresponding to the bond's cash flows and terms. Here’s what to enter for each variable:

  1. N (Number of periods): This represents the total number of semi-annual periods remaining until maturity. As calculated, you have 7 years remaining on the bond, and since the coupons are paid semi-annually:

    \[ N = 7 \text{ years} \times 2 \text{ (since it's semi-annual)} = 14 \]

  2. I/Y (Interest rate per period): This is the required return per semi-annual period. You wanted a 6.44% APR, which needs to be divided by 2 to convert it to a semi-annual rate:

    \[ I/Y = \frac{6.44%}{2} = 3.22 \]

  3. PV (Present Value): This is what you’re solving for, the price of the bond. When entering values in a calculator, you'll typically leave this as 0 since the calculator computes it based on other inputs.

  4. PMT (Payment): This is the semi-annual coupon payment. The bond pays a coupon rate of 7.375% annually on a face value of $1,000. The semi-annual coupon payment can be calculated as:

    \[ PMT = \frac{7.375% \times 1000}{2} = 36.875 \]

  5. FV (Future Value): This is the face value of the bond that will be received at maturity. For this bond:

    \[ FV = 1000 \]

Summary of values to enter:

  • N: 14
  • I/Y: 3.22
  • PV: 0 (or leave it blank if solving for PV)
  • PMT: 36.875
  • FV: 1000

Once you enter these values into your finance calculator, make sure to solve for PV (Present Value), which will give you the current price of the bond.