Trek Star Productions has bonds trading in the secondary market that mature in 14.00 years. Each bond pays an annual coupon of $102.75 with a face value of $1,000.00. Investors in Trek Star debt currently seek an 12.00% return.

Question

What price are investors willing to pay for Trek Star debt?

Answer 1

To find the price that investors are willing to pay for the bonds issued by Trek Star Productions, we can use the formula for the present value of a bond, which consists of two components: the present value of the annual coupon payments and the present value of the face value at maturity.

The formula for the price of the bond (P) is given by:

\[ P = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^n} \]

where:

• \( C \) = annual coupon payment ($102.75)
• \( F \) = face value of the bond ($1,000.00)
• \( r \) = market interest rate (12.00% or 0.12)
• \( n \) = number of years to maturity (14.00 years)

Now, let's calculate it step by step.

Step 1: Calculate the present value of the coupon payments

The present value of the annual coupon payments \( C \) can be calculated using the present value of an annuity formula:

\[ PV_{\text{coupons}} = C \times \left(1 - (1 + r)^{-n}\right) / r \]

Substituting the values:

\[ PV_{\text{coupons}} = 102.75 \times \left(1 - (1 + 0.12)^{-14}\right) / 0.12 \]

Calculating \( (1 + 0.12)^{-14} \):

\[ (1.12)^{-14} \approx 0.2261 \]

Now, substitute this back into the formula:

\[ PV_{\text{coupons}} = 102.75 \times \left(1 - 0.2261\right)/0.12 \] \[ PV_{\text{coupons}} = 102.75 \times \left(0.7739\right)/0.12 \] \[ PV_{\text{coupons}} = 102.75 \times 6.4492 \approx 661.84 \]

Step 2: Calculate the present value of the face value

The present value of the face value \( F \) is calculated as follows:

\[ PV_{\text{face value}} = \frac{F}{(1 + r)^n} \] \[ PV_{\text{face value}} = \frac{1000}{(1 + 0.12)^{14}} \]

Calculating \( (1.12)^{14} \):

\[ (1.12)^{14} \approx 4.0588 \]

Now substitute back into the formula:

\[ PV_{\text{face value}} = \frac{1000}{4.0588} \approx 246.86 \]

Step 3: Add the present values to get the price of the bond

Now, we can sum the present values of the coupon payments and the face value:

\[ P = PV_{\text{coupons}} + PV_{\text{face value}} \] \[ P \approx 661.84 + 246.86 \approx 908.70 \]

Thus, the price that investors are willing to pay for the bonds from Trek Star Productions is approximately $908.70.

Answer 2

what values do i enter for N, i/y, PV, PMT, and FV to solve n a finance calculator?

Answer 3

To enter the values for a bond pricing calculation on a financial calculator, you need to identify what each of the variables represents and align them with the bond's characteristics. Here's how to configure the inputs for a standard financial calculator:

1. N (Number of Periods): This is the number of years until the bond matures. In your case, this is 14 years.

2. I/Y (Interest Rate per Year): This is the annual yield or return that investors are seeking. In your case, this is 12% (enter as 12).

3. PV (Present Value): This is the current price of the bond. Since you're trying to find the price, you will calculate it, but you can leave this blank or enter it later if you're using the calculator iteratively.

4. PMT (Payment): This represents the annual coupon payment. In your case, this is $102.75.

5. FV (Future Value): This is the face value of the bond that will be received at maturity. In your case, this is $1,000.

Now, to summarize:

• N = 14
• I/Y = 12
• PV = ? (you'll calculate this)
• PMT = 102.75
• FV = 1000

Using these inputs, you would typically solve for the PV (present value) using the bond pricing functionality on your finance calculator. The calculator should return the price of the bond, which you expect to be around $908.70, as calculated earlier.