Suppose we have a bond issue currently outstanding that has 20 years left to maturity.
The coupon rate is 8%, and coupons are paid semiannually. The bond is currently selling for $828 per $1,000 bond.  What is the cost of debt?

5  b. 6  c. 7   d. 8   e.  9   f.    10  g. 11  h. 12   i. 14   j. 16 

To calculate the cost of debt for the bond, we need to determine the yield to maturity (YTM). The YTM is the internal rate of return (IRR) on the bond, which equates the present value of all future cash flows (coupons and face value) with the current price of the bond.

Given:
- **Coupon rate (C):** 8% annually (which is 4% semiannually)
- **Face value (F):** $1,000
- **Bond price (P):** $828
- **Time to maturity (N):** 20 years (which is 40 semiannual periods)
- **Semiannual coupon payment:** $ \frac{8\% \times 1000}{2} = 40 $

We need to solve for the semiannual YTM $ r $, which can be calculated using the bond price formula:

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

This equation requires iterative methods to solve for $ r $, as it cannot be solved algebraically. However, we can use approximation methods or a financial calculator to estimate $ r $, and then double it to get the annual YTM.

### Using a financial calculator or Excel, let's estimate $ r $:

1. **Enter the following inputs:**
   - $ N = 40 $ (semiannual periods)
   - $ PV = -828 $ (current price, negative because it's an outflow)
   - $ PMT = 40 $ (semiannual coupon payment)
   - $ FV = 1000 $ (face value)

2. **Calculate the semiannual YTM $ r $:**

After computation, you would find:

\[
r \approx 0.05 \text{ (semiannual)}
\]

3. **Annual YTM (cost of debt):**
   \[
   YTM = 2 \times r \approx 10\%
   \]

Thus, the cost of debt for this bond is approximately **10%**, so the correct answer is **f. 10**.

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Would you like a more detailed explanation or have any other questions?

Here are some related questions you might be interested in:
1. How does the time to maturity affect the cost of debt?
2. What is the impact of a bond's price below par on its YTM?
3. How would a change in the coupon rate affect the cost of debt?
4. What are the differences between YTM and the current yield?
5. How does the frequency of coupon payments influence the cost of debt?

**Tip:** When calculating YTM, remember that it reflects the bond’s total return if held until maturity, considering both interest payments and any capital gain or loss.

Learn how to calculate the cost of debt for a bond with an 8% coupon rate, 20 years to maturity, and currently priced at $828. Detailed solution including bond price formula, yield to maturity calculation, and financial implications. Suitable for finance professionals.

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