Sheet Price 1,050.00 Coupon 40.00 Face value 1,000.00 ✓ Solved

Problem 1: What is the cost of new AND existing debt if the current price of the bonds is $1,050? The bonds pay a semiannual coupon of $80 ($40 every six months), mature in 12 years, and have a face value of $1,000. The flotation cost for debt is 5%.

The cost of existing debt is calculated using the formula for the yield to maturity (YTM). Without flotation or issuance costs, the components are as follows: C=$80, FV=$1,000, PV=$1,050, and time t=12 years. The yield to maturity on the firm's bonds is represented as:

YTM = [C + (FV - PV) / t] / [(FV + PV) / 2]

Substituting the values, we arrive at:

YTM = [80 + (1,000 - 1,050) / 12] / [(1,000 + 1,050) / 2] = (80 - 5) / (2,050/2) ≈ 7.398%

This yield to maturity represents the cost of existing debt.

The calculation of the cost of new debt takes into account the flotation cost. By adjusting the YTM with the flotation cost, we have:

Rd = YTM * (1 - flotation cost) = 7.398% / (1 - 5%) ≈ 7.79%

Thus, the cost of new debt is approximately 7.79%.

Problem 2: Assume that you are considering the purchase of a $1,000 par value bond that pays interest of $70 each six months (a total of $140 per year) and has 10 years to go before it matures. If you buy this bond, you expect to hold it for 5 years and then sell it in the market. You (and other investors) currently require a nominal annual rate of return of 16%, but you expect the market to require a nominal rate of return of only 12% when you sell the bond due to a general decline in interest rates. How much should you be willing to pay for this bond today?

The price of the bond can be calculated using the present value formula for an annuity. As established, when the required nominal annual rate of return is 16%, the price of the bond will be lower than at the rate of 12% due to the inverse relationship between bond price and yield. The present value annuity due is calculated as:

PVA = PMT * [1 - 1/(1 + r)^n] / r

Calculating at the return rate of 12%, we have:

PVA = $70 [1 - 1/(1 + 0.12)^(25)] / 0.12 ≈ $395.52

Now, calculating at the 16% return rate:

PVA = $70 [1 - 1/(1 + 0.16)^(25)] / 0.16 ≈ $338.33

The computed price of the bond at the 12% return rate ($395.52) is higher than at the 16% rate ($338.33). Therefore, you should be willing to pay no more than approximately $395.52 for the bond today.

Paper For Above Instructions

The cost of debt is a critical aspect of a firm’s financial decision-making process as it directly affects the capital structure and overall financial health of the organization. Understanding both new and existing debt financing is essential for evaluating investment opportunities and managing financial risks. This paper aims to determine the costs associated with existing and new debt based on a hypothetical bond scenario, providing a comprehensive analysis and a conclusion on investment decisions regarding bond purchasing.

To commence with Problem 1, we note that valuing existing debt involves calculating a bond's yield to maturity (YTM). In the given example, we have a bond priced at $1,050 that offers a semiannual coupon payment of $40 for a total annual coupon of $80, with a face value of $1,000 and maturing in 12 years. The formula to compute the YTM is given, and substituting the values results in a YTM of roughly 7.398%. This metric not only informs investors of the bond's return based on its current market price but also serves as a proxy for the cost of existing debt for the issuing firm. When evaluating existing debt, it’s crucial to recognize that YTM represents the expected returns required by investors based on current market conditions and perceived risk associated with the debt.

Furthermore, the cost of new debt financing must account for flotation costs—expenses incurred during the process of issuing new debt. In this instance, the flotation cost is estimated to be 5%. Adjusting the YTM accordingly reveals that the overall cost of new debt becomes approximately 7.79% after factoring in these costs. This insight underlines the importance of evaluating not just the nominal returns on investments, but also the associated costs that could influence financing choice and overall capital expenditures.

Shifting focus to Problem 2, the analysis centers around the purchasing of a $1,000 par value bond that pays semiannual interest of $70, maintains a ten-year maturity period, and anticipates a hold period of five years. The potential investor aims to assess how much to pay today based on varying expected nominal rates of return. Present value calculations are used to gauge the bond's value under two separate anticipated yield scenarios—16% while holding the bond and 12% upon selling the bond in the future. It’s noted that the bond's price is inversely related to yield; thus, as expected future returns from the market diminish, the bond’s present value increases. Using the present value annuity formula, direct calculations provide a price of the bond worth approximately $395.52 assuming a 12% return rate. In contrast, a return rate of 16% results in a lower bond price of approximately $338.33.

These respectively highlighted pricing scenarios provide valuable insights for potential investors. The higher price ($395.52) suggests attractiveness under anticipated market conditions, emphasizing why having a strategy for bond valuation based on yield expectations is vital for investment decisions. It is noteworthy that investors are advised to exercise caution and prioritize their yield requirements while factoring in variables such as maturity duration and expected market movements.

In conclusion, both problems offer a thorough investigation into the mechanics of bond valuation, yielding critical implications for corporate financing and individual investment strategies. Understanding cost structures associated with existing and new debt, as well as bond price negotiations based on yield expectations, equates to a better-informed investing landscape that can drive long-term financial decisions.

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