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Chapter 14: Problem 9

Conversion Value \(\quad\) A \(\$ 1,000\) par convertible debenture has a conversion price for common stock of \(\$ 125\) per share. With the common stock selling at \(\$ 90,\) what is the conversion value of the bond?

Short Answer

Expert verified
The debenture can be exchanged for 8 shares of common stock, with each share currently selling at $90. The conversion value of the bond is calculated as the conversion ratio (8 shares) multiplied by the current price of common stock ($90), giving a conversion value of $720.

Step by step solution

01

Calculate the conversion ratio

We start by calculating the conversion ratio, which is the number of shares the debenture can be exchanged for. The conversion ratio can be calculated using the formula: Conversion ratio = (Par value of debenture) / (Conversion price per share) Using the given values: Conversion ratio = (\(1,000) / (\)125) = 8 shares So, the debenture can be exchanged for 8 shares of common stock.
02

Calculate the conversion value of the bond

Now that we know the debenture can be converted into 8 shares, we will find the current market value of these shares. We are given the current selling price of the common stock, which is $90 per share. The conversion value will be equal to the market value of the shares it can be exchanged for. Conversion value = (Conversion ratio) 脳 (Current price of common stock) Using the values from step 1: Conversion value = (8 shares) 脳 (\(90) = \)720 The conversion value of the bond is $720.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Convertible Debenture
A convertible debenture is a type of debt instrument that can be exchanged for a specific number of shares of the issuing company's common stock. This unique feature provides a hybrid mix of both debt and equity characteristics.
Key Characteristics:
  • It earns regular interest payments like a traditional bond.
  • Holders have the flexibility to convert it into stock, depending on the terms set at issuance.
  • Conversion often occurs when the stock price rises above a certain level, making the conversion appealing.
Investors find convertible debentures attractive because they provide a fixed income stream (interest) while offering the potential for greater returns through stock appreciation. This makes them particularly appealing in situations where there is potential for significant company growth.
Conversion Ratio
The conversion ratio is a pivotal concept because it indicates how many shares of common stock an investor can obtain by converting their debenture. It serves as a key link between fixed-income securities and equities.
How to Calculate:
  • The formula used is: Conversion ratio = \( \frac{\text{Par value of debenture}}{\text{Conversion price per share}} \)
  • This tells investors how much equity they can gain, providing insight into the potential value unlocked through conversion.
In the example given, with a par value of \(1,000 and a conversion price of \)125 per share, the conversion ratio is 8. This means each convertible debenture can be exchanged for 8 shares of common stock. Understanding this ratio helps in evaluating the potential benefits and timing of conversion.
Par Value
Par value, or face value, is the nominal value of a bond or stock as stated by the issuer. It is important in understanding the base amount upon which interest or dividends are calculated.
Importance of Par Value in Convertible Debentures:
  • While par value for stocks is often merely an accounting figure, in debentures, it represents the principal amount that will be repaid at maturity.
  • It serves as a baseline for calculating the conversion ratio, making it crucial for potential investors to grasp its implications on conversion.
In the context of the exercise, a $1,000 par value helps determine the number of common shares you can obtain and calculates the bond's conversion value.
Common Stock Price
The common stock price plays a critical role in calculating the conversion value of a convertible debenture. As the stock market fluctuates, so does the attractiveness of conversion.
Why Common Stock Price Matters:
  • The current selling price of common stock determines the market value of the shares obtained upon conversion.
  • When the stock price is high, converting the debenture into equity can be more profitable.
  • In our exercise scenario, with the stock price at $90, the conversion value of the bond comes out to be $720, indicating how much the stock portion is currently worth.
Investors keep a close watch on the stock price relative to their conversion price to decide the optimal timing for conversion.

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Most popular questions from this chapter

T-bills currently yield 6 percent. Stock in Christina Manufacturing is currently selling for 50 dollars per share. There is no possibility that the stock will be worth less than 45 dollars per share in one year. a. What is the value of a call option with a 40 dollars exercise price? What is the intrinsic value?b. What is the value of a call option with a 30 dollars exercise price? What is the intrinsic value?c. What is the value of a put option with a \(\$ 40\) exercise price? What is the intrinsic value?

A one-year call option contract on Cheesy Poofs Co. stock sells for \(\$ 1,400 .\) In one year, the stock will be worth \(\$ 40\) or \(\$ 60\) per share. The exercise price on the call option is \(\$ 55 .\) What is the current value of the stock if the risk-free rate is 5 percent?

We are examining a new project. We expect to sell 6,000 units per year at \(\$ 65\) net cash flow apiece for the next 10 years. In other words, the annual operating cash flow is projected to be \(\$ 65 \times 6,000=\) \(\$ 390,000 .\) The relevant discount rate is 16 percent, and the initial investment required is \(\$ 1,750,000\).a. What is the base-case NPV? b. After the first year, the project can be dismantled and sold for \(\$ 1,250,000\). If expected sales are revised based on the first year's performance, when would it make sense to abandon the investment? In other words, at what level of expected sales would it make sense to abandon the project? c. Explain how the \(\$ 1,250,000\) abandonment value can be viewed as the opportunity cost of keeping the project in one year.

Option to Wait Your company is deciding whether to invest in a new machine. The new machine will increase cash flow by \(\$ 180,000\) per year. You believe the technology used in the machine has a 10 -year life, in other words, no matter when you purchase the machine, it will be obsolete 10 years from today.The machine is currently priced at \(\$ 1,000,000\). The cost of the machine will decline by \(\$ 100,000\) per year until it reaches \(\$ 500,000,\) where it will remain. If your required return is 12 percent, should you purchase the machine? If so, when should you purchase it?

Volunteer Industries has a bond issue with a face value of \(\$ 1,000\) that is coming due in one year. The value of Volunteer's assets is currently \(\$ 1,200 .\) Phil Fulmer, the \(C E O\), believes that the assets in the firm will be worth either \(\$ 800\) or \(\$ 1,400\) in a year. The going rate on one-year T-bills is 4 percent. a. What is the value of Volunteer's equity? The value of the debt? b. Suppose Volunteer can reconfigure its existing assets in such a way that the value in a year will be \(\$ 500\) or \(\$ 1,700\). If the current value of the assets is unchanged, will the stockholders favor such a move? Why or why not?
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