Question No.1 (a): Consider the following projects:

Project C0 C1 C2 C3 C4 C5

A (1,000) 1,000 0 0 0 0

B (2,000) 1,000 1,000 4,000 1,000 1,000

C (3,000) 1,000 1,000 0 1,000 1,000

i) If the opportunity cost of capital is 10 percent, which projects have a positive NPV?

ii) Calculate the payback period for each project.

iii) Which project would a firm using the payback rule accept, if the cutoff period were 3 years?

Answer:

Project A:

Year Expected Cash Flows

PVIF@10% Present Value

0 (1,000) 1 (1,000)

1 1,000 .909 909

2 0 .826 0

3 0 .751 0

4 0 .683 0

5 0 .621 0

NPV = Present Value – Initial Cost

NPV = 909-1,000

NPV = (91)

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Project B:

Year Expected Cash Flows

PVIF@10% Present Value

0 (2,000) 1 (2,000)

1 1,000 .909 909

2 1,000 .826 826

3 4,000 .751 3,004

4 1,000 .683 683

5 1,000 .621 621

NPV = Present Value – Initial Cost

NPV = 6,043-2,000

NPV = 4,043

Project C:

Year Expected Cash Flows

PVIF@10% Present Value

0 (3,000) 1 (3,000)

1 1,000 .909 909

2 1,000 .826 826

3 0 .751 0

4 1,000 .683 683

5 1,000 .621 621

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NPV = Present Value – Initial Cost

NPV = 3,039-3,000

NPV = 39

Comments: Project B & C have a positive NPV

ii) Pay Back Period = Initial Investment – Cash in flows

Project A (PBP) = 1 year

Project B (PBP) = 2 year

Project C (PBP) = 4 year

iii) If cutoff period is 3 years then firm will select project A&B.

Question No.2: Consider the following three stocks:

a) Stock A is expected to provide a dividend of Rs.10 a share forever.

b) Stock B is expected to pay dividend of Rs.5 next year. Thereafter, dividend growth is expected to be 4 percent a year forever.

c) Stock C is expected to pay a dividend of Rs.5 next year. Thereafter, dividend growth is expected to be 20 percent a year for 5 years (I.e., until year 6 and zero thereafter).

If the market capitalization rate for each stock is 10 percent, which stock is the most valuable? What if the capitalization rate is 7 percent?

Answer:

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a) Stock A:

Expected dividend (D1) = Rs.10/share forever

Market capitalization rate (r ) = 10%

Present Value of Stock (P0) = D1/r

Present value of stock (P0) = 10/0.1

Present value of stock (P0) = Rs.100 Ans.

a) Stock B:

Expected dividend (D1) = Rs.5/share forever

Market capitalization rate (r ) = 10%

Growth (g) = 4% a year forever

Present Value of Stock (P0) = D1/r+g

Present value of stock (P0) = 5/0.1+.04

Present value of stock (P0) = Rs.50.04 Ans.

c) Stock C:

Expected dividend (D1) = Rs.5/share forever

Market capitalization rate (r ) = 10%

Growth (g) = 20% a year for 5 years until 6 year

Expected dividend 1st year (D1) = Rs.5

Expected dividend 2nd year (D2) = D1(1+g)

Expected dividend 2nd year (D2) = Rs.5(1+.20) = Rs.6

Expected dividend 3rd year (D3) = Rs.6(1+.20) = Rs. 7.2

Expected dividend 4th year (D4) = Rs.7.2(1+.20) = Rs. 8.64

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Expected dividend 5th year (D5) = Rs.8.64(1+.20) = Rs.10.36

Expected dividend 6th year (D6) = Rs.10.36(1+.20) = Rs. 12.44

Value of Stock (P0) = D1/(1+r)+D2/(1+r)2+ D3/(1+r)3+D4/(1+r)4+ D5+D6/(1+r)5

(P0) = 5/(1+0.1)+6/(1+0.1)2+ 7.2/(1+0.1)3+8.64/(1+0.1)4+ 10.36+12.44/(1+0.1)5

Value of Stock (P0) = 4.54+4.95+5.41+5.90+14.16 = Rs.34.96 Ans.

Note: If the market capitalization rate is 10% then stock A is the most valuable stock.

b) Stock A:

Expected dividend (D1) = Rs.10/share forever

Market capitalization rate (r ) = 7%

Present Value of Stock (P0) = D1/r

Present value of stock (P0) = 10/0.07

Present value of stock (P0) = Rs.142.85 Ans.

b) Stock B:

Expected dividend (D1) = Rs.5/share forever

Market capitalization rate (r ) = 7%

Growth (g) = 4% a year forever

Present Value of Stock (P0) = D1/r+g

Present value of stock (P0) = 5/0.07+.04

Present value of stock (P0) = Rs.71.47 Ans.

b) Stock C:

Expected dividend (D1) = Rs.5/share forever

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Market capitalization rate (r ) = 7%

Growth (g) = 20% a year for 5 years until 6 year

Expected dividend 1st year (D1) = Rs.5

Expected dividend 2nd year (D2) = D1(1+g)

Expected dividend 2nd year (D2) = Rs.5(1+.20) = Rs.6

Expected dividend 3rd year (D3) = Rs.6(1+.20) = Rs. 7.2

Expected dividend 4th year (D4) = Rs.7.2(1+.20) = Rs. 8.64

Expected dividend 5th year (D5) = Rs.8.64(1+.20) = Rs.10.36

Expected dividend 6th year (D6) = Rs.10.36(1+.20) = Rs. 12.44

Value of Stock (P0) = D1/(1+r)+D2/(1+r)2+ D3/(1+r)3+D4/(1+r)4+ D5+D6/(1+r)5

(P0) = 5/(1+.07)+6/(1+.07)2+7.2/(1+.07)3+8.64/(1+.07)4+10.36+12.44/(1+.07)5

Value of Stock (P0) = 4.67+5.24+5.88+6.59+16.26 = Rs.38.64 Ans.

Question No.3 (a): The total market value of the common stock of the Alfalah Real Estate Company is Rs.6 million and the total value of its debt is Rs.4 million. The treasurer estimates that the beta of the stock is currently 1.5 and the expected risk premium on the market is 9 percent. The Treasury bill rate is 8 percent.

i) What is the required return of Alfalah stock?ii) What is the beta of the company’s existing

portfolio of assets?

iii) Estimate the company’s cost of capital.

iv) Estimate the discount rate for an expansion of the company’s present business.

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Answer:

i) Risk free rate (Rf) = 8%

Market rate (Rm) = 9%

Beta (B) = 1.5

Required rate of return (r ) = Rf+(Rm-Rf)B

Required rate of return ( r ) = 0.08+(0.09-0.08)1.5

Required rate of return (r ) = 9.5% Ans.

ii) B Assets = D/D+E(B debt) + E/D+E(B equity)

B Assets = 4/(4+6)x(0) + 6/(4+6)x(1.5)

B Assets = 4/10x(0) + 6/10x(1.5)

B Assets = 0 + 0.9 = 0.9 Ans.

iii) Risk free rate (Rf) = 8%

Market rate (Rm) = 9%

Beta (B) = 0.9

Company cost of capital = Rf+(Rm)B

Company cost of capital = 0.08+(0.09)0.9

Company cost of capital = 16.1% Ans.

iv) Estimated discount rate (r ) = 16.1% Ans.

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Note: same working as above in part (iii).

Question No.3 (b): Suppose that there is no relation between beta and expected returns. Do you think that beta is an uninteresting statistic? What would you do as an investor? What strategies should a corporation adopt?

Answer:

The CAPM is a model for pricing an individual security (asset) or a portfolio. For individual security perspective, we made use of the security market line (SML) and its relation to expected return and systematic risk (beta) to show how the market must price individual securities in relation to their security risk class. The SML enables us to calculate the reward-to-risk ratio for any security in relation to the overall market’s. Therefore, when the expected rate of return for any security is deflated by its beta coefficient, the reward-to-risk ratio for any individual security in the market is equal to the market reward-to-risk ratio, thus:

Individual security’s = Market’s securities (portfolio)Reward-to-risk ratio

,

The market reward-to-risk ratio is effectively the market risk premium and by rearranging the above equation and solving for E(Ri), we obtain the Capital Asset Pricing Model (CAPM).

Where:

is the expected return on the capital asset

is the risk-free rate of interest

(the beta coefficient) the sensitivity of the asset returns to market

returns, or also ,

is the expected return of the market

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Is sometimes known as the market premium or risk premium (the difference between the expected market rate of return and the risk-free rate of return). Note 1: the expected market rate of return is usually measured by looking at the arithmetic average of the historical returns on a market portfolio (i.e. S&P 500). Note 2: the risk free rate of return used for determining the risk premium is usually the arithmetic average of historical risk free rates of return and not the current risk free rate of return.

Asset Pricing:

Once the expected return, E(Ri), is calculated using CAPM, the future cash flows of the asset can be discounted to their present value using this rate (E(Ri)), to establish the correct price for the asset.

In theory, therefore, an asset is correctly priced when its observed price is the same as its value calculated using the CAPM derived discount rate. If the observed price is higher than the valuation, then the asset is overvalued (and undervalued when the observed price is below the CAPM valuation).

Alternatively, one can "solve for the discount rate" for the observed price given a particular valuation model and compare that discount rate with the CAPM rate. If the discount rate in the model is lower than the CAPM rate then the asset is overvalued (and undervalued for a too high discount rate).

Asset-specific required return:

The CAPM returns the asset-appropriate required return or discount rate - i.e. the rate at which future cash flows produced by the asset should be discounted given that asset's relative riskiness. Betas exceeding one signify more than average "riskiness"; betas below one indicate lower than average. Thus a more risky stock will have a higher beta and will be discounted at a higher rate; less sensitive stocks will have lower betas and be discounted at a lower rate. The CAPM is consistent with intuition - investors (should) require a higher return for holding a more risky asset.

Since beta reflects asset-specific sensitivity to non-diversifiable, i.e. market risk, the market as a whole, by definition, has a beta of one. Stock market indices are frequently used as local proxies for the market - and in that case (by definition) have a beta of one. An investor in a large, diversified portfolio (such as a mutual fund) therefore expects performance in line with the market.

Risk and diversification:

The risk of a portfolio comprises systemic risk and specific risk which is also known as idiosyncratic risk. Systemic risk refers to the risk common to all

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securities - i.e. market risk. Specific risk is the risk associated with individual assets. Specific risk can be diversified away to smaller levels by including a greater number of assets in the portfolio. (Specific risks "average out"); systematic risk (within one market) cannot. Depending on the market, a portfolio of approximately 30-40 securities in developed markets such as UK or US (more in case of developing markets because of higher asset volatilities) will render the portfolio sufficiently diversified to limit exposure to systemic risk only.

A rational investor should not take on any diversifiable risk, as only non-diversifiable risks are rewarded within the scope of this model. Therefore, the required return on an asset, that is, the return that compensates for risk taken, must be linked to its riskiness in a portfolio context - i.e. its contribution to overall portfolio riskiness - as opposed to its "stand alone riskiness." In the CAPM context, portfolio risk is represented by higher variance i.e. less predictability. In other words the beta of the portfolio is the defining factor in rewarding the systemic exposure taken by an investor.

Question No.4: You need to choose between making a public offering and arranging a private placement. You have the following data for each: Offer A: A public issue of Rs.10 million face value of

10 years debt. The interest rate on the debt would be 8.5 percent and the debt would be issued at face value. The underwriting spread would be 1.5 percent and other expenses would be Rs.80,000.

Offer B: A private placement of Rs.10 million face value of 10 years debt. The interest rate on the private placement would be 9 percent, but the total issuing expense would be only Rs.30,000. a) What is the difference in the proceeds to the

company net of expenses?b) Other things equal, which is the better deal?c) What other factors beyond the interest rate

and issue cost would you wish to consider before deciding between the two offers?

Answer:

a) Net Proceeds:Net Proceeds = Face value – underwriting & other exp.i) Net Proceed of public issue (offer A) = 10,000,000-150,000-80,000 Net Proceed of public issue (offer A) = Rs.9,770,000

ii) Net Proceed of Pvt. Investment (offer B) = 10,000,000-30,000 Net Proceed of Pvt. Investment (offer B) = 9,970,000

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Offer B interest rate = 9%Less: Offer A interest rate = 8%

Difference = 0.5%

b) Present Value of Extra Interest on Pvt. Placement:

= 0.005 x 10,000,000/(1.085)t

= Rs.328,000 Extra cost of Rs.328,000 of higher interest on Pvt. Placement more than outweighs saving in issue. Cost N.b. we ignore taxes.

C) Pvt. Placement Debt can be custom-tailored and terms more easily renegotiated.

Question No.5 (a): What are the main differences between corporate debt and equity? Why do some firms try to issue equity in the guise of debt?

Answer:

Corporate Debt and Equity:

A Corporate bond is a bond issued by a corporation, as the name suggests. The term is usually applied to longer term debt instruments, generally with a maturity date falling at least 12 months after their issue date (the term "commercial paper" being sometimes used for instruments with a shorter maturity).

Sometimes, the term "corporate bonds" is used to include all bonds except those issued by governments in their own currencies, although, strictly speaking, it only applies to those issued by corporations (those which are subsumed by neither category include the bonds of local authorities and supranational organizations).

Corporate bonds are often listed on major exchanges (such bonds being described as "listed" bonds) and ECNs like Market Acess, and the coupon (i.e. interest payment) is usually taxable. However, despite being listed on exchanges, the vast majority of trading volume in corporate bonds in most developed markets takes place in decentralized, dealer-based, over-the-counter markets.

Compared to government bonds, they generally have a higher risk of default (although this risk depends, of course, upon the particular corporations, the current market conditions and governments being compared).

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Corporate debt is securities short and long term debt issued by corporate. Short term debt is issued as commercial paper. Long term debt is issued as bonds/notes. Issuers place paper in their own domestic market or they may widen their investor base by issuing in a foreign market or in the international market - the Euro market - in any number of currencies.

Shareholders are owners of the company and receive returns (dividends) related to the company’s profitability.

Holders of debt securities are creditors of the company. Their return is a fixed rate of interest paid regularly until the loan is re-paid at maturity by the company. As creditors, holders of debt securities rank higher than shareholders in the event of company liquidation. This means they receive their money back before shareholders if the company is liquidated.

Holders of debt securities carry a lower risk than shareholders, because they have a guaranteed stream of income in the form of interest payments. Therefore the return on debt securities can be lower than the return from shares.

Holders of debt securities are re-paid their investment at a set date whereas shares have no fixed maturity. Shareholders decide when they no longer want to be an investor in the company, sell the shares and accept the prevailing market price.

Corporate Equity:

An instrument that signifies an ownership position, or equity, in a corporation, and represents a claim on its proportionate share in the corporation's assets and profits. However, the claim to a company’s assets and earnings of most stockholders is subordinated to the claim that the company's debtors have on its assets and earnings. Also called equities or equity securities or corporate stock.

1. The residual value of a business or property beyond any mortgage thereon and liability therein.

2.a. The market value of securities less any debt incurred. b. Common stock and preferred stock.

3. Funds provided to a business by the sale of stock.

Equity in Guise of Debt:

In financial markets, stock is the capital raised by a corporation through the issuance and distribution of shares.

A person or organization which holds share of stocks is called a shareholder. The aggregate value of a corporation's issued shares is its market capitalization.

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In the United Kingdom, the word stocks refer to a completely different financial instrument: the bond. It can also refer more widely to all kinds of marketable securities. The term "share" still means the stock issued by a corporation, however. These definitions also hold true for Australia.

Type of Stocks:

There are several types of stock:

Common Stock:

Common stock also referred to as common shares or ordinary shares, are, as the name implies, the most usual and commonly held form of stock in a corporation. Shareholders of common stock have voting rights in corporate decision matters. It is the residual corporate interest that bears the ultimate risks of loss and receives the benefits of success.

Preferred Stock:

Preferred stock, sometimes called preference shares, have priority over common stock in the distribution of dividends and assets.

Most preferred shares provide no voting rights in corporate decision matters. However, some preferred shares have special voting rights to approve certain extraordinary events (such as the issuance of new shares, or the approval of the acquisition of the company), or to elect directors.

Dual Class Stock:

Dual class stock is shares issued for a single company with varying classes indicating different rights on voting and dividend payments. Each kind of shares has its own class of shareholders entitling different rights.

Treasury Stock:

Treasury stock is shares that have been bought back from the public. Treasury Stock is considered issued, but not outstanding.

Stock Derivatives:

A stock derivative is any financial claim which has a value that is dependent on the price of the underlying stock. Futures and options are the main types of derivatives on stocks. The underlying security may be a stock index or an individual firm's stock, e.g. single-stock futures.

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Stock futures are contracts where the buyer, or long, takes on the obligation to buy on the contract maturity date, and the seller, or short takes on the obligation to sell. Stock index futures are generally not delivered in the usual manner, but by cash settlement.

A stock option is a class of option. Specifically, a call option is the right (not obligation) to buy stock in the future at a fixed price and a put option is the right (not obligation) to sell stock in the future at a fixed price. Thus, the value of a stock option changes in reaction to the underlying stock of which it is a derivative. The most popular method of valuing stock options is the Black Scholes model.

Shareholder:

A shareholder or stockholder is an individual or company (including a corporation) that legally owns one or more shares of stock in a joint stock company. Companies listed at the stock market strive to enhance shareholder value.

Stockholders are granted special privileges depending on the class of stock, including the right to vote (usually one vote per share owned) on matters such as elections to the board of directors, the right to share in distributions of the company's income, the right to purchase new shares issued by the company, and the right to a company's assets during a liquidation of the company. However, stockholder's rights to a company's assets are subordinate to the rights of the company's creditors. This means that stockholders typically receive nothing if a company is liquidated after bankruptcy (if the company had had enough to pay its creditors, it would not have entered bankruptcy), although a stock may have value after a bankruptcy if there is the possibility that the debts of the company will be restructured.

Stockholders or shareholders are considered by some to be a partial subset of stakeholders, which may include anyone who has a direct or indirect equity interest in the business entity or someone with even a non-pecuniary interest in a non-profit organization. Thus it might be common to call volunteer contributors to an association stakeholders, even though they are not shareholders.

Although directors and officers of a company are bound by fiduciary duties to act in the best interest of the shareholders, the shareholders themselves normally do not have such duties towards each other.

However, in a few unusual cases, some courts have been willing to imply such a duty between shareholders. For example, in California, majority shareholders of closely held corporations have a duty to not destroy the value of the shares held by minority shareholders.

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The largest shareholders (in terms of percentages of companies owned) are often mutual funds, and especially passively managed exchange-traded funds.

Application:

The owners of a company may want additional capital to invest in new projects within the company. They may also simply wish to reduce their holding, freeing up capital for their own private use.

By selling shares they can sell part or all of the company to many part-owners. The purchase of one share entitles the owner of that share to literally share in the ownership of the company a fraction of the decision-making power, and potentially a fraction of the profits, which the company may issue as dividends.

In the common case of a publicly traded corporation, where there may be thousands of shareholders, it is impractical to have all of them making the daily decisions required to run a company. Thus, the shareholders will use their shares as votes in the election of members of the board of directors of the company.

In a typical case, each share constitutes one vote (except in a co-operative society where every member gets one vote regardless of the number of shares he holds). Corporations may, however, issue different classes of shares, which may have different voting rights. Owning the majority of the shares allows other shareholders to be out-voted - effective control rests with the majority shareholder (or shareholders acting in concert). In this way the original owners of the company often still have control of the company.

Shareholder rights:

Although ownership of 51% of shares does result in 51% ownership of a company, it does not give the shareholder the right to use a company's building, equipment, materials, or other property. This is because the company is considered a legal person, thus it owns all its assets itself. This is important in areas such as insurance, which must be in the name of the company and not the main shareholder.

In most countries, including the United States, boards of directors and company managers have a fiduciary responsibility to run the company in the interests of its stockholders. Nonetheless, as Martin Whitman writes:

"...it can safely be stated that there does not exist any publicly traded company where management works exclusively in the best interests of OPMI [Outside Passive Minority Investor] stockholders. Instead, there are both "communities of interest" and "conflicts of interest" between stockholders (principal) and management (agent). This conflict is referred to as the principal/agent problem. It would be naive to think that any

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management would forego management compensation, and management entrenchment, just because some of these management privileges might be perceived as giving rise to a conflict of interest with OPMIs."

Even though the board of directors runs the company, the shareholder has some impact on the company's policy, as the shareholders elect the board of directors. Each shareholder typically has a percentage of votes equal to the percentage of shares he or she owns. So as long as the shareholders agree that the management (agent) is performing poorly they can elect a new board of directors which can then hire a new management team. In practice, however, genuinely contested board elections are rare. Board candidates are usually nominated by insiders or by the board of the directors themselves, and a considerable amount of stock are held and voted by insiders.

Owning shares does not mean responsibility for liabilities. If a company goes broke and has to default on loans, the shareholders are not liable in any way. However, all money obtained by converting assets into cash will be used to repay loans and other debts first, so that shareholders cannot receive any money unless and until creditors have been paid (most often the shareholders end up with nothing).

Means of financing:

Financing a company through the sale of stock in a company is known as equity financing. Alternatively, debt financing (for example issuing bonds) can be done to avoid giving up shares of ownership of the company. Unofficial financing known as trade financing usually provides the major part of a company's working capital (day-to-day operational needs). Trade financing is provided by vendors and suppliers who sell their products to the company at short-term, unsecured credit terms, usually 30 days. Equity and debt financing are usually used for longer-term investment projects such as investments in a new factory or a new foreign market. Customer provided financing exists when a customer pays for services before they are delivered, e.g. subscriptions and insurance.

Trading:

A stock exchange is an organization that provides a marketplace (either physical or virtual) for trading shares, where investors (represented by stock brokers) may buy and sell shares in a wide range of companies. A given company will usually list its shares by meeting and maintaining the listing requirements of a particular stock exchange. In the United States, through the inter-market quotation system, stocks listed on one exchange can also be bought or sold on several other exchanges, including relatively new internet-only exchanges. Stocks are broadly grouped into NYSE-listed and NASDAQ-listed stocks. Exchanges where NYSE-listed stocks may be bought are generally not the same group as the exchanges where NASDAQ-listed stocks may be bought. Many large foreign companies

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choose to list on a U.S. exchange as well as an exchange in their home country in order to broaden their investor base. These shares are called American Depository Receipts (ADRs) -- or, in the case of companies such as UBS and Daimler Chrysler -- "foreign ordinary shares."

Question No.5 (b): Occasionally it is said that issuing convertible bonds is better than issuing stock when the firm shares are undervalued. Suppose that the financial manager of Decent furniture Company does in fact have inside information indicating that decent stock price is too low. Decent furniture earnings will in fact be higher than investor’s expectations. Suppose further that the inside information can not be released without giving away a valuable competitive secret. Clearly, selling shares at the present low price would harm Docent’s existing shareholders. Will they also lose if convertible bonds are issued? If they do lose in this case, is the loss more or less than it would if common stock is issued?

Now suppose that investors forecast earnings, but still under value the stock because they overestimate Docent’s actual business risk. Does this change your answer to the questions posed in the preceding paragraph? Explain.

Answer:

Convertible Bond:A convertible bond is a bond which can be converted into a company's common stock. Convertible bonds can provide a substantial additional profit opportunity for investors. Use these resources to get more information on convertible bonds.

Stock:

In financial markets, stock is the capital raised by a corporation through the issuance and distribution of shares.

A person or organization which holds at least a partial share of stocks is called a shareholder. The aggregate value of a corporation's issued shares is its market capitalization.

In the United Kingdom, South Africa and Australia, the term share is used the same way, but stocks there refer to either a completely different financial instrument, the bond, or more widely to all kinds of marketable securities.

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Common Stock:

Common stock also referred to as common or ordinary shares, are, as the name implies, the most usual and commonly held form of stock in a corporation. The other type of shares that the public can hold in a corporation is known as preferred stock. Common stock that has been re-purchased by the corporation is known as treasury stock and is available for a variety of corporate uses.

Common stock typically has voting rights in corporate decision matters, though perhaps different rights from preferred stock. In order of priority in a liquidation of a corporation, the owners of common stock are near the last. Dividends paid to the stockholders must be paid to preferred shares before being paid to common stock shareholders.

Convertible Bond:

A convertible bond is a type of bond that can be converted into shares of stock in the issuing company, usually at some pre-announced ratio. Although it typically has a low coupon rate, the holder is compensated with the ability to convert the bond to common stock, usually at a substantial premium to the stock's market value.

Other convertible securities include exchangeable bonds, where the stock underlying the bond is different from that of the issuer; convertible preferred stock, which is similar in valuation to a bond, but with lower seniority in the capital structure; and mandatory convertible securities, which are short duration securities---generally with high yields---that are mandatory convertible upon maturity into a variable number of common shares based on the stock price at maturity.

From the issuer's perspective, the key benefit of raising money by selling convertible bonds is a reduced cash interest payment. However, in exchange for the benefit of reduced interest payments, the value of shareholder's equity is reduced due to the dilution expected when bondholders convert their bonds into new shares.

From a valuation perspective, a convertible bond consists of two assets: a bond and a warrant. Valuing a convertible requires an assumption of 1) the underlying stock volatility to value the option and 2) the credit spread for the fixed income portion that takes into account the firm's credit profile and the ranking of the convertible within the capital structure. Using the market price of the convertible, one can determine the implied volatility (using the assumed spread) or implied spread (using the assumed volatility).

This volatility/credit dichotomy is the standard practice for valuing convertibles. What makes convertibles so interesting is that, except in the case of

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exchangeable (see above), one cannot entirely separate the volatility from the credit. Higher volatility (a good thing) tends to accompany weaker credit (bad). The true artists of convertibles are the people who know how to play this balancing act.

A simple method for calculating the value of a convertible involves calculating the present value of future interest and principal payments at the cost of debt and adds the present value of the warrant. However, this method ignores certain market realities including stochastic interest rates and credit spreads, and does not take into account popular convertible features such as issuer calls, investor puts, and conversion rate resets. The most popular models for valuing convertibles with these features are finite difference models such as binomial and trinomial trees.

Why Convertibles?

A growing number of companies are interested in raising money through convertibles because these bonds are a less expensive form of corporate debt than junk bonds. Companies can issue convertible bonds with lower yields than traditional bonds because they have the added feature of being convertible into stock shares once a pre-set stock price is reached. Individual investors are finding that, of late, some of these investments have performed better than stocks.

The Convertible Bond: A New Solution

Convertible bonds give their holders an option to exchange each bond for a pre-specified number of shares of common stock of the company under certain conditions. The pre-specified number of shares for each bond is called convertible ratio.

The features of a convertible bond through the following hypothetical example. Suppose a convertible bond that is issued by DECENT FURNITURE at par value of 1,000 is convertible into 40 shares of a firm's stock, implying a conversion price of 25 per share. If the current stock price is 20, the option to convert is not profitable, and the bondholder will hold the bond and choose not to convert. If the stock price rises to 30, it would become profitable for the bondholder to convert the bond into shares, since each bond can be converted into 1,200 worth of stock, compared to the bond's face value of 1,000. Therefore, convertible bonds give their holders the ability to share in price appreciation of the company's stock. When first issued, convertible bonds offer lower coupon rates than nonconvertible ones. To the bond issuer, it is more cost effective. However, the actual return on the convertible bond has the potential to exceed its stated yield to maturity given its convertibility feature. Meanwhile, the straight bond value acts

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as a "bond floor," since even if the stock price stays low during the whole holding period, a bondholder can still retain the bond's value. Thus, a convertible bond provides a downside protection for the investors.

In the Western countries, convertible bonds tend to be issued by smaller and more speculative companies, because it is costly to assess their business risks and there are concerns that the company management may not act in the bondholders' interest. Notice that convertible bonds represent unsecured and generally subordinated debt. Very often, the issuer is in a new line of business, making it difficult for investors to assign a fair discount rate by assessing the probability of business failure and bond default. The convertibility feature aligns the interests of the holders of convertible bonds with those of the company's management, allowing the investors to profit when the company's share price rises and to minimize losses when its share price falls.

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