You purchased one of Big Corp.\'s 8% 10-year convertible bonds at it\'s $1,000 p

Question

You purchased one of Big Corp.'s 8% 10-year convertible bonds at it's $1,000 par value a year ago when the company's common stock was selling for $20. Similar bond without conversion feature returned 12% at the time. The bon is convertible into stock at a price of $30. The stock is now selling for 5. Assume no dividends. A.) you exercise the coversion feature today and immediately sold the stock you received. Calculate the total return on your investment. B.) What would you return have been if you had invested $1000 in Big's stock instead of bond?

Explanation / Answer

This is a simple calculation, but it reminds us that we need to include dividends (where appropriate) when figuring the return of a stock. Here is the formula: (Value of investment at the end of the year – Value of investment at beginning of the year) + Dividends / Value of investment at beginning of the year = Total Return For you bought a stock for $7,543 and it is now worth $8,876, you have an unrealized gain of $1,333. You also received dividends during this time of $350. What is the total return? ($8,876 - $7,543) + $350 / $7,543 = Total Return $1,333 + $350 / $7,543 = Total Return $1,683 / $7,543 = Total Return 0.2231 or 22.31% = Total Return You can use this calculation for any time period, which is a weakness since it doesn’t take into account the time value of money. Simple Return Simple return is similar to total return, however it is used to calculate your return on an investment after you have sold it. Here is the formula: Net Proceeds + Dividends / Cost Basis - 1 Let’s run through an example. Suppose you bought a stock for $3,000 and paid a $12 commission. Your cost basis is $3,012. You sell the stock for $4,000 and there is another $12 commission, so your net proceeds are $3,988. Dividends amounted to $126. $3,988 + $126 / $3,012 - 1 = Simple Return $4,114 / $3,012 – 1 = Simple Return 1.36 – 1 = Simple Return 0.36 or 36% = Simple Return Like the Total Return calculation, the Simple Return tells you nothing about how long the investment was held. If you want to see after-tax returns, simply substitute “net proceeds after taxes” for the first variable and use an after tax dividend number. Compound Annual Growth Rate For investment held more than one year, you may want to look at this more sophisticated, but not much more complicated calculation. The Compound Annual Growth Rate shows you the time value of money in your investment. A 40 percent return over two years is great, but a 40 percent return over ten years leaves much to be desired. Many people find math challenging, but there are a couple of simple formulas that can help you understand your return from stock investments. These formulas answer the question: What is the return on my investment? You use them to figure out where you are (how much profit or loss) and what your next step should be. You use the formulas when you sell an investment to calculate your return. You can also use these formulas to see where you are at any particular point in time, even if you don’t plan to sell or if you want to know the return as a factor in your sell or hold decision. The first formula is known as the Simple Return. It gives you a quick number, but it has some limitations, as you’ll see in a minute. Formula The formula is: Return = net proceeds + any dividends / what you paid - 1 Now let’s plug some numbers in and see how it works. If you bought 200 shares of Kumquat Ltd. for $30 per share and paid an $18 commission, the total cost would be $6,018 (200 x $30 = $6,000 + $18 = $6,018). You sold the stock for $36 per share and paid an $18 commission. If you received dividends of $1 per share, that equals $200. Plugging those numbers in, we get: $36 x 200 = $7,200 - $18 = $7,182 for net proceeds. Putting it all together: Simple Return = $7,182 + $200 / $6,018 - 1 Simple Return = $7,382 / $6,018 -1 Simple Return = 1.23 – 1 Simple Return = .23 or 23% Helpful While this is helpful information, it doesn’t tell the whole story and is really only valid for investment held for very short periods. To get a valid picture of how a stock or other investment has done over time, you need to calculate the compound annual growth rate. The compound annual growth rate gives you a better picture of what an investment has done for you because it takes into account the time value of money and evens out the ups and downs so you can see the growth as a single number. To get the compound annual growth rate, you use the Simple Return with an adjustment. The adjustment is eliminating the subtraction of 1 at the end of the calculation. Simple Return From our example above, the Adjusted Simple Return would be 1.23. The next step is to factor in the length of time you have held an investment. Let’s assume you have held the Kumquat stock for 4 years. Divide 1 by the number of years the investment has been held (4) and this will give you the factor to adjust the return: 1 / 4 = .25 power or exponent Compound annual growth rate = adjusted simple return (raised to the power) - 1 Compound annual growth rate = 1.23 (.25) -1 Compound annual growth rate = 1.05311 -1 Compound annual growth rate = .05311 or 5.31 percent Need Calculator You will need a calculator that allows you to enter the exponent or power. You can also make the calculations using Microsoft Excel. In the “Insert Function” under the “Insert” menu, pick “Math & Trig” from the drop down box and scroll down to “POWER.” This function allows you to enter the number and the power you want to raise it to. As you can see, our 23 percent Simple Return looked pretty good until we factored in the time you held the stock. The Annual Compound Growth Rate of 5.31 percent is nothing to get excited about. By the time you pay taxes and factor in inflation, this investment lost money. Once you have the compounded annual growth rate you are in a better position to see what the stock has actually done. If you want an after-tax calculation, substitute after tax proceeds and after-tax dividend numbers. Conclusion Compound annual growth rate calculations give you an accurate picture of how your investment is doing over time and let you get beyond the “peaks and valleys” to a constant number that you can confidently use in your decision making.

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