Valuation %u2013 convertible bond You purchased one of AAA Corp.%u2019s 9%, 15-y
ID: 2699366 • Letter: V
Question
Valuation %u2013 convertible bond
You purchased one of AAA Corp.%u2019s 9%, 15-year convertible bonds at its $1,000 par value a year ago when the company%u2019s common stock was selling for $25. Similar bonds without a conversion feature returned 10% at the time. The bond is convertible into stock at a price of $35. The stock is now selling for $40.
Assume no dividends.
a) You exercise the conversion feature today and immediately sold the stock you received. Calculate the total return on your investment.
b) What would your return have been if you had invested $1,000 in AAA%u2019s stock instead of the 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 %u2013 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%u2019t 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%u2019s 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 %u2013 1 = Simple Return
1.36 %u2013 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 %u201Cnet proceeds after taxes%u201D 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%u2019t 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%u2019ll see in a minute.
Formula
The formula is:
Return = net proceeds + any dividends / what you paid - 1
Now let%u2019s 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 %u2013 1
Simple Return = .23 or 23%
Helpful
While this is helpful information, it doesn%u2019t 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%u2019s 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 %u201CInsert Function%u201D under the %u201CInsert%u201D menu, pick %u201CMath & Trig%u201D from the drop down box and scroll down to %u201CPOWER.%u201D 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 %u201Cpeaks and valleys%u201D to a constant number that you can confidently use in your decision making.
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