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Confused by Investing - Maybe It`s the New Math

If there`s something about your investment portfolio that doesn`t seem to add up, maybe you should check your math. Lots of folks are perplexed by the mathematics of investing, so I thought a refresher course might help. Here`s a look at some key concepts:

10 Plus 10 Is 21

Imagine you invest $100, which earns 10% this year and 10% next. How much have you made? If you answered 21%, go to the head of the class. Here`s how the math works. This year`s 10% gain turns your $100 into $110. Next year, you also earn 10%, but you start the year with $110. Result? You earn $11, boosting your wealth to $121. Thus, your portfolio has earned a cumulative 21% return over two years, but the annualized return is just 10%. The fact that 21% is more than double 10% can be attributed to the effect of investment compounding, the way that you earn money each year not only on your original investment, but also on earnings from prior years that you`ve reinvested.

The Rule of 72

To get a feel for compounding, try the rule of 72. What`s that? If you divide a particular annual return into 72, you`ll find out how many years it will take to double your money. Thus, at 10% a year, an investment will double in value in a tad over seven years.

What Goes Down Comes Back Slowly

In the investment world, winning is nice, but losses can really sting. Let`s say you invest $100, which loses 10% in the first year, but bounces back 10% the next. Back to even? Not at all. In fact, you`re down to $99. Here`s why. The initial 10% loss turns your $100 into $90. But the subsequent 10% gain earns you just $9, boosting your account`s value to $99. The bottom line: To recoup any percentage loss, you need an even greater percentage gain. For instance, if you lose 25%, you need to make 33% to get back to even.

Not All Losses Are Equal

Which is less damaging, inflation of 50% or a 50% drop in your portfolio`s value? If you said inflation, join that other bloke at the head of the class. Confused? Consider the following example. If you have $100 to spend on cappuccino and your favorite cappuccino costs $1, you can buy 100 cups. What if your $100 then drops in value to $50? You can only buy 50 cups. And if the cappuccino`s price instead rises 50% to $1.50? If you divide $100 by $1.50, you`ll find you can still buy 66 cups, and even leave a tip.

PRESENT VALUE OF MULTIPLE CASH FLOWS

When we calculate the present value of a future cash flow, we are asking how much that cash flow would be worth today. If there is more than one future cash flow, we simply need to work out what each flow would be worth today and then add these present values.

Cash Up Front versus an Installment Plan

Suppose that your auto dealer gives you a choice between paying $15,500 for a new car or entering into an installment plan where you pay $8,000 down today and make payments of $4,000 in each of the next two years. Which is the better deal? Before reading this material, you might have compared the total payments under the two plans: $15,500 versus $16,000 in the installment plan. Now, however, you know that this comparison is wrong, because it ignores the time value of money. For example, the last installment of $4,000 is less costly to you than paying out $4,000 now. The true cost of that last payment is the present value of $4,000.

Assume that the interest rate you can earn on safe investments is 8 percent. Suppose you choose the installment plan. As the time line in Figure 1.9 illustrates, the present value of the plan`s three cash flows is:

Present Value

Immediate payment $8,000 = $8,000.00

Second payment $4,000/1.08 = 3,703.70

Third payment $4,000/(1.08)2 = 3,429.36

Total present value = $15,133.06

Because the present value of the three payments is less than $15,500, the installment plan is in fact the cheaper alternative.

The installment plan`s present value equals the amount that you would need to invest now to cover the three future payments. Let`s check to see that this works. If you start with the present value of $15,133.06 in the bank, you could make the first $8,000 payment and be left with $7,133.06. After 1 year, your savings would grow with interest to $7,133.06 1.08 = $7,703.70. You then would make the second $4,000 payment and be left with $3,703.70. This sum left in the bank would grow in the last year to $3,703.70 1.08 = $4,000, just enough to make the last payment.

The present value of a stream of future cash flows is the amount you would have to invest today to generate that stream.