## Posts Tagged ‘future value’

### Measuring the value of an investment

Thursday, July 3rd, 2008

If you have not realised already, our previous article, Is the value of an asset its price?, is the beginning of a series explaining the concept of value investing. If you understand value investing, you will then be able to understand the investment philosophy of Warren Buffett, the famous investor who is currently the richest man on earth.

Mind you, value investing is counter-intuitive. It requires that you truly understand the difference between price and value- price is what you pay for and value is what you get. The problem is, the financial market/industry often uses these two words interchangeably, which means that their meaning gets merged in our sub-consciousness. To be an outstanding investor, it is important for you to de-merge the meaning of these two words in your mind. What we are trying to do here is to expand on what Rich Dad, Poor Dad taught about what an asset truly is.

In the context of investing, when you pay a price for an asset, you are sacrificing current consumption in order to receive the asset’s future cash flow for future consumption.

For example, if you pay \$100 for a newly issued 10-year government bond that pays 6% per annum, you are sacrificing \$100 of today’s consumption in order to receive \$6 per year for the next 10 years. That 6% is your rate of return on your investment. Now, let’s say you decide to sell your government bond to Tom at \$90. The rate of return for Tom is 6/90 = 6.67%. Let’s say Tom sells the bond to Dick at \$110, the rate of return for him will be 6/110 = 5.45%. Thus, the rate of return of the bond is inverse to the price paid for it.

Next, let’s suppose you pay \$100 for a rate of return of 10% per annum. When you receive that \$10 at the end of the year, you re-invest it into another asset that also pays 10% rate of return. At the end of the second year, you will receive \$11, for which you re-invest it into yet another asset that pays the same rate of return. You do that for all the money that you receive at the end of the year for the next 8 years. What will you have in 10 years time? The answer is \$259. In Excel, the formula is “=FV(10%,10,0,-100)”. That \$259 is the future value of the \$100 at 10% compounding (i.e. you re-invest all returns in the intermediate years) rate of return. The \$100 is the present value of the \$259.

Now, let’s say you have a business enterprise that is as risk-free as long-term government bonds. Let’s say your business can earn \$200 of cash per year for the next 10 years. How much should you sell your business to someone else? The way to calculate it is to add up all the present value of each of the \$200 of future cash inflow per year. But which interest rate should you use in your present value calculation? Since your business is as risk-free as government bonds, it should be the rate of return of a long-term government bond based on its current market price. Let’s say that the current market price of 6% government bond is \$110 (the price that Dick paid). Then the current rate of return (yield) for that bond is 5.45%. That 5.45% that we use in our present value calculate is called the discount rate (we will explain what discount rate means later). We will put all that calculation on a table:

Discount Rate: 5.45%

 Year Cash-flow Present value of cash flow 1 \$200.00 \$189.66 2 \$200.00 \$179.86 3 \$200.00 \$170.57 4 \$200.00 \$161.75 5 \$200.00 \$153.39 6 \$200.00 \$145.46 7 \$200.00 \$137.94 8 \$200.00 \$130.81 9 \$200.00 \$124.05 10 \$200.00 \$117.64

Total present values=\$1511.15.

That is, if you pay \$1511.15 for a long term government bond today with a rate of return of 5.45% and re-invest all the cash inflow each year, you will end up with \$2569.06 in 10 years time. On the other hand, if you re-invest all the \$200 that your business earns each year in the same bond, you will also end up with \$2559.06 in 10 years time too. Since your business is as risk-free as long-term government bonds, you are indifferent between the two options. Therefore, the present value of your business is \$1511.15. If you can sell your business above the present value of your business, then you are better off doing so.

Now, what if your business is much riskier (as all businesses are) than the government bond? Then the investor who is about to pay for your business will have to demand a higher rate of return. To do so, he has to pay a lower price than \$1511.15 (remember, we said above that the “rate of return of the bond is inverse to the price paid for it.”). The lower price reflects the higher rate of return that the investor demands for taking the risk of your business failing. To reflect the higher risk of the business, we turn up the discount rate from 5.45% to, say, 10%. This time, the table will look like this:

Discount Rate: 10%

 Year Cash-flow Present value of cash flow 1 \$200.00 \$181.82 2 \$200.00 \$165.29 3 \$200.00 \$150.26 4 \$200.00 \$136.60 5 \$200.00 \$124.18 6 \$200.00 \$112.89 7 \$200.00 \$102.63 8 \$200.00 \$93.30 9 \$200.00 \$84.82 10 \$200.00 \$77.11

Total present values=\$1228.91.

Say, if the investor believes that a higher return of 10% is sufficient to compensate him for the additional risk, then he will be willing to pay not more than \$1228.91.

So far, this is the theory behind value investing. In practice, in a world of uncertainty and Black Swans, it is not possible to know the exact amount of future cash flow of any business. Also, risk is not something that we can easily quantify nicely in order to derive a value for the discount rate. That is the ‘art’ of investing.

In the next article, we will explain how inflation is related to the value of your investment.