Posts Tagged ‘present value’

Revealed: The error in the Buffett logic

Tuesday, March 10th, 2009

In our previous article, we asked our readers to spot the flaw in Warren Buffett’s logic. Today, we will reveal the answers. Before you read on, please take the time to understand our guide, Value investing for dummies.

As Buffett said, staying in cash and cash equivalent (e.g. government bonds) is a bad move because price inflation is likely to be very high in the future. This, we agree. But does it mean one should switch from cash to stocks today? If the answer is “yes,” then there’s an error in logic.

First, by that very statement, Buffett was implying that the yields of government bonds are far too low. Essentially, this means that those who buy and hold those bonds will have their wealth frittered away by price inflation.

Next, as we explained in Value investing for dummies, value is a relative concept. Stocks are valued relative to risk-free government bonds, which in turn is suppose to reflect future price inflation. If the yields in government bonds are wrong by a long shot, then stock valuation will be wrong.

To explain this point better, let’s use an example. Let’s suppose the following conditions:

  1. 30-year Treasury bond yield is 3.5%.
  2. An almost risk-free business with monopolistic powers (let’s imagine it is Woolsworth).
  3. That business can raise prices and grow its earnings at 25% per year.
  4. The first year earnings of the business is $100.

If we apply a 5% discount rate on 10 years of that business’s earnings, we get a present value of $2358.76. That 5% is arbitrary chosen from the fact that it is a little above the Treasury bond yield.

As long as the long-run average price inflation is around the vicinity of the 30-year Treasury bond yield, buying the stock at below the present value of its earnings is a bargain. But what if the bond yield is way way way wrong? Let’s say the price inflation rate turns out to be, say 25% (in other words, the business earnings grow fast enough to merely keep up with inflation). You can see that applying a discount rate of only 5% will give you a return far below price inflation (but slightly higher than Treasury bond yields). If you want a return higher than price inflation, your discount rate will have to be north of 25%.

If we apply a 30% discount rate on 10 years of that business’s earnings, we get a present value of only $648.87! That 30% is arbitrary chosen from the fact that it is a little above the price inflation rate.

So, if you believe that government bonds are severely under-pricing future price inflation and you have no idea how the ravages of price inflation will look like, then how can you value stocks correctly? If the price inflation turns out to be Zimbabwean-style hyperinflation, then you will lose big money (in real terms) investing at today’s stock price.

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.

Now, back to the crux of this article…

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.