Posts Tagged ‘discount rate’

How well will stocks do in times of high inflation?

Tuesday, April 28th, 2009

As we all know, governments all over the world are engaging in expensive and wasteful bailouts, stimulus and printing of money. Naturally, this resulted in many investors being worried about the long-run impact on price inflation. Already, contrarians like Marc Faber, Warren Buffett and Jimmy Rogers are making the high inflation call.

Investors are scrambling for ways to hedge against high inflation. One of the asset class being considered to do that job is stocks. Indeed, Zimbabwe is a great example of the world’s ‘best performing’ stock market in the midst of hyperinflation (see Zimbabwe: Best Performing Stock Market in 2007?). In a hyper-inflationary economy, earnings can soar in nominal terms through the sheer force of price inflation. Therefore, stock prices will definitely rise in nominal terms.

So, should you rush out to buy any stocks if you are worried about hyperinflation in the future? Before you do so, take note of these points:

  1. A hyper-inflationary economy is in deep trouble. Unemployment can be very high (e.g. the stagflation of the 1970s, 90% unemployment rate in Zimbabwe), many businesses will fail and there will be social problems. You will likely witness depleted store shelves as there will be shortages of goods. Therefore, in such economic environment, not all businesses will survive. This means that many stock prices are going to be zero. You will not want to buy into one of them.
  2. Our theory is that in hyper-inflationary times, while stock prices can go up tremendously in nominal terms, their price-earning (PE) ratios will decline. The reason is not so much due to earnings growth expectation. Instead, it will be due to higher discount rate applied by the market. Remember back in Quantitaive demonstration of the effects of price inflation on your investment, we showed you how high inflation can easily make a mockery of your investment returns if you apply a discount rate that turns out to be far below the inflation rate. Historically, the rate of inflation for hyper-inflations increases exponentially. This may translate to higher and higher inflation expectations, which result in higher and higher discount rates, which in turn imply lower and lower PE ratios.

Zimbabwe’s experience shows that in nominal terms, stocks are great investments. But in real terms, their performances are very restrained.

Quantitaive demonstration of the effects of price inflation on your investment

Thursday, March 12th, 2009

For the hypothetical business in our previous article, Revealed: The error in the Buffett logic, we will show you how earnings are valued (using the discounted cash-flow method) and the effects inflation with a table:

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Here are the explanations for the columns on the table:

  1. Year – The table shows the year-by-year outcome in a 20-year period. This column denotes the year.
  2. Earnings – It shows the earnings of a business. You can see, at the end of the first year, the business will generate $100 of earnings. Earnings will grow at a rate denoted by the corresponding entry on the 6th column (Earnings Growth). In this example, earnings are growing at a rate of 25% per year. You can see, at the end of the 20th year, that business will earn $6938.89.
  3. PV of Earnings – This is the present value of earnings earned at the end of the year. The discount rate used in the present value calculation is 30%, which is defined in the 7th column of the table. As you can see, the present value of the 20th year of earnings ($6938.89) is only $36.51. As you can see, if you add up first 10 figures of that column, you will get $648.87, which is the number we gave in the previous article.
  4. Total PV – This is the sum total of the previous column. This is also the valuation of 20 years worth of earnings at the discount rate of 30%.
  5. Accumulated Re-invested Earnings – What happens if you re-invest all the earnings at an investment return rate that is the same as the discount rate (30%)? Each row of this column will show you what your total accumulation of that business’s earnings. As you can see, at the end of year 20, you will have accumulated $206,626.93.
  6. Inflation Rate – This column define the price inflation rate.
  7. FV of Total PV Due to Inflation – What if inflation is allowed to do its work to devalue your cash? In this column, it shows how much $1,087.23 (the valuation of 20 years worth of earnings) at the beginning of the first year will have to be in order to maintain the purchasing power at the end of the year. As you can see,  $94,301.83  at the end of the 20th year can only buy as much as $1,087.23 at the beginning of the first year, given price inflation of 25% for every year.

As this table shows, as long as you can re-invest the earnings of the business at a compounded return equivalent to the discount rate (30%), which is higher than the price inflation rate (25%), you will beat inflation. That is, your wealth in real terms will rise. But if you decide to stuff your earnings as unproductive cash under the bed, you will lose out to inflation. That is, at the end of the 20th year, you will have accumulated $34,294.47 in cash but price inflation will mean your original $1,087.23 investment have to grow to $94,301.83 in order to preserve its purchasing power.

If you apply a discount rate of only 10%, the valuation will balloon to $7,928.52, which is equivalent to  $687,689.46 in 20 years time due to inflation. But if you can only re-invest your earnings (which is growing at 25%- the same as inflation) at 10% (compounded), you will only accumulate $53,339.12, which means inflation will destroy your wealth in real terms.

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.

Two uncertainties of valuing a business- risk & earnings

Monday, September 29th, 2008

In our previous article, Measuring the value of an investment, we learnt about the theory and mathematics behind the valuation of a business under artificial conditions that are clearly defined. Under such conditions, we know exactly the business’s future earnings and its risk relative to government bonds. Therefore, valuing artificial businesses is easy and straightforward. But in the real world, earnings and risks are the very things that cannot be so easily and clearly defined and quantified. As we said in that article,

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.

Thus, we should not be under the impression that the dollar number that is produced from the valuation of a real-world business is a scientifically precise number. Rather, no matter how precise that number is, it is just an estimate. And it is far more important for that number to be accurate than for it to be precise. If you are confused with what this means, we suggest that you read our previous article, Confusion between precision & accuracy and Example of precisely inaccurate information.

First, we will discuss the earnings of a business. Stock analysts spend a lot of effort trying to divine the future cash flows of the business that they are analysing. However, not all businesses are the same. Some are so straightforward that it is very easy to have a very accurate estimate of their future earnings. Others are so complicated that any attempts at estimating their future earnings are at best rough guesstimates. For some, they can even be unpredictable or volatile. To be a successful investor, you will do better to avoid businesses that you find difficult to come up with accurate earnings estimates. We will explain the characteristics of businesses that favour accurate earnings estimates in future articles.

Next, we will discuss the risk of a business. The mainstream finance uses volatility of prices to define risk. As we said before in How do you define risk?,

In today?s financial services industry, a large part of risk is defined by the volatility of the price?the more volatile the investment is, the more ?risky? it is. This definition of risk arises from the fact that retail investors tend to perceive the safety of an investment in terms of how much of its value can be preserved within a given period of time.

But we see risk differently. As we explained before in Measuring the value of an investment, the risk in value investing is a relative concept. The payments of government bonds are assumed to be completely risk-free whereas the earnings of a business are not so certain. Risk relates to how secure the future earnings of a business is. To illustrate this concept, let’s suppose there are two different businesses with identical earnings estimates. One is located in a geologically stable place (e.g. Singapore) while the other is located in an earthquake prone area (e.g. Tokyo). We can say that the latter one carries more risk because its earnings can be cut due to an earthquake. Therefore, it will carry a higher discount rate.

Between earnings and risk, the latter is the most subjective of all in the business’s valuation. In a world of Black Swans, risk is not something that can be easily quantified into a precise number (discount rate). It is also a number that cannot be verified for correctness. For earnings, all we have to do is to compare earnings estimates with the actual earnings to have a gauge of the estimate’s accuracy. But you cannot do so for the discount rate. Thus, in any valuation of a business, the discount rate is the first to be fudged by analysts.

Bear that in mind when you look at analyst reports on the price targets of stocks.

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.