Wednesday, April 3, 2013

What is the INTRINSIC or TRUE VALUE of an investment asset? Part III

Spreadsheet stuff – Intrinsic Value

So let’s put in practice what we have learned. Say an investment’s purchase price is $28.04. To buy it, you have to pay out of cash flow $28.04, in other words you have at time 0 a negative cash flow of $28.04.


Figure 1. Cash flow from investment including purchase in year 0 and sale in year 5 is shown in column 2. Cumulative Cash Flow shows when you have received back your investment funds. Investment Value is the potential market value of the investment in Years 0 through 5. The last column is the Cash flow expressed in Today's Dollars (i.e. Year 0).
A year later you receive dividends equal to 5% of the purchase price. Investors say then that the dividend yield is 5%. Thus you receive at the end of you first year $0.93, i.e. you have a positive cash flow of $0.93. If you had bought additional shares that year, say $10 worth of shares, then the cash flow for year 1 would have been $0.93-$10= $-9.07.
Taking additional share purchases or other expenditures such as brokerage charges or interest on money borrowed to purchase the shares into account would make our example too complex and that defeats the purpose of this exercise. So in our case, we only receive dividends - $0.93 in year 1.

Dividends tend to rise with rising corporate profits and our investment is made in an excellent company that increases its dividend every year. So in year 2 we’re having a positive cash flow of $0.96 and the year there after $0.99, and so on.

Let’s assume that we sell our investment at the end of year 5. The share price has increased to $37.00 (see investment value column) at the time of sale. Thus cash flow in Year 5 is: dividend plus sales proceeds: $1.05 + $37.00 = $38.05. Now we have constructed the cash flow stream over the 5 year life of our investment (Figure 1).

In the third column of our spreadsheet you see the cumulative cash flow; the total cash flow received up to a particular year (row). E.g. in year 3, we had a total cash flow of negative $25.17. In year 4 we received dividends of $1.02 which created for that year positive cash flow of $1.02. Thus the total or cumulative cash flow received between Year 0 and Year 4 was negative $25.17 plus $1.02 which equals negative $24.15.

The term Net Present Value means “what is $1.00 in Year 4 worth in Year 0.” Think inflation. What can $1.00 that you receive four years from now buy you today?

What if you borrowed money and you paid 6% interest and you get four years from now $1.00, how much would you pay for that dollar today? Correct, you would pay $1.00 minus the interest paid over those four years (assuming there is no inflation). The interest rate you paid is called the ‘Discount Rate’ it is a measurement of how much you have to pay to borrow the money, i.e. the Cost of Money.

If you could invest your money risk free for 6% and you get the chance to invest in a riskier opportunity, then to  invest in this riskier investment you would want to get a better return than 6%. In fact, the higher the risk the higher a return you would require.

You can express Net Present Value in terms of today’s purchasing power, in other words correct it (or in accounting lingo, discount it) at today’s inflation rate. However, many corporations and investors look at either the cost of borrowing the money or the costs of forgoing investing in a risk free opportunity compared to a riskier one.

Thus many corporation set the discount rate for calculating NPV at the rate of return they can get on a ‘risk free’ investment – typically somewhere between 10 and 20%.

What rate of return can you get on a risk free investment today? GICs are often guaranteed by the government and over five years you may get interest at a rate of 2.7% This is probably the best ‘risk free’ return you can get as a small investor and this maybe a suitable discount rate for you to see how much more you will make when investing in the shares of a riskier stock purchase.

Fig 2. At the top we calculate in the red boxed column the Net Present Value of the entire investment including purchase price in Year 0 dollars. Note since we assume that typically investment income is received at year's end, Year 0 is basically the start (i.e. January 1) of Year 1. Thus $0.93 received on December 31 of Year 1 is worth $0.84 the the start of Year 1 which we call: Year 0. This is one of the quirks of a NPV calculation. Figure 2 shows the INTRINSIC VALUE of the investment, i.e. the proper purchase price, which is the Net Present Value of all dividends and sales proceeds received over the five year live of our investment. If the market price is below intrinsic value you will make a return better than the required 10% (discount rate), while if you buy at a higher market price then you return will be less than the discount rate.
In our example we pretend to be a big business that requires a 10% discount rate. Thus we can now ask, what is $0.94 in dividends a year from now worth today discounted at 10%? In other words, what is the Net Present Value of $0.93 using a discount rate of 10%?
The answer is: $0.84 because at a rate of return of 10%, we’ll have $0.84 + $0.084 = $0.93 (rounded off) by year’s end. If we received two years from now $0.96 in dividends that would be worth $0.79 in today’s dollars:

$0.79+ $0.079 = $0.87 in year 1 plus $0.87*10% = $0.087 in year 2 or 0.79 + 0.079 + 0.087 = 0.96. In other words $0.96 dividends in year 2 is worth $0.79 today (year 0).

In the column ‘NPV of Cash Flow', I have converted the cash flow for each year into ‘Year 0’ dollars or NPV. When you add up the yearly NPV from year 0 to year 5, we’re calculating the Net Present Value of the entire cash flow stream of the investment including the initial purchase price and the final sales price.  It shows a negative NPV of $1.34. Apparently, this investment will not return the 10% that we want from our investments.

In fact, if we want a NPV = 0 for this particular investment we would need a discount value of 8.9%. The discount rate that would give an investment a NPV of $0 is often called the Internal Rate of Return or IRR. So our investment’s IRR is 8.9%

Now we’re finally ready to ask the question: Given that we receive dividends in five successive years of $0.93, $0.96, $0.99, $1.02 and $1.05 plus final sale proceeds of $37.00 and given that we require a 10% annual rate of return would you pay today $28.04 for this investment?

Your answer should be no, because the intrinsic value of this investment is less than $28.04. For us to earn 10% per year, I would pay only the net present value of this income stream discounted at 10% which is: $26.70 or the sum of the NPV of years 1 through 5. The Intrinsic Value of our stock investment is $26.70.
 
Calculating the intrinsic value to determine how much we are willing to pay for an investment takes a lot of emotions out of our investment decision. Two important questions remain. The first question is: How confident are we that the dividend payments are as forecasted? In other words: How wide is your moat?  This issue we discussed in the previous post.

The second question is how do we make a reliable prediction as to what the final sales price will be? In order to do that, we will have to look at the earnings yield, i.e. earnings/purchase price (E/P) rather than the dividend yield. If we could forecast what the earnings by our investment would be five years from now and assuming the earnings yield will not change, then the stock's end value would equal the forecasted earnings divided by the earnings yield. We’ll discuss this in the next post.


 A final point: When does this investment payout? Let me rephrase the question: When have we received dividends equal to the original purchase price? The answer is: when Cumulative Cash Flow equals 0 (Figures 1 and 2 - column 3). Or… assuming the dividend yield of 5% does not change over the next five years, we calculate that in year 20 (=1/dividend yield) we will have received dividends totalling the initial purchase price.

For those amongst us who really like math:

 

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