## Quantitaive demonstration of the effects of price inflation on your investment

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: 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.

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