The “Mean Realizable Present Value” of a future income

The “Mean Realizable Present Value” of a future income

by tonytran2015 (Melbourne, Australia).

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(Blog No. 3xx).

#inflation, #present value, #inflation discount, #probability,

Many investors have run into losses due to their blind application of inappropriate valuations. They just blindly buy a bond if it is sold at less than its “present value” and thought that they have bought such a thing at a discount only to find out later on that they have paid too much.

Here I propose that they should use a more appropriate “mean realizable present value”
instead of “present value” for stream of incomes such as bonds.

1. The “present value” commonly used by investors.

The “present value” of some future income is an amount of money needed at present to buy and store a wealth to match that income when it arrives.

The present value of an uncertain future income is therefore also uncertain like that income.

Common application of “present value” to a stream of future incomes has simply equated it to the “inflation discounted value” of that stream of income.

For example, when a bond issuer commits to pay the bond holder 3 yearly installments of 1000 dollars each, the “present value” of that bond is often valued by only compensating for inflation to be

1000×(1-Inf) + 1000×(1-Inf)×(1-Inf) + 1000×(1-Inf)×(1-Inf)×(1-Inf)

At a rate of inflation of 3% per year, it will be

1000×(0.97) + 1000×(0.97)×(0.97) + 1000×(0.97)×(0.97)×(0.97) = 2911 dollars.

Many investors have run into losses due to their blind adoption of such inappropriate “present value” for their bond. They just blindly buy the bond if it is sold at less than 2911 dollars and thought that they have bought a “debt at a discount”.

If and when the bond issuer goes bankrupt, they lose all uncollected payments and the reality is they receive much less than the 2911 dollars of inflation discounted value in their formula.

Therefore such definition of “(inflation-discounted) present value” is inappropriate for investors. It is proposed here that investors should use instead the “mean realizable present value” defined as in the following.

2. The “mean realizable present value” of a future income.

It is more appropriate for investors to use a “mean realizable present value” of a future income defined to be the “mean of all possible present values” from that income.

Figure 1: The question is “Would you exchange 1 bird in your hand for 3 birds in the bush?”.

For example, when a bond issuer commits to pay the bond holder 3 yearly installments of 1000 dollars each, the “mean realizable present value” of that bond should be valued according to the following.

1000×(1-Inf)×(Pr. of 1st payment) + 1000×(1-Inf)×(1-Inf)×(Pr. of 2nd payment) + 1000×(1-Inf)×(1-Inf)×(1-Inf)×(Pr. of 3rd payment).

At a rate of inflation of 3%, the present value of that bond will be

1000×(0.97)×(Pr. of 1st payment) + 1000×(0.97)×(0.97)×(Pr. of 2nd payment) + 1000×(0.97)×(0.97)×(0.97)×(Pr. of 3rd payment)

It is equal to 2911 dollars only if the Probability of each payment is 1, that is when there is no possibility of any default.

Generally the present value of that bond will be

1000×(0.97)×(Pr. of 1st payment) + 1000×(0.97)×(0.97)×(Pr. of 2nd payment) + 1000×(0.97)×(0.97)×(0.97)×(Pr. of 3rd payment) << 2911 dollars.

Using the past records for the survival of new small companies we can guess the probabilities of survival for any new small company in Australia as:

Prob. of surviving longer than 12 month = 66%,

Prob. of surviving longer than 24 month = 66%×90% = 59%,

Prob. of surviving longer than36 month = 66%×90%×90% = 53%.

Therefore the “mean realizable present value” of a bond issued by a new small Australian company will be

1000×(0.97)×66% + 1000×(0.97)×(0.97)×59% + 1000×(0.97)×(0.97)×(0.97)×53% = 640 + 555 + 484 = 1679 << 2911 dollars.

So the “mean realizable present value” is only 1679 dollars, a much lower value than 2911 dollars of “(inflation-discounted) present value” often advocated in uncritical financial analyses.

3. Dependence on the survivability of the payer.

crystalballc70.jpg

Figure 2: A crystal ball is needed to determine accurately the probability of any given company surviving in the future.

The difficulty in working out the probability of survival of the payer is one essential problem in investment.

The disadvantage of using “mean realizable present value” is that the probabilities in use may NOT be agreed upon between transactional parties whereas the “inflation-discounted present value” has always been mutually accepted as the analysis based on the best case.

However, using this new “mean realizable present value” gives a more appropriate valuation for investors. It presents a combination of the current “present value” and the commercial “rating” of that income. This “realizable present value” reduces to zero when the payer goes bankrupt and the “inflation-discounted present value” is only the upper limit of this “mean realizable present value”. The upper limit is reached when the payer survives past the final payment.

4. Conclusion

This “mean realizable present value” of an income stream can be applied to the income streams of bonds or of commercial loans. If it is used instead of the “present value” in the balance sheet of any economic entity the balance sheet of that entity would give a better estimate of its net worth.

This “mean realizable present value” explains to investors why some certain company issued bond may become worthless when the chance for the company to survive to repay to its bond holders vanishes. The value does increase and decrease with market conditions and can better quantify the market values of “loans” hold by any lender (or bank). It would be easy for investors to then understand the sudden vanishment of “wealth” hold by banks or investment funds.

Using these “mean realizable present values” the balance sheets of central banks may also look vastly different after they bought all bonds on the markets to support all companies on the Stock Exchanges.

References:

[1]. Inflation is vicious to fiat money users posted Mar 29th, 2017.

[2]. Investors-beware-dividend-growth is misleading, posted on September 01, 2017

[4]. Why does the Federal Reserve aim for 2 percent inflation over time?, Board of Governors of the Federal Reserve System,https://www.federalreserve.gov/faqs/economy_14400.htm, updated January 26, 2015, accessed 03 Mar 2017.

[5]. Your fiat money, posted January 9, 2017.

[6]. Your fiat money (Part 2), posted January 12, 2017.

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