=>A Method Of Estimating How Long It Will Take (In Years) To Double Your Money Using Compound Interest At A Given Rate.
=> A Method Of Estimating At What Rate Of Compound Interest It Will Take (In A Whole Number Percentage) To Double Your Money In A Given Number Of Years.
In finance, the rule of 72, the rule of 70 and the rule of 69 are methods for estimating an investment’s doubling time. The rule number (e.g., 72) is divided by the interest percentage per period to obtain the approximate number of periods (usually years) required for doubling. Although scientific calculators and spreadsheet programs have functions to find the accurate doubling time, the rules are useful for mental calculations and when only a basic calculator is available.
These rules apply to exponential growth and are therefore used for compound interest as opposed to simple interest calculations. They can also be used for decay to obtain a halving time. The choice of number is mostly a matter of preference, 69 is more accurate for continuous compounding, while 72 works well in common interest situations and is more easily divisible. There are a number of variations to the rules that improve accuracy. For periodic compounding, the exact doubling time for an interest rate of r per period is
where T is the number of periods required. The formula above can be used for more than calculating the doubling time. If you want to know the tripling time, for example, simply replace the constant 2 in the numerator with 3. As another example, if you want to know the number of periods it takes for the initial value to rise by 50%, replace the constant 2 with 1.5.
You can amaze your friends and colleagues by doing compound interest computations in your head (or on a napkin, if you require one).
For example, the amount of time that is required to double your investment at a compound interest rate of 4% would be 72/4, or 18 years, while the time required to double your investment at a rate of 8% would be 72/8, or 9 years.
As another example, the rate of compound interest required to double your money in 5 years would be 72/5, or 14.4%, while the rate of compound interest required to double your money in 10 years would be 72/10, or 7.2% per year.
It’s a very good system for quick and dirty estimates of time and compound interest. Use it, and enjoy it.
Douglas E. Castle
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A temporary cash crunch situation is something that occurs in the ordinary course of business in most every organization, especially when the business is of a seasonal nature or when the businesses is in a rapid stage of growth, i.e., inundated with purchase orders but without sufficient cash to fill them and to also pay recurring expenses. But if a cash crunch situation is chronic, a diagnosis of the reason must be made, and appropriate actions must be taken. This article will give you the ability to do both.
Bear in mind that when I speak of revenues, I mean total sales, both as computed on the cash basis and the accrual basis, but when I speak of expenses, I actually mean cash outflows of every nature. Throw away the accounting and auditing textbooks for just a bit so that we can deal with bare bones economic reality. Also by current, I mean as either generated or paid in the ordinary course of operations.
Most every enterprise experiences a period or periods of cash crunch, especially if those businesses are either seasonal or rapidly-growing companies which are generating purchase orders, but do not have adequate cash to fill them while still meeting their obligations, such as payroll, occupancy and the like. There are remedies for both of these situations because they are either predictable or can be financed with short-term debt to enable them to either withstand the “tight season” or to let their cash flow catch up with their market demand.
If cash crunch is chronic, and is an ongoing problem, there is something wrong with the business on a fundamental level. Either revenues are too low, or current expenses (outflows — remember that we’re using lose terminology here) are too high.
If the expenses or outflows are not truly for operations but payable to a lender in the form of , for example, a short-term self-amortizing debt where the payments are large and swollen with principal, the lender may be negotiated with to arrive at an interest-only loan with a provision for a rollover of the principal at the end of its term (optimal for maximizing utilizable cash flow), or possibly a longer amortization period where the payments are lower, conserving more cash flow for operations.
Sometimes a business is improperly capitalized and it requires equity to be infused in order to retire debt. Many businesses which have good fundamentals need to de-leverage themselves by retiring existing debt with equity. This is appropriate unless the equity is used to cover current expenses.
The test is this: If you deduct the debt payments from the total current outflows, and you subtract the number obtained thereby from the revenues, the resulting number should be positive. This means that the business is not properly capitalized, but is probably fundamentally sound. These companies are good candidates for refinancing.
If the number obtained is still negative, then it is highly likely that the business is fundamentally unsound, either due to its core purpose, mismanagement or some improper assumptions which have gone uncorrected for too long. Revenues can be increased by increasing sales through better marketing and sales, or by increasing prices if the market will tolerate this.
When certain food or beverage prices are suddenly increased, a restaurant may hike up its prices and say, for example that “due to the increase in the cost to us of coffee, we are sorry to have to raise the price per cup to $2.25. If the market tolerates this it is a wonderful strategy, especially if done in steps, or if accompanied by a re-packaging or the product or service to somehow differentiate it from what it was previously. The perception of added-value tends to justify an increase in price.
The other possibility is more difficult, and the prospects less pleasant: You may have to negotiate with your employees (or terminate some of their positions), cut back on the use of your contractors, or re-negotiate costs with your vendors. Vendors can often be persuaded to reduce their charges by 1) indicating that the situation is temporary, and that they’ll receive a premium after you’ve reached a certain sales level or after a certain amount of time has passed or 2) an incentive wherein the vendor participates in either your revenue when you’ve reached a certain threshold, or in you company’s ownership (this is an example of a partial vertical integration strategy).
The acid test of the fundamental soundness of any simple business model is this: If debt service is eliminated, do revenues exceed current expenses. Put more realistically, without considering debt, do your revenues (where the earnings process is complete and they are either in the form of cash or accounts receivable) consistently exceed your ordinary current operating outflows including product (inventory purchases as required) or service purchases? If not, can they be restructured to fit the aforementioned parameters? If the answer to both questions is “no,” your business model is fatally flawed, and that must be dealt with — we’ll discuss this at another time.
If you increased your sales volume, increased your prices to customers, eliminated any idle personnel, negotiated with your suppliers, and gotten your bank loan replaced with equity, then you still may be suffering because your customers are not paying you on a timely basis, while you’re paying your vendors promptly.
If your average days to payment on your accounts receivable is 55, and your average days to payment of your current expenses is 35, that 20-day discrepancy can be killing your business, depending upon your profit margins. Sadly, you can’t pay your vendors with your receivables. There are two things to be done to eliminate that 20-day discrepancy:
1) Collect the receivables faster; and
2) Pay your vendors more slowly.
That gap between average days that your business waits to collect its receivables, and the average days its takes to pay its vendors must be reduced to zero, or to a negative number.
You can collect your receivables faster by offering some of your less creditworthy customers less credit, and giving some of your better, faster-paying customers more credit. You can offer early payment incentives or cash payment discounts. You can collect partial payments in cash. Use some imagination. Any of these approaches alone or in combination will cut that 55 days significantly if you focus on achieving this.
You might even get a line of credit up to some percentage of your “acceptable” accounts receivable, factor your receivables, or utilize single invoice financing in order to get that number down a great deal further. Often the real cost of factoring or similar arrangements is about equal to what you might sacrifice if all of your customers took advantage of a discount for paying in less than 30 days.
To eliminate turning a simple article into a doctoral dissertation, suffice it to say that slowing down payments to your vendors requires some diplomacy, some negotiation, and some creativity — but then, if you are in business in these times, you must have an abundance of creativity.
Quick, Easy Metrics:
1) Your average collection days on your receivables (it’s a weighted average) should equal or exceed your average payment days on your current bills;
2) Your average collections days on your receivables divided by your average payment days on your current bills should be equal to or (hopefully) greater than 1.0;
3) The value of all of your cash and all of your receivables divided by the amount of your current bills should always be significantly greater than 1.0 (i.e., no contribution margin). While this is not a measure of cash availability, it is a measure of your gross profit on sales. The bigger the dividend produced by this computation, the greater your basic profit margin and the greater the contribution of your sales to ultimately cover fixed overhead.
The idea is to avoid a cash crunch (assuming that your basic business concept is fundamentally sound) by collecting and hoarding as much cash as you can, and holding off on the payment of bills as long as you can. Remember: If you business is sound, a cash crunch crisis is a phenomenon only created by bad timing. And it’s quite curable.
As part of the Action Plan in any business turnaround, or in any plan of emergence from Chapter 13, reduction and restructuring of debt will play a key role, provided that the business involved in the emergence or “rescue” effort is inherently profitable by its nature — in other words — has an otherwise viable business model which was just mishandled or mismanaged in its execution. If debt can be reduced or eliminated, that is optimal; however, the second alternative which is more palatable to most lenders involves debt restructuring.
You have two restructuring objectives in dealing with lenders or bondholders – one is to defer the payment of the principal (the “balloon”) of the debt and to try to pay it on an interest-only basis for a business recovery period; the other, which is far more popular and easier to negotiate is to restructure the debt amortization or payment schedule. This second alternative permits you, as the acting Chief BusinessRestructuring Officer, to offer your creditors an option where the debt can be paid in a self-liquidating schedule, but simply over a longer time. In fact, if the length of the loan payoff schedule is sufficiently lengthened, you may even offer the creditors a small sweetener, such as a slightly higher interest rate on the loan or bond principal amount as a risk premium for their patience. Even after doing this, your payments to retire the debt in full may still be substantially lower than they would have been at a shorter (i.e., more rapid) amortization schedule.
Let’s see how this rescheduling of amortization works, Mr. Turnaround Expert:
Firstly, we’ll assume that the remaining principal amount of debt on one of our client’s loans is $80,000,000, and that at present, the client is paying off the loan at an interest rate of 8% over a five-year amortization period, fully self-liquidating. This means that the client’s monthly debt service due on the loan is approximately $162,211.
Going further, let’s assume that the client’s Chief Restructuring/ Turnaround Officer has projected (conservatively) that the cash flow available to service the loan will be approximately $175,000. This gives us a narrow margin for error. If we calculate the debt service ratio [divide the available cash flow by the the monthly loan payment obligation], it comes out to be a very, very uncomfortable 1.07884. As a lender, I would much rather see a debt service ratio that approaches 1.50000… that would make me quite comfortable, assuming that the available cash flow projections are reasonable.
If our Chief Restructuring/Turnaround Officer is a very good negotiator, and convinces the lender to reschedule the amortization of the remaining balance over a nine-year term, with a rate of 9% (our turnaround expert has given the lender an extra 1% as a risk premium for lengthening the amortization timeline), the monthly debt payments would now be $108,343.27 — we’ve cut $53,867.73 from our monthly fixed debt payment by doing this. Our new debt service ratio (assuming the $175,000 cash flow available to service the debt is the same, as it should be) will be 1.615236 instead of 1.07884. I now have a debt service ratio which exceeds the 1.50000 standard.
Amortization gives you the opportunity to stay alive longer, but yet to generate sufficient cash flows to pay off this debt, simply by changing its associated amortization schedule. We have restructured the debt brilliantly, assuming no other changes in terms on the part of the creditor, and no additional concessions to the creditor (with the exception of the 1% risk premium) on the part of our turnaround advocate, The Chief Restructuring Officer. Note that he might have chosen to cal himself the Chief Turnaround Officer, but that is too obvious and is on the edge of being Politically Incorrect. “Restructuring” sounds more positive than “Turnaround,” which conjures up images of the grim reaper following the client company’s president around.
This has given us additional cash flow margin (for coverage of other expenses of more than $53,000 per month.
Why would the creditor (a bank, represented by the officer who approved the original loan and who is responsible for handling the relationship with the client) agree to this?
Our negotiator simply took the bank officer aside and apprised him of the following facts and conclusions, gently but firmly:
1. If the client company were to go out of business and liquidate (Chapter 7, perhaps), the proceeds left to pay the bank would be less than 50% of the remaining loan principal. That would mean a substantial loss to the bank attributable directly to the officer’s decision to extend credit;
2. The foregoing could be very injurious for the officer’s career objectives, or perhaps the ability to remain employed by the bank at all;
3. If the client company remained in business, there would be no write-down or loss relating to the loan (the principal would be paid in full), and the officer would have made a good financial and career decision. His decision to allow the rescheduling of the loan has made it possible for the client company to stay in business and pay off the loan in full. Plus, the officer can speak about how “good a deal maker he was” by adding a loan premium of 1%, increasing the bank’s yield on the loan;
4. The client company keeps its deposits, its payroll account, all of its 100 or so employees have consumer loan, credit card, car loan or lease, deposits, checking or other business with the bank, all of which will now will definitely stay intact due to the officer’s “goodwill gesture to keep the company in business and everyone employed”. Interestingly, the officer also gets a credit for funds supplied to the bank (i.e., deposits — especially to demand deposit accounts (i.e., business checking), and this client has kept an average total balance in the bank of close to $1.5 million, all of which the bank earns interest on (this is called in the banking trade “playing the float”) while the client, who receives no interest waits for funds to “clear” and the bank puts this money out on overnight interest-bearing transactions with its under-reserved or slightly illiquid brethren;
5. It becomes apparent that the Chief Restructuring Officer can make the bank officer (with his own stationery, business cards, lapel pin and pens) look like a clever, prudent potentially promotable businessperson in the eyes of the client and his superiors in the bank, whom the Chief Restructuring Officer has promised to speak with (in laudatory terms) in his behalf.
The theme is not only that amortization is like fiscal alchemy — it is also that if a focal point of a turnaround Action Plan can be addressed with everyone emerging benefited (or at least not damaged as much), it can be negotiated.
Debt restructuring is a crucial part of most turnaround operations. Now you’ve gained a better insight.