How to Account for Forward Contracts

How to Account for Forward Contracts.

A forward contract is a type of derivative financial instrument that occurs between two parties. The first party agrees to buy an asset from the second at a specified future date for a price specified immediately. These types of contracts, unlike futures contracts, are not traded over any exchanges; they take place over-the-counter between two private parties. The mechanics of a forward contract are fairly simple, which is why these types of derivatives are popular as a hedge against risk and as speculative opportunities. Knowing how to account for forward contracts requires a basic understanding of the underlying mechanics and a few simple journal entries.

Part 1 Accounting for Forward Contracts.
1. Recognize a forward contract. This is a contract between a seller and a buyer. The seller agrees to sell a commodity in the future at a price upon which they agree today. The seller agrees to deliver this asset in the future, and the buyer agrees to purchase the asset in the future. No physical exchange takes place until the specified future date. This contract must be accounted for now, when it is signed, and again on the date when the physical exchange takes place.
For example, suppose a seller agrees to sell grain to a buyer in 3 months for $12,000, but the current value of the grain is only $10,000. In one year, when the exchange takes place, the market value of the grain is $11,000, so in the end, the seller makes a profit of $1,000 on the sale.
The spot rate, or current value, of the grain is $10,000.
The forward rate, or future value, of the grain is $12,000.
2. Record a forward contract on the contract date on the balance sheet from the seller’s perspective. On the liability side of the equation, you would credit the Asset Obligation for the spot rate. Then, on the asset side of the equation, you would debit the Asset Receivable for the forward rate. Finally, debit or credit the Contra-Asset Account for the difference between the spot rate and the forward rate. You would debit, or decrease the Contra Asset Account for a discount and credit, or increase it for a premium.
Using the example above, the seller would credit the Asset Obligation account for $10,000. He has made a commitment to sell his grain today, and today it is worth $10,000.
But, he is going to receive $12,000 for the grain. So he debits Assets Receivable for $12,000. This is what he’s going to be paid.
To account for the $2,000 premium, he credits the Contra-Asset Account for $2,000.
3. Record a forward contract on the contract date on the balance sheet from the buyer’s perspective. On the liability side of the equation, you would credit Contracts Payable in the amount of the forward rate. Then you would record the difference between the spot rate and the forward rate as a debit or credit to the Contra-Assets Account. On the asset side of the equation, you would debit Assets Receivable for the spot rate.
Using the example above, the buyer would credit Contracts Payable in the amount of $12,000. Then he would debit the Contra-Assets Account for $2,000 to account for the difference between the spot rate and the forward rate.
Then he would debit Assets Receivable for $10,000.
4. Record a forward contract on the balance sheet from the seller’s perspective on the date the commodity is exchanged. First, you close out your asset and liability accounts. On the liability side, debit Asset Obligations by the spot value on the contract date. On the asset side, credit Contracts Receivable by the forward rate, and debit or credit the Contra-Assets account by the difference between the spot rate and the forward rate.
Using the above example, on the liability side you would debit Asset Obligations by $10,000.
On the asset side, you would credit Contracts Receivable by $12,000/
Then you would debit the Contra-Asset account by $2,000, the difference between the spot rate and the forward rate.
5. Recognize any gain or loss on the commodity sold from the seller’s perspective. Determine the current market value of the commodity. This is its value on the date of the physical exchange between the buyer and seller. Next, debit, or increase, your cash account by the forward rate. Then credit, or decrease, your Asset account by the current market value of the commodity. Finally, recognize the gain or loss, which is the difference between the forward rate and the current market value, with a debit or credit on the Asset Account.
In the example above the current market value of the grain on the date of the physical exchange is $11,000.
First, the seller must increase cash based on the contracted amount, so he would debit cash by $12,000.
Next he must reduce the Asset account by the current market value by recording a credit of $11,000.
Then, to recognize the gain of $1,000 (which is the current value, $11,000, less the spot rate, $10,000), he would record a credit on the Asset Account of $1,000.
6. Record a forward contract on the balance sheet from the buyer’s perspective on the date the commodity is exchanged. First, you close out your asset and liability accounts. On the liability side, debit Contracts Payable by the forward rate, and debit or credit the Contra-Assets account by the difference between the spot rate and the forward rate. On the asset side, credit Assets Receivable by the spot rate on the date of the contract.
Using the example above, on the liability side, the buyer would debit Contracts Payable by $12,000 and credit the Contra-Asset Account by $2,000.
On the asset side, he would credit Assets Receivable by $10,000.
7. Recognize any gain or loss on the commodity sold from the buyer’s perspective. Decrease, or credit the Cash account by the amount of the forward rate. Then, record the difference between the forward rate and the current market value as an additional credit or debit to the Cash account. Finally, increase, or debit, the Asset account by the current market value of the commodity.
In the above example, the buyer would debit Cash by $12,000.
The difference between the market value, $11,000, and the forward rate $12,000, is $1,000. They buyer lost $1,000, so he would record a debit to Cash of $1,000.
Next, he would debit the Asset account by $11,000.

Part 2 Understanding Forward Contracts.
1. Understand the definition of a forward contract. A forward contract is an agreement between a buyer and a seller to deliver a commodity on a future date for a specified price. The value of the commodity on that future date is calculated using rational assumptions about rates of exchange. Farmers use forward contracts to eliminate risk for falling grain prices. Forward contracts are also used in transactions using foreign exchange in an effort to reduce the risk of losses due to changes in the exchange rates.
2. Learn the meaning of derivatives. A derivative is a security with a price that is based upon, or derived, from something else. Forward contracts are considered derivative financial instruments because the future value of the commodity is derived from other information about the commodity.
The future value of the commodity for the forward contract is derived from the current market value, or spot price, and the risk-free rate of return.
3. Learn the meaning of hedging. In investing, hedging means minimizing risk. In forward contracts, buyers and sellers attempt to minimize risk of losses by locking in prices for commodities in advance. Buyers lock in a price in hopes that they will end up paying less than the current market value of a commodity. Sellers hedge their risks with forward contracts in an attempt to protect themselves from falling prices.

Part 3 Negotiating a Forward Contract.
1. Know the difference between the long position and the short position. The party agreeing to purchase the commodity assumes the long position. The party agreeing to sell the commodity is assuming the short position.
The buyer, who is in the long position, is the person who stands to benefit if the price of the commodity rises higher than expected.
The seller, who is in the short position, stands to lose if the price of the commodity rises.
2. Know the difference between the spot value and the forward value. The spot value and the forward value are both quotes for the rate at which the commodity will be bought or sold. The difference between the two has to do with the timing of the settlement and delivery of the commodity. Both parties in a forward contract need to know both values in order to accurately account for the forward contract.
The spot rate is the current market value for the asset in question. It is the value of the commodity if it were sold today. For example, a farmer selling grain for the spot value agrees to sell it immediately for the current price.
The forward rate is the agreed-upon future price in the contract. For example, suppose the farmer in the above example wants to enter into a forward contract in an effort to hedge against falling grain prices. He can agree to sell his grain to another party in six months at agreed-upon forward rate. When the time comes to sell, the grain will be sold for the agreed-upon forward rate, despite fluctuations that occur in the spot rate during the intervening six months.
3. Understand the relationship between the spot value and the forward value. The spot rate can be used to determine the forward rate. This is because a commodity’s future value is based in part on its current value. The other factor that is used to determine the forward value is the risk-free rate.
The risk-free rate is the rate at which the commodity is expected to change in value with zero risk. It is usually based on the current interest rate of a three-month U.S. Treasury bill, which is considered the safest investment you can make.

April 10, 2020

How to Use the Rule of 72

How to Use the Rule of 72.

The Rule of 72 is a handy tool used in finance to estimate the number of years it would take to double a sum of money through interest payments, given a particular interest rate. The rule can also estimate the annual interest rate required to double a sum of money in a specified number of years. The rule states that the interest rate multiplied by the time period required to double an amount of money is approximately equal to 72.
The Rule of 72 is applicable in cases of exponential growth, (as in compound interest) or in exponential "decay," as in the loss of purchasing power caused by monetary inflation.

Method 1 Estimating "Doubling" Time.
1. Let R x T = 72. R is the rate of growth (the annual interest rate), and T is the time (in years) it takes for the amount of money to double.
2. Insert a value for R. For example, how long does it take to turn $100 into $200 at a yearly interest rate of 5%? Letting R = 5, we get 5 x T = 72.
3. Solve for the unknown variable. In this example, divide both sides of the above equation by R (that is, 5) to get T = 72 ÷ 5 = 14.4. So it takes 14.4 years for $100 to double at an interest rate of 5% per annum. (The initial amount of money doesn't matter. It will take the same amount of time to double no matter what the beginning amount is.)
4. Study these additional examples:
How long does it take to double an amount of money at a rate of 10% per annum? 10 x T = 72. Divide both sides of the equation by 10, so that T = 7.2 years.
How long does it take to turn $100 into $1600 at a rate of 7.2% per annum? Recognize that 100 must double four times to reach 1600 ($100 → $200, $200 → $400, $400 → $800, $800 → $1600). For each doubling, 7.2 x T = 72, so T = 10. So, as each doubling takes ten years, the total time required (to change $100 into $1,600) is 40 years.

Method 2 Estimating the Growth Rate.
1. Let R x T = 72. R is the rate of growth (the interest rate), and T is the time (in years) it takes to double any amount of money.
2. Enter the value of T. For example, let's say you want to double your money in ten years. What interest rate would you need in order to do that? Enter 10 for T in the equation. R x 10 = 72.
3. Solve for R. Divide both sides by 10 to get R = 72 ÷ 10 = 7.2. So you will need an annual interest rate of 7.2% in order to double your money in ten years.

Method 3 Estimating Exponential "Decay" (Loss).
1. Estimate the time it would take to lose half of your money (or its purchasing power in the wake of inflation). Let T = 72 ÷ R. This is the same equation as above, just slightly rearranged. Now enter a value for R. An example.
How long will it take for $100 to assume the purchasing power of $50, given an inflation rate of 5% per year?
Let 5 x T = 72, so that T = 72 ÷ 5 = 14.4. That's how many years it would take for money to lose half its buying power in a period of 5% inflation. (If the inflation rate were to change from year to year, you would have to use the average inflation rate that existed over the full time period.)
2. Estimate the rate of decay (R) over a given time span: R = 72 ÷ T. Enter a value for T, and solve for R. For example.
If the buying power of $100 becomes $50 in ten years, what is the inflation rate during that time?
R x 10 = 72, where T = 10. Then R = 72 ÷ 10 = 7.2%.
3. Ignore any unusual data. If you can detect a general trend, don't worry about temporary numbers that are wildly out of range. Drop them from consideration.

Method 4 Derivation.
1. Understand how the derivation works for periodic compounding.
For periodic compounding, FV = PV (1 + r)^T, where FV = future value, PV = present value, r = growth rate, T = time.
If money has doubled, FV = 2*PV, so 2PV = PV (1 + r)^T, or 2 = (1 + r)^T, assuming the present value is not zero.
Solve for T by taking the natural logs on both sides, and rearranging, to get T = ln(2) / ln(1 + r).
The Taylor series for ln(1 + r) around 0 is r - r2/2 + r3/3 - ... For low values of r, the contributions from the higher power terms are small, and the expression approximates r, so that t = ln(2) / r.
Note that ln(2) ~ 0.693, so that T ~ 0.693 / r (or T = 69.3 / R, expressing the interest rate as a percentage R from 0-100%), which is the rule of 69.3. Other numbers such as 69, 70, and 72 are used for easier calculations.
2. Understand how the derivation works for continuous compounding. For periodic compounding with multiple compounding per year, the future value is given by FV = PV (1 + r/n)^nT, where FV = future value, PV = present value, r = growth rate, T = time, and n = number of compounding periods per year. For continuous compounding, n approaches infinity. Using the definition of e = lim (1 + 1/n)^n as n approaches infinity, the expression becomes FV = PV e^(rT).
If money has doubled, FV = 2*PV, so 2PV = PV e^(rT), or 2 = e^(rT), assuming the present value is not zero.
Solve for T by taking natural logs on both sides, and rearranging, to get T = ln(2)/r = 69.3/R (where R = 100r to express the growth rate as a percentage). This is the rule of 69.3.
For continuous compounding, 69.3 (or approximately 69) gives more accurate results, since ln(2) is approximately 69.3%, and R * T = ln(2), where R = growth (or decay) rate, T = the doubling (or halving) time, and ln(2) is the natural log of 2. 70 may also be used as an approximation for continuous or daily (which is close to continuous) compounding, for ease of calculation. These variations are known as rule of 69.3, rule of 69, or rule of 70.
A similar accuracy adjustment for the rule of 69.3 is used for high rates with daily compounding: T = (69.3 + R/3) / R.
The Eckart-McHale second order rule, or E-M rule, gives a multiplicative correction to the Rule of 69.3 or 70 (but not 72), for better accuracy for higher interest rate ranges. To compute the E-M approximation, multiply the Rule of 69.3 (or 70) result by 200/(200-R), i.e., T = (69.3/R) * (200/(200-R)). For example, if the interest rate is 18%, the Rule of 69.3 says t = 3.85 years. The E-M Rule multiplies this by 200/(200-18), giving a doubling time of 4.23 years, which better approximates the actual doubling time 4.19 years at this rate.
The third-order Padé approximant gives even better approximation, using the correction factor (600 + 4R) / (600 + R), i.e., T = (69.3/R) * ((600 + 4R) / (600 + R)). If the interest rate is 18%, the third-order Padé approximant gives T = 4.19 years.
To estimate doubling time for higher rates, adjust 72 by adding 1 for every 3 percentages greater than 8%. That is, T = [72 + (R - 8%)/3] / R. For example, if the interest rate is 32%, the time it takes to double a given amount of money is T = [72 + (32 - 8)/3] / 32 = 2.5 years. Note that 80 is used here instead of 72, which would have given 2.25 years for the doubling time.


FAQ.
Question : When would I need to use the rule of 72?
Answer : It's a handy shortcut when considering compounded, monetary gains or losses. For example, you might want to know how long it would take for invested money to double in value, given a specific rate of interest.
Question : How do I calculate compound interest?
Answer : The formula for annual compound interest (A) is: P [1 + (r / n)]^(nt), where P=principal amount, r = the annual interest rate as a decimal, n = the number of times the interest is compounded per year, and t = the number of years of the loan or investment.
Question : What is APY for an APR of 3.5% compounded?
Answer : It depends on how often the interest compounds: annually, semi-annually, quarterly, monthly or daily.

Tips.

Let the Rule of 72 work for you by starting to save now. At a growth rate of 8% a year (the approximate rate of return in the stock market), you would double your money in nine years (72 ÷ 8 = 9), quadruple your money in 18 years, and have 16 times your money in 36 years.
The value of 72 was chosen as a convenient numerator in the above equation. 72 is easily divisible by several small numbers: 1,2,3,4,6,8,9, and 12. It provides a good approximation for annual compounding at typical rates (from 6% to 10%). The approximations are less exact at higher interest rates.
You can use Felix's Corollary to the Rule of 72 to calculate the "future value" of an annuity (that is, what the annuity's face value will be at a specified future time). You can read about the corollary on various financial and investing websites.

Warnings.
Let the rule of 72 convince you not to take on high-interest debt (as is typical with credit cards). At an average interest rate of 18%, semiretired credit card debt doubles in just four years (72 ÷ 18 = 4), quadruples in eight years, and becomes completely unmanageable after that.

April 10, 2020