Читать книгу The Art of Mathematics in Business - Dr Jae K Shim - Страница 8
ОглавлениеEvaluating the Cost of Bank Loans, Business Loans, Trade Credit, and Other Financing
1. Understanding Simple Interest
Introduction
The fee charged for the use of money, or principal, is called interest. It is the amount charged by a lender to a borrower. The interest rate is usually stated on an annual basis. The sum of the principal and the interest due is called the accumulated value, amount due, or maturity value. Compound interest is discussed in Sec. 60, How Do You Calculate Future Values? How Money Grows?
How is it Computed?
The amount of interest due is based on three factors: the principal, the rate of interest, and the time period during which the principal is used. One year is generally used as the time period. Simple interest is calculated on original principal only. The formula for simple interest is:
Interest = principal × rate × time
I = Prt
The maturity value S is given as:
Maturity value = principal + interest
Although the time span of a loan may be given in days, months, or years, the rate of interest is an annual rate. Thus, when the duration of a loan is given in months or days, the time must be converted to years. When the time is given in months, the formula is:
Example 1
A business owner obtains a 2-year loan of $10,000 from the Amalgamated Bank. The bank charges an annual simple interest rate of 10 percent. The rate of interest charged for 1 year is $1,000, calculated as follows:
$10,000 × 10% × 1 year = $1,000
The total simple interest for the 2-year period is $2,000, calculated as follows:
$1,000 × 2 years = $2,000
The maturity value (S) of the loan is $12,000, calculated as follows:
I = Prt
S = P + 1 = $10,000 + $2,000 = $12,000
Example 2
A business owner obtains a 3-month loan of $10,000 from Fidelity Bank. The bank charges an annual simple interest rate of 10 percent. The interest charged for the 3-month period is $250, and the maturity value of the loan is $10,250, calculated as follows:
P = $10,000r = 10% or 0.10t = 3/12 month
I=Prt
$10,000 × 0.10 × 3/12 month = $250
The maturity value of the loan is
S = P + I
$10,000 + $250 = $10,250
How is it used and applied?
The owner must know how to determine the cost of money in a debt or lease agreement. By knowing the cost of borrowing, the owner can better plan a business strategy to obtain an adequate return on his or her money and to provide sufficient funds to pay principal and interest.
The business owner who seeks a loan should shop around to obtain the best interest terms possible. Excessive interest rates, although they are tax deductible, are a drain on an owner’s profits. Large outstanding loans, coupled with high interest rates, can substantially reduce an owner’s profits and impair a business’ credit rating. A balance sheet showing high interest-bearing loans can also result in lenders charging even higher rates of interest because of the possibility of default and even bankruptcy if the loans are not paid at their maturity date.
See Sec. 2, Real (Effective) Interest Rate.
2. Real (Effective) Interest Rate
Introduction
The stated rate of interest does not tell the whole story: you need to be sure you understand all the fees and charges that might affect the real interest rate. The real rate of interest on a loan is expressed as an annual percentage applicable for the life of the loan.
How is it computed?
For a discounted loan, which is a common form of loan, interest is deducted immediately in arriving at the net proceeds - which increases the effective interest rate. A bank may require a compensating balance, i.e., a deposit that offsets the unpaid loan. In this case, no interest is earned on the compensating balance, which is stated as a percentage of the loan. A compensating balance also increases the effective interest rate.
Example
A business takes out a $10,000, 1-year, 10% discounted loan. The compensating balance is 5 percent. The effective interest rate is:
How is it used and applied?
Business owners compute the effective interest rate to determine the true cost of borrowing.
See Sec. 3, The Cost of Credit: Annual Percentage Rate.
3. The Cost of Credit: Annual Percentage Rate
Introduction
The annual percentage rate (APR) is a true measure of the effective cost of credit. It is the ratio of the finance charge to the average amount of credit in use during the life of the loan, and is expressed as a percentage rate per year.
How is it computed?
We present below a discussion of the way the effective APR is calculated for various types of loans.
Single-Payment Loans
The single-payment loan is paid in full on a given date. There are two ways of calculating APR on single-payment loans: the simple interest method and the discount method.
1.Simple interest method
Recall from Sec. 1 that, under the simple interest method, interest is calculated only on the amount borrowed (proceeds):
Example 1
A business owner took out a single-payment loan of $1000 for 2 years at a simple interest rate of 15 percent. The interest charge is: $300 ($1,000 × 0.15 × 2 years). Hence the APR is:
Under the simple interest method, the stated simple interest rate and the APR are always the same for single-payment loans.
Discount method
Under the discount method, interest is determined and then deducted from the amount of the loan. The difference is the actual amount the borrower receives. In other words, the borrower prepays the finance charges.
Example 2
Using the same figures as in Example 1, the actual amount received $700 ($1,000 - $300), not $1,000. The APR is:
The rate the lender must quote on the loan is 21.43 percent, not 15 percent.
The discount method always gives a higher APR than the simple interest method for single-payment loans at the same interest rates because the proceeds received are less.
Installment Loans
Most consumer loans are the add-on method. One popular method of calculating the APR for add-on loans is the constant-ratio method. The constant-ratio formula is:
Example 3
Assume that a business owner borrows $1,000 to be repaid in 12 equal monthly installments of $93 each for a finance charge of $116. The APR under the constant-ratio method is computed as follows:
Note that some lenders charge fees for a credit investigation, a loan application, or for life insurance. When these fees are required, the lender must include them in addition to the finance charge in dollars as part of the APR calculations.
How is it used and applied?
The lender is required by the Truth in Lending Act (Consumer Credit Protection Act) to disclose to a borrower the effective annual percentage rate (APR) as well as the finance charge in dollars.
Banks often quote their interest rates in terms of dollars of interest per hundred dollars. Other lenders quote in terms of dollars per payment. This leads to confusion on the part of borrowers. Fortunately, APR can eliminate this confusion. By comparing the APRs of different loans, a borrower can determine the best deal.
Example 4
Bank A offers a 7 percent car loan if a business owner puts down 25 percent. That is, if the owner buys a $4,000 auto, she will finance $3,000 over a 3-year period with carrying charges that amount to $630 (0.07 × $3,000 × 3 years). The owner will make equal monthly payments of $100.83 for 36 months.
Bank B will lend $3,500 on the same car. In this case the business owner must pay $90 per month for 48 months.
Which of the two quotes offers the best deal?
The APR calculations (using the constant-ratio formula) follow.
In the case of Bank B, it is necessary to multiply $90 × 48 months to arrive at a total cost of $4320. Therefore, the total credit cost is $920 ($4,320 - $3,500).
Based on the APR, the business owner should choose Bank B over Bank A.
4. Calculating Due Dates
Introduction
The due date, also called maturity date, is the exact date when a loan must be repaid.
How is it computed?
Some loans specify the maturity date while other loans state the period of the loan in days or months. When the maturity date is given in days, the date is determined by counting the days from the day the loan was secured. The day on which the loan is procured is not counted. For example, a 120-day loan obtained on October 17, 20×7, is due on February 15, 20×8. When the period is given in months, the loan’s maturity date falls on the same day of the month as the date the loan is issued. For example a 6-month loan dated March 15 matures on September 15. If the due date of the loan falls on a nonbusiness day, the maturity date is the next business day, with an additional day(s) added to the period for which interest is charged.
Example
Motor Parts, Inc., obtained a 90-day loan dated March 16, 20×7. The maturity date of the loan is June 15, 20×7, as determined below.
To determine the maturity date, calculate forward for the exact number of days in the loan period. Do not count the day on which you actually received the loan. Remember that some months have 30 days and some have 31.
How is it used and applied?
Due dates are not approximations; they are precise and final. On that date, you must be prepared to make full payment. Failure to do so means that you have defaulted on a loan and that can have disastrous consequences for your business.
It is critical, therefore, that you know the exact date well in advance so you can make certain you will have the funds available.
5. Promissory Notes and Bank Discounts
Introduction
A business may both make a promissory note and receive one. Notes receivable and notes payable are formal arrangements promising payment. Often a debtor signs a promissory note, which serves as evidence of a debt. The promissory note is a written promise to pay principal with interest at a maturity date. A business owner might discount a note if cash is needed quickly and he or she does not wish to hold the note until its maturity date.
How is it computed?
As with loans, some notes specify the maturity date, while others state the period of the note, in days or months. When the maturity value is given in days, the maturity date is determined by counting the days from issue. Interest is usually computed on the basis of a 360-day year (12 months × 30 days per month.) Recall from Sec. 1 that the following formula is used:
Interest = principal × interest rate × time
For example, the maturity date of a 90-day note issued May 6, 20×8, is August 4, 20×8, computed as follows:
When the period is given in months, the note’s maturity date falls on the same day of the month as the date of the note is issued. For example a 6-month note dated January 15 matures on July 15. If the due date of the note falls on a nonbusiness day, the maturity date is the next business day, with the additional day(s) added to the period for which interest is charged.
If you are holding a promissory note from a supplier or other party, you may find yourself in the position of needing more money before the due date, in which case you may discount the note receivable at a bank or finance company.
The proceeds received by the holder at the time the note is discounted are equal to the maturity value less the bank discount (interest charge). The bank discount is based on the period of time the bank will hold the note and the note’s interest rate. The interest rate charged by the bank need not be the same as the interest rate on the marker’s note. In fact, it is usually higher, because the bank generally charges a higher interest rate. The rate may also be different because of changes in the going interest rate since the note was originally written. The maturity value of the note is found as follows:
Maturity value = face value of note + interest income
The bank discount is:
Bank discount = maturity value × bank discount × period of time held by bank
Example 1
On June 30, 20××, Susan Ray, a business owner, issued a 180-day, 18 percent note to the Denmark Company to pay a short-term business loan. The note’s interest rate 6 months later will be $900, calculated as follows:
Principal × rate of interest × time = interest
$10,000 × 18% × 6 months = $900
Example 2
The Solvay Tool Company received the following notes:
The due date and amount of interest on each note is:
| Due Date | Interest Rate (%) | Face Amount |
| (a) Nov. 30 | $ 20 ($1,000 × 4/12 × 6%) | $1,020.00 |
| (b) Oct. 10 | 100 ($7,500 × 60/360 × 8%) | 7,600.00 |
| (c) Oct. 24 | 22.50 ($7,200 × 45/360 × 9%) | 2,022.50 |
| (d) Aug. 18 | 150 ($5,000 × 90/360 × 12%) | 5,150.00 |
Example 3
On June 20, 20×8, the Bunyan Grass Seed Company received a 90-day, 12 percent note receivable for $5,000. On August 5 the company, in need of cash, discounts the note at its bank. The bank charges a discount rate of 15 percent. The proceeds from the discounted note are 5,077.04 calculated as follows:
Bank discount = maturity value × discount rate × period note is held by bank
| Face value of note dated June 20 | $5,000.00 |
| Add: Interest on note ($5,000 × 12% × 90/360) | $150.00 |
| Maturity value of note due Sept. 18 | $5,150.00 |
| Bank discount on maturity value ($5,000 × 12% × 90/360) | $72.96 |
The net proceeds received by the payee at the time of discounting are:
Net proceeds = maturity value - bank discount
| Maturity value of note dated Sept. 18 | $5,150.00 |
| Less: Discount period (Aug. 5 – Sept. 18 = 34 days) | |
| Discount on maturity value (34 days at I5%) | $72.96 |
| Net proceeds of note after discounting | $5,077.04 |
How is it used and applied?
When a note receivable is sold or discounted to a bank or other financial institution, the seller (business owner) of the note remains contingently liable until the maker pays at maturity. If the original maker of the note does not pay the note at its maturity, the bank will seek payment from the seller of the note. The party who originally discounted the note will not be forced to pay and must seek reimbursement from the original maker of the note.
1.6 Trade Credit
Introduction
When you buy supplies or materials on credit, you are agreeing to pay the supplier within a certain period after receiving the goods. This is called trade credit, because it is a sale within the trade (as opposed to a sale to the public at large), and it is in effect a form of loan: you get the materials now and pay for them later. Many suppliers also offer a discount if you pay early.
How is it computed?
Trade credit is usually extended for a specific period of time; 30 days is common. This means that payment is due 30 days after you receive the merchandise. If a supplier offers a discount, there is also a specific period during which the discount may be taken. One very common arrangement is 2/10, net 30, sometimes written 2/10, n/30, which means that if you pay the invoice within 10 days, you can take a 2 percent discount; otherwise, the full amount is due within 30 days. The cost of not taking the discount is referred to as the opportunity cost of credit; it can be substantial.
The cost of credit if a cash discount is not taken is:
Example 1
Suppose that a supplier has extended $900 of trade credit to a business owner on terms of 2/10, net 30. The owner can either pay $900 × 0.98 = 822 at the end of the 10-day period, or wait for the full 30 days and pay the full $900. By waiting the full 30 days, the owner effectively borrows $882 for an additional 20 days, paying $900 - $882 or $18 in interest. Now, $18 may not seem like much of a savings, but if you can it in annual terms, it is significant.
This information can be used to compute the credit cost of borrowing this money:
It is important for a buyer to take advantage of all available discounts, even though it may be necessary to borrow the money to make the payment.
Example 2
Andover Supply receives a $2,000 invoice, discount terms 2/10, n/30, for goods purchased from Czar Wholesalers. Andover borrows the money for the remaining 20 days of the discount period at an annual interest rate of 12% and saves $26.93, computed as follows:
| Discount of 2% on $2,000 | $40.00 |
| Interest for 20 days, at a rate of 12% on $1,960 ($2,000 - $40) | $13.07 |
| Savings effect by borrowing | $26.93 |
How is it used and applied?
Computing the cost of credit is an essential part of doing business. You should always be weighing the savings gained by paying early against the benefit of holding onto your money longer. Which is more advantageous to you: paying a smaller amount sooner, or paying more later by having the use of the funds in the meantime? The only way to answer those questions is to work through the numbers both ways, and compare the results.
If you do not take the discount, you are losing the savings; the amount lost is the true cost of the credit. However, that cost may be of secondary importance to you if other forms of finance are not available. On the other hand, if bank credit is not a problem, you may be better to forgo the discount and invest the money short term in something that generates revenue.
Doing this now/later analysis is a continual process. Your decisions may change from one month to the next, as your cash flow changes. You should also be aware that the amounts of discount offered to you will often change to reflect the overall economic climate. Thus the cost of not taking trade credit usually declines as discount terms are reduced. Also, you may be available to negotiate with your major suppliers for a more favorable discount, especially if you have a strong record with them or they are particularly eager for cash.
7. Receivables and Inventory Financing
Introduction
You may be able to improve your business’ cash flow by using receivables or inventory as collateral for loans. Both these assets represent important financing sources because they are significant in amount and relate to recurring business activities.
1Receivable Financing
Receivable financing is the use of short-term financing backed by financing backed by receivables, under either a factoring or an assignment arrangement. The financing of accounts receivable is facilitated if customers are financially strong, sales returns are minimal, and title to the goods is received by the buyer at shipment.
Factoring of Accounts Receivable
Factoring is the outright sale of accounts receivable to a third party without recourse; the purchaser assumes all credit and collection risks. The factor will usually advance you up to 80 percent, meaning that the factor buys the receivables for 80 percent of face value. The factor collects the full amount from the customer and keeps the difference. The proceeds you receive equal face value minus commission, fee and discount. The amount the factor will advance depends on the quality of the accounts receivable. The cost of factoring includes the factor’s commission for credit investigation of the customer, interest charges, and the discount from the face value of the receivables. The factor’s total fee depends on the volume of business you give the factor and the credit-worthiness of your customers. Billing and collection are done by the factor.
How is it computed?
The cost of a factoring agreement is computed as follows:
Factor fee + cost of borrowing = total cost
Example 1
You have $10,000 per month in accounts receivable that a factor will buy, advancing you up to 75 percent of the receivables for an annual charge of 15 percent and a 1.0 percent fee on receivables purchased. The cost of this factoring arrangement is:
| Factor fee [0.01 × ($10,000 × 121)] | $1,200 |
| Cost of borrowing [0.15 × ($10,000 × 0.751)] | 1,125 |
| Total cost | $2,375 |
Assignment of Accounts Receivable
Assignment is the transfer of accounts receivable to a finance company with recourse: if the customer does not pay, you (as borrower) have to pay. The accounts receivable act as collateral, and new receivables substitute for receivables collected. Ownership of accounts receivable is not transferred. Customer payments continue to be made directly to you.
How is it computed?
The finance company usually advances between 50 and 85 percent of the face value of the receivables in cash. You incur a service charge and interest on the advance, and you absorb any bad debt losses. The cost is computed as follows:
Service charge + interest + bad debt = total cost
2 Inventory Financing
Inventory financing is the use of inventory as collateral for a loan. This typically occurs when you have fully exhausted your borrowing capacity on receivables.
Inventory financing requires the existence of marketable, nonperishable, standardized goods with fast turnover. Inventory should preferably be stable in price; expenses associated with its sale should be minimal.
How is it computed?
The cost of inventory financing is computed as:
Interest + warehouse cost = total cost
Example 2
You want to finance $250,000 of inventory. Funds are required for 2 months. An inventory loan may be taken out at 14 percent with an 80 percent advance against the inventory’s value. The warehousing cost is $2,000 for the 2-month period. The cost of financing the inventory is:
| Interest (0.14 × 0.80 × $250,000 × 2/12) | $4,667 |
| Warehousing cost | 2,000 |
| Total cost | $6,667 |
How is it used and applied?
The advantages of receivables financing are that it (1) avoids the need for long-term financing and (2) provides needed cash flow. Its major disadvantage is its high administrative cost if the business has many small accounts.
The advantages of factoring are that (1) you receive immediate cash, (2) overhead is reduced because credit investigation is no longer needed, (3) you can obtain advances as needed on a seasonal basis, and (4) there are no loan restrictions or required account balances. Disadvantages are that factoring involves (1) high cost, (2) possible negative customer reaction and (3) possible antagonism from customers who are past due and who are subject to pressure from the factor.
Advantages of assignment are that (1) cash is immediately available, (2) cash advances are received on a seasonal basis, and (3) it avoids negative customer reaction. Its disadvantages are (1) its high cost, (2) the continued credit function, and (3) significant credit risks.
The advance on inventory financing is usually higher for readily marketable goods. A bank will typically lend about 50 percent of the market value of merchandise at an interest rate about 3 to 50 points over the prime interest rate.
Disadvantages of inventory financing include its high interest rate and the restrictions often placed on the inventory.
8. Estimating the Cost of Debt and Equity Financing
Introduction
The business owner should observe that if she invests money today to receive benefits in the future, she must be absolutely certain that the business earns at least as much as it costs to acquire the funds for the business. This amount is called the minimum acceptable return. If funds cost the business 10 percent, the owner must be sure that she is earning at least this rate of return. To satisfy this test, the business must determine the cost of its funds, or, more properly stated, the cost of capital.
The business owner must ascertain which combination of debt and equity will result in the lowest cost of capital.
How is it computed?
The best way to calculate a business’ cost of capital is to examine each element of its capital structure. The capital structure of a business may be based on long-term debt, preferred stock and common stock. (Stock may only be issued by a corporation.) Capital structure is the mix of long-term debt and equity used by the business to finance.
The cost of debt is the interest rate paid to noteholders. The simplest case would be a $1,000 note paying $100 annually and thus costing the business 10 percent. The holder of the note would then say that the note’s yield is 10 percent. The after-tax cost of the debt to the business is the yield to maturity times 1 minus the tax rate. The formula is:
Cost of debt = Y (1 – tax)
where Y is the yield.
The cost of preferred stock is similar to the cost of debt in that a constant annual payment is made only if the stock pays dividends. Note, however, that preferred stock has no maturity date, so the business owner merely has to divide the annual dividend by the current price to calculate the annual percentage cost of the preferred stock. Costs are converted to percentages so that they may be compared. The formula is:
The cost of common stock is similar to the cost of preferred stock in that an annual dividend payment may exist. Like preferred stock, common stock has no maturity date, so the business owner merely has to divide the annual dividend by the current price to calculate the annual cost of the common stock. The formula is:
A business corporation that issues notes, preferred stock, and common stock would combine all elements to arrive at a weighted-average cost of capital. It would be calculated as follows:
Example 1
The Max Clothing Company signed a note for $10,000 at 10 percent. The business is in the 15 percent corporate tax bracket. The after-tax cost of the note is 8.5 percent, calculated as follows:
| Cost of debt | = | Y (1 – tax) |
| = | 10%(1 – 0.15) | |
| = | 10%(0.85) | |
| = | 8.5% |
Example 2
The Palo Wire Company sold 100 shares of preferred stock for $100 a share to an investor. The preferred stock will pay a guaranteed annual dividend of $9 per share. The cost of the stock is 9 percent annually, calculated as follows:
Example 3
The Rex Photo Development Company sold 100 shares of its common shares for $100 a share to an investor. All common shareholders expect a guaranteed annual dividend of $7.50 per share. The cost of the common stock is 7.5 percent annually, calculated as follows:
Example 4
The Halo Paint Company raised capital by issuing a $20,000 bond at 11 percent; selling $20,000 of $100-par-value, 8 percent preferred stock, and selling $10,000 of 6 percent common stock. The company is in the 25 percent tax bracket and estimates that it will earn 10 percent on its capital. The company’s weighted-average cost of capital is 7.7 percent, and it is earning 2.3 percent more than its cost of financing. Halo’s weighted-average cost of capital is determined as follows:
Cost of $10,000 common stock:
How is it used and applied?
The weighted-average cost of capital is compared to the business’ return on capital to see whether the business owner is at least earning the cost of financing his/her operations.
A business owner may need a certain amount of money to develop a new product and in so doing has to weigh the costs of various funding sources.
The minimum expected rate of return of any business must exceed its cost of capital if the business is to survive. While debt is usually the easiest form of financing because it merely entails borrowing money, excessive debt may increase the financial risk of the business and drive up the costs from all sources of financing.
