Money, Banking, and International Finance ( PDFDrive )

Money, Banking, and International Finance

PEMEX experienced a gain of 17,627,605 pesos from currency exchange. Thus, the U.S. dollar must have appreciated against the Mexican peso during 2005.

Table 1. The 2005 Income Statement for PEMEX

The Mexican national government relies on PEMEX to pay taxes because the company paid 580,629,293 pesos in taxes and duties. Consequently, PEMEX earned a 64,265,231 peso loss because it paid a large amount of taxes to the Mexican government. If you want to know the approximate U.S. dollar value, then divide all numbers in the Table 1 by 11 because the pesodollar exchange rate roughly equaled $1 = 11 pesos in 2005.

Balance Sheet is the second financial statement and shows the financial position of a business on a specific date. Balance sheet itemizes a business’s assets, liabilities, and equity. Assets are economic resources owned by a business while liabilities are debts and financial obligations of the business. Finally, equity equals total assets minus total liabilities that we also call net assets. We express equity in Equation 1. Moreover, creditors want businesses to have a positive equity. If a business cannot repay its debts, the creditors can legally force the business to sell its assets to repay debts. We list several assets and liabilities in Table 2.

A corporation divides its equity into two capital accounts: Contributed Capital and Retained Earnings. Contributed Capital is the amount of capital that a corporation sold. In other words, the amount of stock that circulates between investors outside of the corporation. Table 3 shows stockholders’ equity for preferred stock and common stock. We list the amounts of authorized and outstanding shares for both stock types. When a corporation earns profits, it records the

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Money, Banking, and International Finance

Table 4. A Balance Sheet for Stores U.S.A.

The Statement of Changes in the Owner’s Equity is the third financial statement and shows the changes in the owner’s equity. For all business organizations, profits or net income always increases equity because the organization has more resources flowing into it. However, proprietors and partners could invest and/or withdraw from the business. Thus, investment increases the equity, while withdrawals reduce it. For corporations, the Statement of Changes in the Owner’s Equity is called the Statement of Retained Earnings. We show an example in Table 5 for XYZ Corporation. Profits or net income increases retained earnings, while dividends declared decreases it. Dividends are similar to a proprietor’s or partners’ withdrawals. If the corporation issues more stock, then the corporation increases investment and records this transaction under the Stockholders’ Equity.

Statement of Cash Flows is the last financial statement and shows the money inflows and outflows of a business. This statement is important because a business needs adequate cash to operate such as paying workers, taxes, rent, and interest payments. A corporation could have a strong balance sheet, excellent income growth, but it fails from poor cash flows. Table 6 lists the

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activities that cause cash inflows and outflows. Financial analysts view the cash flow statement importantly because future business expansion impacts the cash flows over time. Furthermore, a company could be financially healthy, but poor cash flows impose hardship on the business. For example, if an employer cannot pay workers’ wages, then some workers quit and leave the employer.

Table 5. Statement of Retained Earnings for Corporation XYZ

Table 6. Activities that Affect a Business’s Cash Flow

We show a Statement of Cash Flows in Table 7. If cash enters a business, then the cash flow is positive. As cash leaves a business, subsequently, the cash flow is negative. Furthermore, the cash flow statement has three sections: operating, investing, and financing activities. For example, the business received $100,000 from customers and paid $20,000 in taxes for the operating activities. The $100,000 is net cash received from customers, which equal total cash sales minus merchandise returns. Then the business invested in the business by purchasing $20,000 in new equipment for the investment activities. Finally, the business issued $50,000 in brand new stock to expand the business and paid $30,000 in dividends for financing activities. Consequently, the business has $110,000 in total cash at the end of the year. You can calculate this amount by starting with the cash on hand at the beginning of the year and add the net cash flow that the business received during the year.

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Single Investment

Financial analysts use the present value formula to price financial securities or calculate mortgage payments. Present value formula places a value of future cash flows in terms of money today. Therefore, the present value emphasizes the present because people want their money now than wait for a future payment. Consequently, an interest rate rewards savers for delaying payment. For example, if you deposit $100 into a bank at 5% interest rate, you earn interest:

After one year, you earn 0.05($100) = $5 in interest. Your ending balance becomes $105.00.

After two years, you earn 0.05($105.00) = $5.25. Your ending balance grows into $110.25. We can use interest compounding to compute the ending balance in Equation 2.

If you let the money earn interest after T years, then you build the sequence in Equation 3. In this case, we multiply the beginning balance by the interest repeatedly. Moreover, the one inside the parenthesis indicates the principal as $1 while the 0.05 reflects the interest.

For example, your $100 grows into $13,150.13 at 5% interest in one-hundred years. We write the mathematical notation as:

 Future Value (FV) in dollars at Time T.

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Of course, we could solve for the interest rate using the Rule of 72. For example, which interest rate do you need for your savings account to double in 5 years? Your interest rate must be 14.4% annually, or 72 ÷ 5.

We could apply the Rule of 72 to economic variables other than financial securities. For example, the Chinese economy grows 10% per year. How many years does Chinese economy need to double in size? The Chinese economy doubles every 7.2 years, or 72 ÷ 10. On the other hand, the U.S. economy grows slowly at 1% per year after the 2008 Financial Crisis. How many years does the U.S. economy double in size? The U.S. economy doubles in size every 72 years, or 72 ÷ 1. What would happen if the U.S. economy begins contracting in size by 1% per year? We cannot use the Rule of 72 for negative growth rates. It is impossible for something to double in size with a negative growth rate.

Multiple Investments

We can alter the analysis, so people receive or pay multiple future payments. For instance, you deposit $500 into the bank account every year at 6% interest.

After the first year, you earn $500 × 0.06 = $30 in interest. Your balance grows into $500 + $30 + $500 = $1,030 because you have the initial $500, and then you deposited another $500 at the end of the year into your account.

After the second year, you earn $1,030 × 0.06 = $61.80 in interest. Your balance grows into $1,030 + $61.80 + $500 = $1,591.80. You added another $500 to your account at the end of the year.

After the third year, you earn $1,591.80 × 0.06 = $95.508 in interest. Your balance becomes $1,591.80 + $95.508 + $500 = $2,187.31. You added the last $500, which did not earn interest.

We calculate the future value of your bank deposits in Equation 8.

= $500(1 + 0.06) + $500(1 + 0.06) + $500(1 + 0.06) + $500(1 + 0.06) (8) = $2,187.31

Last term in Equation 8 is the final deposit. Although you multiply this term by an interest rate, the exponent equals zero setting the term inside the parenthesis to a one. Consequently, the exponent indicates how many years of interest that specific $500 earned over the course of three years.

We can reverse our logic and calculate the value of these cash flows today if you receive $500 now, $500 in one year, $500 in two years, and $500 in three years. We calculate the present value of $1,836.51 in Equation 9.

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= ( . ) + ( . ) + ( . ) + ( . ) = $1,836.51 (9)

If you received $1,836.51 as a lump sum today, you could invest this money into a savings account and earn $2,187.31 in three years at 6% interest. We converted a multiple stream investment into a single deposit investment.

Present value formula is flexible because it can handle uneven withdrawals and investments. For example, you do the following activities with your bank account in Table 8.

Table 8. Withdrawals and Deposits for a Bank Account

Withdrawal or deposit determines the sign. A withdrawal is negative, while a deposit is positive. Furthermore, the interest plus balance column in Table 8 includes the interest rate that the deposit would earn if held it until the end of the third year. For example, you deposited $100 into your account at Time 0 that grew into $148.15 in 3 years at 14% interest. Moreover, you withdrew $50 in Time 2, which would earn $57 for the next two years. However, you withdrew it, making it negative. Value of your withdrawals and deposits equals $520.03 at the end of Year 3.

We use the present value formula to calculate today’s value of these cash flows. You would be indifferent about receiving a lump-sum payment of $351.01 today or $520.03 in three years. We calculated the present value in Equation 10.

If you invested $351.01 today at 14% interest, then in 3 years, you would have $520.04, the final balance of your bank account.

Compounding Frequency

Financial analysts always define an interest rate as an annual term, called the Annual Percentage Rate (APR). The APR come from the Federal Reserve’s regulation that helps prevent fraud. For example, do you consider a 1% interest rate a good interest rate to charge a borrower? Unfortunately, we do not know the time period this interest rate applies to because the time period was omitted. If the 1% is annual, then it is an excellent interest rate for a loan.

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However, if it is daily, subsequently, this rate is terrible. Borrower took money from a loan shark. For this book, we define all interest rates in annual terms, unless otherwise stated.

Banks and finance companies usually calculate interest payments and deposits monthly. Thus, we adjust the present value formula for different time units. If you refer to Equation 11, we add a new variable, m, the compounding frequency while APR is the interest rate in annual terms. In the monthly case, m equals 12 because a year has 12 months.

For example, you deposit $10 in your bank account for 20 years that earns 8% interest (APR), compounded monthly. Consequently, we calculate your savings grow into $49.27 in Equation 12: If your bank compounded your account annually, then you would have $46.61.

Although the compounding frequency is usually 12 months, we could use semi-annually (two payments per year, or m equals 2), or quarterly (four payments per year, or m equals 4).

We can convert any compounding frequency into an APR equivalent interest rate, called the effective annual rate (EFF). From the previous example, we convert the 8% APR interest rate, compounded monthly into an annual rate without compounding, yielding 8.3%. We show the calculation in Equation 13. The EFF is the standard compounding formula removing the years and the present value terms.

If you deposited $10 in your bank account for 20 years that earn 8.3% APR with no compounding (or m equals 1), then your savings would grow into $49.27, which is the identical to an interest rate of 8% that is compounded monthly. We calculate this in Equation 14.

We can adapt the present value formula for frequency compounding. For example, what is the present value if you receive $50 in a month, $100 in six months, and $75 in 13 months at 10% APR? We must adjust our time units to months, which the smallest time unit.

We expressed the interest rate in APR, so divide it by 12 to obtain the monthly interest rate, yielding 0.8333% in our case.

All time subscripts are monthly.

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