Time Value For Money

Time Value of Money – A Quick Overview The Time Value of Money (“TVM”) is a concept on which the rest of finance theory rests on. Therefore, it is critical that students understand this concept well. We expand on the Time Value of Money under the following headings: 1) What does the “Time Value of Money” mean or capture? Most students agree that what $10, today, will buy will be more than what $10 will buy in 5 years in the future. Similarly, they also agree $10 would have got them a lot more 5 years ago than what it will get them today. Since they agree that this is true, I tell them that they have understood the time value of money concept! This is exactly what the time value of money concept in finance is trying to show. As time flows the value of money declines. 2) Why does the Value of Money Decline? The value of money declines due to the combined impact of the following: 1. Inflation in the economy; 2. Risks involved in delayed receipts of cash or financial transactions; and 3. Opportunity cost of capital delayed. While each of these forces alone can cause the value of money to decline individually, all the three usually act with different degrees of impact to cause a decline in the value of money as time flows. 3) The Present Value Formula The present value formula quantifies how fast the value of money declines. This formula shows you how much once single cash payment (FV) received in a future time period (t) is worth in today’s terms (PV).

Present Value (PV) stands for the value of the money in today’s terms. Future Value (FV) stands for the amount of cash received in the future. r is the discount rate or the speed at which the decline in value is happening (covered in detail later).it is the time period in which the future value or cash is received. 4) Infographic on the Time Value of Money The GraduateTutor.com finance team has put together this infographic on the Time Value of Money for the visual learners. We have a follow up infographic on the commonly used Time Value of Money formulas. Please feel free to embed this infographic using the code below this post. Do provide us credit for this poster by linking to us.

Time Value of Money – An infographic by the finance tutoring team at GraduateTutor.com. (Content below is contributed by Prof. Alan Anderson) 5) Computing the Time Value of Money If a sum is invested today, it will earn interest and increase in value over time. The value that the sum grows to is known as its future value. Computing the future value of a sum is known as compounding. The present value of a sum is the amount that would need to be invested today in order to be worth that sum in the future. Computing the present value of a sum is known as discounting. The Future Value of a Sum The future value of a sum depends on the interest rate and the interval of time over which the sum is invested. This is shown with the following formula: FVt = PV*(1+r)t where: FVt = future value of a sum invested for t periods r = periodic interest rate PV = present value t = number of periods until the sum is received Each period may be a year, a month, a week, etc. The terms in the formula must be consistent with each other; for example, if it is measured in months, then r must be a monthly rate of interest. As an example, suppose that a sum of $1,000 is invested for four years at an annual rate of interest of 3%. What is the future value of this sum? In this case, t = 4, r = 3% and PV = $1,000. FVt = PV(1+r)t FV4 = 1,000(1+.03)4 FV4 = 1,000(1.12551) FV4 = $1,125.51 The Present Value of a Sum

The formula for computing the present value of a sum is: Note that the present value is simply the inverse of the future value. As an example, how much must be deposited in a bank account that pays 5% interest per year in order to be worth $1,000 in three years? In this case, t = 3, r = 5% and FV 3 = $1,000. Present Value Or What must be deposited to get $1,000 = 1,000/(1.1576) = $863.84 6) Interest Rates and Compounding Frequencies Compounding refers to the frequency with which interest rates are charged or paid during a given year. In practice, interest rates can be compounded anywhere from once per year to once per day; the theoretical limiting case is known as continuous compounding, in which rates are compounded at every instant in time. Compounding frequency is one of the most important determinants of the future value and the present value of a sum. For example, if a bank offers a 4% rate of interest with annual compounding, an investor who holds $1,000 in the bank for one year will have a balance of: $1,000(1 + 0.04) = $1,040 at the end of the year. In other words, the future value of this sum is $1,040.

If the interest is compounded semi-annually, then the investor will receive half of the annual rate twice per year; i.e., 2% every six months during the year. At the end of six months, the investor will have a balance of: $1,000(1 + 0.02) = $1,020 at the end of the year, the investor will have a balance of: $1,020(1 + 0.02) = $1,000(1 + 0.02)(1 + 0.02) = $1,000(1 + 0.02)2 = $1,040.40 In this case, since the principal is $1,000, the total interest is $40.40. Of this: $40 is simple interest (interest on principal) $0.40 is compound interest (interest on interest) In this case, the investor received an interest payment of $1,000(0.02) = $20 at the end of six months, for a balance of $1,020. The interest payment at the end of the year was based on the principal ($1,000) and the interest ($20) in the account. The interest paid on the principal was $1,000(0.02) = $20 and the interest paid on the interest was $20(0.02) = $0.40. Combined with the $20 interest paid at the end of six months, the total interest paid during the year was $20 + $20 + $0.40 = $40.40. Of this, the $40 was based on the principal; this is the simple interest. The remaining $0.40 was based on the interest earned during the year; this is the compound interest. As the compounding frequency increases, the simple interest earned during a given period remains fixed, but the compound interest increases. For example, with quarterly compounding, the investor in the previous example will receive 1% every three months; at the end of the year the investor will have a balance of: $1,000(1 + 0.01)(1 + 0.01) (1 + 0.01)(1 + 0.01) = $1,000(1 + 0.01)4 = $1,040.60 In this case, the total interest is $40.60. Of this: $40 is simple interest (interest on principal) $0.60 is compound interest (interest on interest) This demonstrates an important result: as the compounding frequency increases, the future value of a sum increases. As another example, suppose that a sum of $1,000 is invested for two years at an annual rate of interest of 8%. What is the future value of this sum based on the following compounding frequencies?  Annual compounding  Semi-annual compounding  Monthly compounding With annual compounding, t = 2, r = 8% and PV = $1,000. FVt = PV*(1+r)^t FV2 = 1,000*(1+.08)^2 FV2 = 1,000*(1.16640) FV2 = $1,166.40 With semi-annual compounding, t = 4, r = 4% and PV = $1,000. The time frame is now 4 semiannual periods, and the rate of interest is 4% per semi-annual period. FVt = PV*(1+r)^t FV4 = 1,000*(1+.04)^4 FV4 = 1,000*(1.16986) FV4 = $1,169.86 With monthly compounding, t = 24, r = 0.6667% and PV = $1,000. FVt = PV*(1+r)^t FV24 = 1,000*(1+.006667)^24 FV24 = 1,000*(1.17289) FV24 = $1,172.89

These results show that the future value of a sum continues to increase as the compounding frequency increases. For the present value, a higher compounding frequency reduces the present value. This is because more compound interest is earned, which reduces the amount that must be saved today to be worth a specified sum in the future. As an example, suppose that an investor has a target of $100,000 in five years, and can invest in a bank account that pays an annual rate of interest of 6%. How much must the investor save today in order to reach this goal based on the following compounding frequencies?  Annual compounding  Semi-annual compounding  Monthly compounding With annual compounding, t = 5, r = 6% and FV5 = $100,000. PV = FVt / (1+r)^t PV = 100,000 / (1+.06)^5 PV = 100,000 / 1.33823 PV = $74,725.82 With semi-annual compounding, t = 10, r = 3% and FV10 = $100,000. PV = FVt / (1+r)^t PV = 100,000 / (1+.03)^10 PV = 100,000 / 1.34392 PV = $74,409.39 With monthly compounding, t = 60, r = 0.5% and FV60 = $100,000. PV = FVt / (1+r)^t PV = 100,000 / (1+.005)^60 PV = 100,000 / 1.34885 PV = $74,137.22 7) Annuities An annuity is a periodic stream of equally-sized payments. The word annuity is derived from the Latin word annum (yearly). In spite of this, any stream of periodic payments of equal size can be treated as an annuity. As an example, mortgage payments are made monthly and are of equal size, and so can be thought of as a type of annuity. The two basic types of annuities are:  Ordinary annuity  Annuity due Ordinary Annuities With an ordinary annuity, the first payment takes place one period in the future. Most annuities are ordinary; some examples are:  Coupons paid by a bond  Dividend payments by a share of preferred stock  Car loan payments  Mortgage payments  Student loan payments  Social security payments The Future Value of an Ordinary Annuity The formula for computing the future value of an ordinary annuity is:

where: FVAt = future value of a t-period annuity C = the periodic cash flow r = periodic interest rate t = number of periods until the sum is received As an example, suppose that a sum of $1,000 is invested each year for four years, starting next year, at an annual rate of interest of 3%. Since the cash flows start next year, this is an ordinary annuity. What is its future value? In this case, t = 4, r = 3% and C = $1,000. Alternatively, the future value of each individual cash flow can be computed and then combined as follows: The first cash flow is invested for three years (from year one to year four): FV3 = PV(1+r)t FV3 = 1,000(1+.03)3 FV3 = 1,000(1.09273) FV3 = $1,092.73 The second cash flow is invested for two years (from year two to year four): FV2 = PV(1+r)t FV2 = 1,000(1+.03)2 FV2 = 1,000(1.06090) FV2 = $1,060.90 The third cash flow is invested for one year (from year three to year four): FV1 = PV(1+r)t FV1 = 1,000(1+.03)1 FV1 = 1,000(1.03) FV1 = $1,030.00 The fourth and final cash flow does not earn any interest since it is not deposited into the bank until year four. The future value is therefore $1,000. The sum of these future values is: $1,092.73 + $1,060.90 + $1,030.00 + $1,000.00 = $4,183.63 The Present Value of an Ordinary Annuity The formula for computing the present value of an ordinary annuity is:

where: PVAt = present value of a t-period ordinary annuity C = the value of the periodic cash flow

As an example, how much must be invested today in a bank account that pays 5% interest per year in order to generate a stream of payments of $1,000 in each of the following three years? In this case, t = 3, r = 5% and C = $1,000. Alternatively, the present value of each individual cash flow can be computed and then combined as follows: The present value of the first cash flow (paid in one year) is: PV = FVt / (1+r)t PV = 1,000 / (1+.05)1 PV = 1,000 / 1.05 PV = $952.38 The present value of the second cash flow (paid in two years) is: PV = FVt / (1+r)t PV = 1,000 / (1+.05)2 PV = 1,000 / 1.10250 PV = $907.03 The present value of the third cash flow (paid in three years) is: PV = FVt / (1+r)t PV = 1,000 / (1+.05)3 PV = 1,000 / 1.15763 PV = $863.84 The sum of these present values is: $952.38 + $907.03 + $863.84 = $2,723.25 Annuities Due With an annuity due, the first payment takes place immediately. This is a less common type of annuity than the ordinary annuity. An example of this would be a lease agreement or a loan where the first payment is due immediately. Due to the timing of the cash flows, the present value and future value of an annuity will be affected by whether the annuity is an ordinary annuity or an annuity due. The Future Value of an Annuity Due The future value of an annuity due is computed as follows: FVAdue = FVA ordinary * (1+r) This shows that the future value of an annuity due is greater than the future value of an ordinary annuity. This is because each cash flow of an annuity due is invested for one additional year. Referring to the previous example, the future value of an annuity due would be: 4,183.63(1+.03) = $4,309.14 This can be confirmed by computing the future value of each cash flow individually. Each cash flow will be invested for one additional year compared with the ordinary annuity. The first cash flow is invested for four years (from today to year four): FV4 = PV(1+r)t FV4 = 1,000(1+.03)4 FV4 = 1,000(1.12551) FV4 = $1,125.51 The second cash flow is invested for three years (from year one to year four): FV3 = PV(1+r)t FV3 = 1,000(1+.03)3 FV3 = 1,000(1.09273) FV3 = $1,092.73

The third cash flow is invested for two years (from year two to year four): FV2 = PV(1+r)t FV2 = 1,000(1+.03)2 FV2 = 1,000(1.06090) FV2 = $1,060.90 The fourth cash flow is invested for one year (from year three to year four): FV3 = PV(1+r)t FV3 = 1,000(1+.03)1 FV3 = 1,000(1.03) FV3 = $1,030.00 The sum of these future values is: $1,125.51 + $1,092.73 + $1,060.90 + $1,030.00 = $4,309.14 The Present Value of an Annuity Due The present value of an annuity due is computed as follows: PVA due = PVA ordinary * (1+r) This shows that the present value of an annuity due is greater than the present value of an ordinary annuity. This is because each cash flow of an annuity due is paid one year sooner, so that the invested principal earns less interest. As a result, a larger sum must be invested in order to generate the appropriate cash flows. Referring to the previous example, the present value of an annuity due would be: 2,723.25(1+.05) = $2,859.41 Alternatively, the present value of each individual cash flow can be computed and then combined as follows: The first cash flow is withdrawn immediately, so the present value equals $1,000. The present value of the second cash flow (paid in one year) is: PV = FVt / (1+r)t PV = 1,000 / (1+.05)1 PV = 1,000 / 1.05 PV = $952.38 The present value of the third cash flow (paid in two years) is: PV = FVt / (1+r)t PV = 1,000 / (1+.05)2 PV = 1,000 / 1.10250 PV = $907.03 The sum of these present values is: $1,000 + $952.38 + $907.03 = $2,859.41 8) Perpetuities A perpetuity is an investment in which interest payments are made forever, but principal is not repaid. As an example, a stock that pays a regular stream of constant dividends can be thought of as a perpetuity. This is because the same cash flows are paid each year, and the stock has an infinite lifetime. Another example is a consol, which is a bond that makes interest payments forever but does not repay the principal. The Present Value of a Perpetuity The present value of a perpetuity that pays an annual cash flow of $C per period is: PV = C/r

As an example, suppose that perpetuity pays $100 per year; assume that the appropriate rate of interest is 5% per year. The present value of the perpetuity is $100/0.05 = $2,000. The Present Value of Growing Perpetuity Suppose that the cash flows provided by perpetuity grow at a fixed rate each year. The present value formula is adjusted as follows: PV = C/(r – g) Where: g = annual growth rate of the perpetuity As an example, suppose that perpetuity currently pays $50 per year; assume that the appropriate rate of interest is 7% per year, and that the cash flow paid by the perpetuity is estimated to grow at a rate of 3% per year. The present value of the perpetuity is: $50/(0.07 – 0.03) = $1,250. 9) Interest Rate Conventions Interest rates for loans, bank accounts, etc. can be quoted in two basic ways: 1. Annual percentage rate (APR) 2. Effective annual rate (EAR) The annual percentage rate reflects the simple interest of a loan or an investment, while the effective annual rate reflects both the simple and compound interest. Converting APR to EAR In order to compare interest rates with different compounding frequencies, they can be converted into an effective annual rate (EAR); this reflects the true cost of borrowing (or the return to lending) when interest is compounded more than once per year. EAR is computed from APR as follows:

where: m = the number of compounding periods per year As an example, suppose that a bank charges an APR of 6% per year, compounded quarterly for a loan, what is the effective annual rate? This can be determined as follows:

This indicates that the borrower is actually paying 6.136% per year for this loan. Converting EAR to APR An effective annual rate may be converted to an annual percentage rate by inverting the previous formula:

As an example, if a bank charges an EAR of 5.25% per year, compounded monthly for a loan, what is the annual percentage rate? This can be determined as follows:

10) Continuous Compounding Continuous compounding is the limit of compounding frequency. Continuous compounding indicates that interest rates are being compounded at every instant in time, which implies that interest is compounded an infinite number of times. A compounding frequency, which is not continuous, is said to be discrete. For example, annual compounding, monthly compounding, daily compounding, etc. are all examples of discrete compounding. Using continuous compounding requires a new set of formulas for computing the future value of a sum, the present value of a sum, EAR and APR. Computing the Future Value of a Sum with Continuous Compounding If interest rates are compounded continuously, the future value of a sum is: FVt = PV*(e^rt) Where: e is a constant that is approximately equal to 2.71828 As an example, suppose that a bank offers a rate of interest of 6%, compounded continuously. An investor who deposits $1,000 in this bank for two years will have an ending balance of: FVt = 1,000(e(0.06)(2)) = $1,127.50 Computing the Present Value of a Sum with Continuous Compounding The present value of a sum with continuous compounding is: PV = FVt*(e^-rt) As an example, suppose that a bank offers a rate of interest of 8%, compounded continuously. An investor who needs to have $10,000 in three years will have to save the following amount today in order to reach this goal: PV = 10,000(e^-(0.08)(3)) = $7,866.28 Computing EAR with Continuous Compounding If interest rates are compounded continuously, EAR is computed as follows: EAR = eAPR – 1 As an example, if a bank charges an APR of 4% per year, what is the EAR with continuous compounding? EAR = e^APR – 1 = e^0.04 – 1 = 1.04081 – 1 = 0.04081 = 4.081% Computing APR with Continuous Compounding If interest rates are compounded continuously, APR is computed as follows: APR = ln*(1 + EAR) As an example, if a bank charges an EAR of 3.5% per year with continuous compounding, what is the APR? APR = ln*(1 + EAR) = ln(1.035) = 0.03440 = 3.440% Next Steps: Now that you have a good understanding of what the time value of money is and the associated concepts, why not continue to read related topics? You can either proceed to learn more about:

Fixed Income Securities; which includes: An Introduction to Bonds, Bond Valuation & Bond Pricing; Understanding Term Structures, Interest Rates and Yield Curves; and Managing Bond Portfolios: Strategies, Duration, Modified Duration, Convexity. How to read financial statements; which includes: Learning how to read a balance sheet; or Learning how to read a cash flow statement; or Learning how to understand and interpret percentage statements.

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How to Read a Cash Flow Statement “Follow the money” If you were asked whether your cash balance increased or decreased over the last year and why, what would your response be? If I were to pose the equivalent question to a company, I may be given the cash flow statement as an answer. I look at the cash flow statement to understand how the company generated or consumed its cash resources during the period. I should be able to answer the following questions after I review the cash flow statement of a company:      

Did the company increase or decrease its cash and cash equivalents during the period? How much money did the company generate from its operations? How much money did the company invest in its business? Did the company sell any assets? How much money did the company pay its shareholders and lenders? Did the company raise money from its shareholders and lenders?

The cash flow statement highlights the cash the company spent or generated from its operating activities, investing activities and financing activities. ‘Cash Equivalents’ is a term applied to temporary investments that are highly liquid as well as marketable securities that can be converted into known amounts of cash. The cash flow statement considers both cash and the cash equivalents alike and explains the changes in the total of cash and the cash equivalents. Overview of the Cash Flow Statements While the balance sheet of the company can tell me what the cash and cash equivalents balance at the beginning of the period and the end of the period were, it cannot tell me how the company generated or consumed the cash. It is the cash flow statement that tells me how the company generated or consumed its cash and cash equivalents. The cash flow statement categorizes its cash activities into three categories which are operating activities, investing activities and financing activities. The sum of changes in these three categories will reflect the overall increase or decrease of cash and cash equivalents during the period. This increase or decrease when added to the cash and cash equivalents at the beginning of the period will give me the cash and cash equivalents at the end of the period.

Select figures from Apple, Inc.’s 2011 Cash Flow Statement

If we look at Apple’s cash flow statement and pull out this information, we will see that Apple generated $38 billion dollars of cash from its operations. It invested about $40 billion of cash into its business. Apple also raised $1.4 billion in funds to invest in the business. The net impact of this was a negative $1.4 billion indicating that it has $1.4 billion less cash and cash equivalents than it had in the beginning of the year. What do you notice in the cash flow statements of Google, WalMart and American Airlines? Operating Activities Section of the Cash Flow Statements The term “operating activities” refers to the core activities of the company or business. It consists of the activities involved in selling goods and/or providing services that generate revenues and expenses for the company. The operating activities of a business will depend on the nature of the business. For example the operating activities of a watch company will be the manufacturing, marketing and selling of watches. The purchase and sale of land will be considered as an operating activity for a real estate company. The operating section of a cash flow statement may be presented in two ways: the indirect method and the direct method. Most companies use the indirect method to report the cash flow statement because the accounting processes and systems commonly used make this convenient. The indirect method starts with the net income figure derived from the income statement and adds or subtracts the difference between cash collected and amounts presented in the income statement to arrive at the actual cash position from operations. It also removes the non-operating activities that were included in the income statement. The direct method presents the cash collected by the business from operations and subtracts the cash paid for operating activities. We will not study the mechanics of computing the cash flow from operating activities of either the direct or indirect method at this level. At this level, it is sufficient to understand the total amount of cash generated by or used in operating activities. Operating activity section of Apple, Inc. 2011 Cash Flow Statement

We can see that although Apple has reported a net income of only $25 billion, it has generated $38 billion from its operating activities. How much cash has Google, Wal-Mart and American Airlines generated or used in operating activity according to their respective cash flow statements? Investing Activities Section of the Cash Flow Statements A company will need to spend money on assets like equipment, buildings, land, etc. to grow or maintain its business. A company will also sell these assets when these are outdated or when it needs to fund the purchase of new assets. These activities are categorized as investing activities. The investing activities section of the cash flow statement will include both the cash generated by selling assets and the cash spent in buying assets. Cash outflows are indicated by negative numbers and cash inflows are indicated by positive numbers in the investing section of the cash flow statement. The investing activities of a business will depend on the nature of the business. For example, the purchase of land will be considered as investing activity for a watch company while it will be considered as an operating activity for a real estate company.

We can see that Apple has both sold and bought assets from the investing section of its cash flow statement. The net impact of Apple’s investing activities is the use of $40 billion of cash and marketable securities. How much money has Google, Wal-Mart and American Airlines used or generated from investing activities? Investing activity section of Apple, Inc. 2011 Cash Flow Statement

Financing Activities Section of the Cash Flow Statements Any activity that involves providing funds to a company is categorized as a financing activity. This includes issuing shares, borrowing money, paying dividends, paying interest on money borrowed, etc. Cash outflows are indicated by negative numbers and cash inflows are indicated by positive numbers in the financing section of the cash flow statement. Financing activity section of Apple, Inc. 2011 Cash Flow Statement

We can see that Apple has issued stock in 2011. It also gained tax benefits and paid taxes related to the issue of stock in 2011. The net impact of these financing activities was a $1.4 billion cash flow into the company. Insight Gained from the Cash Flow Statements The cash flow statement will reveal the liquidity position of the company. It will show you if the company will be able to fund its operations without resorting to outside funds. This is important in preparing for and surviving lean periods or economic downturns. The cash flow statement also reveals the life stage of a company. Is a company growing, mature or declining? A growing company may have a negative cash flow from operating and investing activities and a positive cash flow from financing activities as it continues to consume money to grow. A mature firm will have a positive cash flow from operating activities and possibly a negative balance in its investing activities. A declining firm may have a positive cash flow from operating and investing activities and a negative cash flow from financing activities as it uses money from its business to pay back its investors. Select figures from Apple, Inc. 2011 Cash Flow Statement

Looking at Apple’s cash flow statement, we can see that Apple is a mature company generating significant cash flow from operating activities and making significant investments to grow its business. What would you conclude about Google, Wal-Mart and American Airlines? Summary of the Cash Flow Statement

The cash flow statements show how the company generated or consumed its cash resources during the period. The cash flow statement categorizes its cash activities into three categories which are operating activities, investing activities and financing activities. The sum of changes in these three categories will reflect the overall increase or decrease of cash and cash equivalents during the period. This increase or decrease when added to the cash and cash equivalents at the beginning of the period will give me the cash and cash equivalents at the end of the period. The cash flow statements reveal the liquidity position of the company. It also indicates the life stage of a company as growing, mature or declining. Understanding the cash flow statements is very important because it is the ability to generate cash flow that determines the true value of a business. Next Steps: Now that you have a good understanding of what is in a cash flow statement and how to read a cash flow statement in a company’s annual report, why don’t you head over to either:

Understanding and Interpreting Percentage Statements If I were to ask how one company is different from another company or its competitors, I may be given a variety of answers focusing on its products, target segments, culture, scope, business model, etc. However, by looking at the company’s percentage statements, I can understand how this company is different from its competitors from the financial perspective. Reviewing a company’s percentage statements will help me answer the following questions:  How is this company different from other companies or its competitors?  Has the company’s financial performance improved or worsened and why?  What are the main components of expenses for this company?  How does the strategy of this company impact its financial performance? Is the company’s strategy working?  What is the financial health of this company? The percentage income statement and percentage balance sheet are prepared from the income statement and the balance sheet respectively. As the name suggests, the components of the percentage statement are not mentioned in dollar terms but in terms of a percentage of another variable. The main advantage of percentage statements is that they can be used to compare companies of different sizes. Percentage Income Statement The percentage income statement is prepared by expressing each component of the income statement as a percentage of the net sales or revenues of the company. For example Apple’s 2011 net sales was $108.25 million and its cost of sales was $64.43 million. So the cost of sales as a percentage of net sales will be $64.43/$108.25 or 60%. Its gross margin in 2011 was $43.82 million or 40% ($43.82/$108.25).

Components Of Expenses A mere glance at this percentage statement for the year 2011 will help us to understand what the key cost components for the company were and how profitable its operations were. A look at Apple’s percentage income statement will reveal some interesting observations. The cost of its goods sold is only approximately 60%. This indicates that for every dollar earned, it spent only 60 cents in making its products leaving it a healthy 40 cents to cover other costs and profits. We can also see that it spends about 2-3% of each dollar earned on research and development as well as about 7-10% of its revenues on sales and other general expenses. What do you notice after looking at the percentage statements of Google, Wal-Mart and American Airlines? Have these companies spent more of its revenues on research and development or on sales and other general expenses? What does this say about where they focus their time, energy and money? Trends over time The percentage statement also helps the reader observe trends over time. We can see if the company’s profit margins have been improving or if its costs have been increasing over time, etc. In the case of Apple, we can see that Apple’s operating margin has been increasing over the last few years. What is causing the increase in operating margins? This could be because of the decreasing proportion of spend on selling and general administration expenses as a result of its increasing sales. What trends do you notice after looking at the percentage statements of Google, Wal-Mart and American Airlines? Understand The Nature Of Business Percentage statements help us understand the nature of different types of businesses. Some businesses are high margin businesses whereas some are low margin high turnover businesses. Some companies intentionally invest in research & development while some companies do not.

Percentage statements help us understand the differences between companies and business patterns. Let’s look at the percentage statements of Apple, Microsoft and Wal-Mart.

We can see striking differences in the way Apple operates when compared to Microsoft, a company that is similar in many ways or Wal-Mart, a company that is in an entirely different business. The cost of goods sold highlights the most obvious difference. Wal-Mart is a retailer and therefore its cost of goods sold is expected to be a significant part of its costs. Apple sells hardware and software so has a lower cost of goods percentage when compared to Wal-Mart. Microsoft mostly sells software and so has lower cost of goods sold than Apple. We can see that Wal-Mart invests nothing in research and development and Microsoft invests a significant amount in research and development. A company’s strategy can also be observed in its percentage statements. For example Wal-Mart’s strategy is to be a low price – high volume business and this will be reflected in its sales revenues and profit margins. These percentages will be different for a company like Neiman Marcus whose strategy is to be a high margin low volume business. If a company has changed its strategy over time, we will see that reflected in the financial statements too. If two companies are in the same business and adopt similar strategies, their percentage income statement will show which of the companies ran its operations more efficiently. Percentage Balance Sheet

The percentage income statement like the percentage balance sheet is helpful to understand the nature of the company and its business. It is prepared by expressing each component as a percentage of total assets or total liabilities of the company. A comparison of the figures for the past few years will give us insights into how the company’s strategy has played out or changed over the years. You will see striking differences in the businesses of Apple, Microsoft and Wal-Mart when you look at the percentage balance sheets of these companies.

You will notice that Wal-Mart has 60% of its assets in property, plant and equipment whereas Apple and Microsoft have far less assets in this category. This reflects the differences in their business models. Wal-Mart requires land and building space throughout the country to run its retail outlets. Apple and Microsoft do not require the kind of footprint Wal-Mart requires. Similarly Apple and Microsoft have less than 1% of its assets in inventories whereas Wal-Mart has 20% in inventories reflecting the investments in merchandise Wal-Mart needs to run its business.

If you observe the percentage balance sheets of Apple, Microsoft and Wal-Mart, you will see that Apple has no debt, Microsoft operates on little debt and Wal-Mart uses a reasonable amount of debt. You will also see that these three companies have had healthy profits over the last few years causing their shareholders equity to be a large portion of their liabilities with Apple having the largest proportion in shareholders’ equity. Summary of the Percentage Statements Reviewing a company’s percentage statements will help me answer the following questions:   

How is this company different from another company or its competitors? Has the company’s financial performance improved or worsened? Why? How does the strategy of this company impact its financial performance? Is the company’s strategy working?

Next Steps: Now that you have a good understanding of what is in a cash flow statement and how to read a cash flow statement in a company’s annual report, why don’t you head over to either: