1)Widget Manufacturing has just completed a major change in its quality control (QC) process. Previously, QC inspectors had reviewed products at the end of each major process, and the company's 10 QC inspectors were charged as direct labor to the operation or job. In an effort to improve efficiency and quality, Widget purchased a computer video QC system for $250,000. The system consists of a minicomputer, 15 video cameras, other peripheral hardware, and software.

The new system uses cameras stationed by QC engineers at key points in the production process. Each time an operation changes or a new operation begins, the cameras are moved and a QC engineer loads a new master picture into the computer. The camera takes pictures of the unit in process, and the computer compares them with the picture of a ?good? unit. Any differences are sent to a QC engineer, who removes the bad units and immediately discusses the flaws with the production supervisors. The new system has replaced the 10 QC inspectors with 2 QC engineers.

The operating costs of the new QC system, including the salaries of the QC engineers, have been included as overhead in calculating the company's plant-wide factory overhead rate, which is based on direct labor dollars.

In short, the company's president is confused. The vice president of production has been commenting on how efficient the new system is, yet the president has observed that there has been a significant increase in the factory overhead rate. The computation of the rate before and after implementation of the new QC system is as follows:

	Before	After
Budgeted overhead	$1,900,000	$2,100,000
Budgeted direct labor	$1,000,000	$700,000
Budgeted overhead rate	190%	300%

?Three hundred percent,? lamented the president. ?How can we compete with such a high factory overhead rate??

Refer " Assignment_accounting" file attached. There is no word limit.

Questions to consider:

1. Discuss the development of factory overhead rates. Why do we need factory overhead rates, and how are they computed? Discuss the accuracy of the computation of a factory overhead rate.
2. Explain why the increase in the overhead rate should not have a negative impact on Widget Manufacturing.
3. Explain, in the greatest detail possible, how the company could change its overhead accounting system to eliminate confusion over product costs.
4. Discusshowanactivity-basedcostingsystemmightbenefitWidgetManufacturing.

2)Whyisitimportanttoknowtheinternalrateofreturnandthehurdlerate?Whatisthedifferenceincashflowandprofit?Whygotothetroubleofdeterminingthepresentvalueforanydecisionwhichflowsintomulti-periods?( Refer to Reading 13 material attached)

Learning Objective 1 - Explain the changes in the modern production environment that have affected cost structures. Learning Objective 2 - Understand the concept of Activity-Based Costing (ABC) and how it is applied. Activity-based costing allocates costs based on activities that drive overhead rather than simple volume or unit-based measures. In a \"labor intensive\" environment, overhead typically makes up a smaller portion of the total cost of a product or service. With labor as the dominant activity, direct labor hours worked is a logical activity base to use to allocate overhead to products. In heavily automated manufacturing environments, direct labor costs have shrunk while overhead costs have soared. As overhead costs increase and make up a larger portion of the total costs of products, accuracy in overhead application has become much more important. Allocating overhead based on activity-based costing is an effective means to improve the accuracy of cost data. ABC allocates overhead costs assuming that activities, not volume of production, drive overhead costs. Activities are procedures or processes that cause work to be accomplished. Activities consume resources, and products consume activities. Overhead costs are assigned to products in an ABC system in two stages. Stage 1Identification of Activities: In Stage 1, activities are identified and costs are assigned to them. Note that overhead costs may be logically traced to more than one activity. For example, utilities may be related to purchasing, engineering, and machining activities. Stage 2Identification of Cost Drivers: In Stage 2, cost drivers for activities are chosen. Cost drivers should cause or drive the occurrence of costs. ABC can be implemented in the service sector as well. Like manufacturing companies, service companies also identify different activities and cost drivers. However, implementing ABC in service companies has its own problems. Analyzing the activities of a service provider can be difficult when the activities differ greatly for each customer or service. Although there are common activities that drive overhead cost, every company should evaluate its activities carefully. Learning Objective 3 - Explain the difference between traditional plant wide and departmental overhead allocation methods and ABC. Recall that overhead costs are assigned using an allocation system. There are generally three methods of overhead allocation: the single plant-wide overhead rate method, the departmental overhead rate method, and the activity-based costing method. Plant-Wide Overhead Rate Method--When overhead costs are closely tied to volume-related measures this method is logical. Total budgeted overhead costs are combined into one overhead cost pool. Next, the cost pool is divided by the chosen allocation base, such as total direct labor hours, to arrive at a single plant-wide allocation rate. This rate is applied to assign overhead costs to all products. Departmental Overhead Rate Method--When overhead resources are consumed in substantially different ways in each department, a better allocation of costs to departments can occur using this method. There are two stages: (1) overhead costs are determined separately for each production department, and (2) an overhead rate is computed for each production department to allocate the overhead costs to products passing through that department. While the departmental overhead rate method is more refined than the plant-wide overhead rate method, different products within the department may differ in batch size and complexity. Activity-Based Costing (ABC) Rates and Method--ABC attempts to more accurately assign overhead costs by focusing on activities. Once production activities have been identified and the cost drivers for each have been determined, a rate to allocate overhead costs to products (cost objects) is found for each activity. ABC emphasizes activities and costs of carrying out these activities. ABC better reflects the complex nature of overhead costs and how these costs are used in making products. One important aspect of ABC systems is the elimination of cross subsidies between products. Cross subsidies occur when highvolume products are assigned more than their fair share of overhead costs; and low-volume products are allocated too little overhead. Volume-based costing systems often result in overcosting high-volume products and under-costing low-volume products. This cross subsidy is eliminated by the use of ABC. ABC systems generally improve the accuracy of cost data, but are often time consuming and expensive to develop. Learning Objective 4 - Describe the implementation of ABC systems. Activity-based costing provides a more accurate overhead cost allocation because there are more cost pools, the costs in each pool are more similar, and allocation is based on activities that cause overhead costs. More effective overhead cost control is achieved by focusing on processes or activities. Management of activities helps managers identify the causes of costs and the activities driving them. The costs to implement and maintain ABC require management commitment and financial resources beyond those required with plant-wide or departmental methods. Uncertainty with decisions remain and management must interpret ABC data with caution in making managerial decisions. Reading 13: Cash Value, Present Value & Multi-period Performance 1 (File024r reference only) Cash Value, Present Value and Multi-period Performance You buy a tract of land, subdivide it and sell it. You introduce a new product nationally. You purchase a piece of new equipment. These decisions require us to evaluate our decision based on income developing over a period of time. Money must be invested to make money, which occurs over a period of time. Three Things Come Into Play: 1. The size of the benefits. 2. The timing of the benefits. 3. The degree of uncertainty associated with receiving the benefits. The question is, \"Does the size of the return justify the investment?\" How you go about determine the value of the investment will depend largely on when you expect to receive the return on the investment (timing). Example: You could make an investment that immediately pays off or you could make the same investment that pays off over several time periods, usually years. Which is better? We will measure the monetary returns of an investment, which is called CASH FLOW. We will measure the effects of timing on the receipt of the CASH FLOW, which is called DISCOUNTED CASH FLOW. Both of these will be addressed assuming certainty of knowledge of the returns available. WHAT IS CASH FLOW? Profit is an accounting term that associates bottom line profit with a specific time period in which revenues less cost of sales and expenses lead to a profit (or loss). There are two generally accepted manners of accounting for profit and loss - cash basis and accrual basis. In the first, only cash transactions are considered. In the latter, end of period (year or month) expenses and income are matched according to the period in which they occur. The receipt or disbursement of cash does not determine profit. We might sell something on Reading 13: Cash Value, Present Value & Multi-period Performance 2 (File024r reference only) credit and take the payment over a time period(s). The sale would be fully recorded, while the cash received would be deferred as a receivable. Cash is a totally different concept from profit. Cash flow is determined when the cash is received or when the cash is spent. Profits and cash flow are not the same. For Example: A three year insurance program is prepaid on January 1 for $15,000. The cash flow is a negative $15,000 but the profit impact (expense) for the year in question will only be $5,000 (accrual basis) for each of the three years. For this insurance payment, you might want to spread the cash flow over three years. This can be done by deferring the payments for the subsequent years to the years in which the expense is incurred. Lack of cash is the biggest reason businesses fail, not lack of profit. INCOME STATEMENT: An income statement may look like the following example. Sales $768,000 Cost of Sales $512,000 Gross Margin $256,000 Expenses Overhead Administrative Operating $87,000 $56,000 $91,000 Net Profit Before Tax $22,000 Taxes @ 38% $ 8,360 Net Profit After Tax $13,640 An income statement is a picture of the business over a period of time, usually a month or quarter or year. Reading 13: Cash Value, Present Value & Multi-period Performance 3 (File024r reference only) CASH FLOW STATEMENT: A cash flow statement may look like the following example. An investment of $128,000 will expand production for three years and allow the company to satisfy customer demand not currently being served. Anticipated revenue will be $108,000 per year and the cost of sales will be $48,000 per year. No increase in G & A will be required, since they will be operating on incremental profit. Inventory and accounts receivable increases in the usage of cash will be a one time cash requirement of $32,000. At the end of the third year there will be an $8,000 salvage value in the equipment. The equipment has been straight-line depreciated and the $8,000 will be the book value, so no gain or loss will be realized on the sale of the equipment. The marginal tax rate is assumed to be 38%. Let's take the facts and put them into a more understandable form or table. Take the facts given above and enter them into the following table. The correct answer table immediately follows this exercise table, but don't peek until you make an attempt. Not all cells will have values, so only use those that are appropriate for the example above. Exercise Table 1: Cash Flow Current Cash Outlay Results End of Year 1 Results End of Year 2 Results End of Year 3 Cash Outlay Incremental Sales Expected Cost of Sales Taxes Changes in Working Capital Salvage Value of Equipment Taxes on Salvage Value Total Cash Flow Per Year Cumulative Cash Flow Taxes may be the only tricky thing since you must make this calculation from the available data and don't forget to include depreciation. 4 Reading 13: Cash Value, Present Value & Multi-period Performance (File024r reference only) Table 1: Cash Flow Results End of Year 1 Results End of Year 2 Results End of Year 3 $108,000 $108,000 $108,000 $ (48,000) $ (7,600) Current Cash Outlay $(48,000) $ (7,600) $(48,000) $ (7,600) Cash Outlay ($128,000) Incremental Sales Expected Cost of Sales Taxes Changes in Working Capital ($ 32,000) $ 32,000 Salvage Value of Equipment $ 8,000 Taxes on Salvage Value Zero Total Cash Flow Per Year Cumulative Cash Flow ($160,000) Negative ($160,000) $ 52,400 Negative ($107,600) $ 52,400 Negative ($55,200) $ 92,400 Positive $ 37,200 Tax Calculations for Table 1: Incremental Sales Less: Cost of Goods Less: Depreciation Profits Before Tax Taxes @38% $108,000 (48,000) (40,000) $ 20,000 $ 7,600 Analyzing the Results: You only gain $5,200 which is the incremental cash flow ($37,200 for making the investment less $32,000 for doing nothing). When you examine this difference and realized it takes you three years to make the gain with the first two having a negative impact, the question should be asked \"Is there any need for going forward with the project?\" In effect you spend $160,000 in current dollars to get back $197,200 at the end of three years. Included in both the current dollars and the cash flow at the end Reading 13: Cash Value, Present Value & Multi-period Performance 5 (File024r reference only) of three years is an initial outlay of $32,000 which goes out in the first year but back in the third year. Incremental Cash Flow is the difference in the cash flow from the investment (for the entire time period) less the cash flow from not making the investment (doing nothing alternative). It is the cash realized between making the investment and doing nothing. When you write a check it is cash outflow and when you make a deposit it is cash inflow. It is very difficult if not impossible to make an exhaustive list of cash flows. Categories or Groups of Cash Flow Elements Initial Outlay Initial Purchase or Investment Changes in Working Capital Changes in Cash Changes in Accounts Receivable Changes in Inventory Changes in Accounts Payable Determine the Salvage Value of Equipment at End of the Project Determine if there are Investment Incentives Offered by Taxing Authorities. Outlays After the Initial Outlay Look for Revenues Generated End of Investment or Project Sales Dividends Interest Payments. Look for Costs Incurred Cost of Goods Sold (materials and manufacturing costs) Changes in Administrative Expenses For Subsequent Investment Costs For Taxes Avoid Expenses That Do Not Change Ignore Expenses that Do Not Change if the Investment Is Not Done. Avoid allocated incremental expenses. Do not credit the investment with cannibalized sales. Reading 13: Cash Value, Present Value & Multi-period Performance 6 (File024r reference only) Finally, Outlays or Recovery at the end of the Investment. Make sure to include the recovery of working capital, any shutdown costs and the salvage value of any equipment. Notice: Do not include depreciation as a cash flow. It is merely an accounting provision whose effects are reflected in the calculation of taxes. Do not include financing costs of an investment because they are excluded from cash flow because of widely accepted practice of separating the evaluation of the investment from the financing of the investment. In effect, you make the assumption you have the cash to make the investment without borrowing. Time Value of Money One of the most important aspects of evaluating an investment is the time value of money. It is also one of the more difficult concepts to wrap our mind around. Current money is more valuable than future money. The cash option on the lottery pays less than the 25 year pay out for this very reason. Money we receive today is more valuable than money we receive in the future. Money we receive today purchases more than money received in the future. Example: A manager has two investments for which the cash flow has been accurately determined. Both investments require a $50,000 investment. Investment A yields a cash flow of $22,000 at the end of each of the next three years ($66,000 total). Investment B yields a cash flow of $12,000 at the end of the next two years and $46,000 in the third year ($70,000 total). Which investment is the best? Both investments return more than the original investment of $50,000. Investment B returns $70,000 ($4,000 more than A), but much of the return for investment B is in the last year of the investment. The questions is does this make any difference in our consideration of the investments? To effectively evaluate the opportunities, we should consider the impact of the time value of money. 7 Reading 13: Cash Value, Present Value & Multi-period Performance (File024r reference only) Table 1: Comparison of Cash Flows of Investment A and B Year by Year without Looking at Time Value. Cash Flows Investment A Investment B Cumulative Difference A Over B Initial Outlay Year 1 Year 2 Year 3 $50,000 $50,000 $22,000 $12,000 Positive $10,000 $22,000 $12,000 Positive $20,000 $22,000 $46,000 Minus -$4,000 None Total Cash Flow Return $66,000 $70,000 Minus -$4,000 Based on this table alone you would probably say that Investment B returns $4,000 more than A so let's make investment B. Of course you did not have to put this in tabular format to know this, but the table is provided so you can take the next step and apply the concept of time value. What is the best possible analysis on which the investment decision should and must be made? What must be known to properly answer this question is the reinvestment opportunity for the cash flows. In other words, what do you do with the cash flow developed each year assuming you don't put it in your sock drawer. The reinvestment rate is simply the best rate of return available to the company in another alternative investment. For purposes of illustration let's assume two rates (so I can complicate your life). One is a 15% rate and the other is a 10% rate, both of which are arbitrarily chosen. For actual analysis, you would actually have to know how much you might be able to receive from alternate investments. Let's develop several tables which are useful in making this evaluation. We will first look at the 15% investment opportunity. There are actually three possibilities - Investment A, Investment B and Neither. The Neither Alternative is to simply take the $50,000 and invest it at the 15% rate. This should also be considered. All three are shown in Table 2 below. You need to take your calculator out and make sure you can develop the numbers shown in the table. 8 Reading 13: Cash Value, Present Value & Multi-period Performance (File024r reference only) Table 2: Investment A and B Cash Flow with Reinvestment Rate of 15%. (Assume End of Year Receipt of Cash) Cash Flows Investmnt A Reinvest. Rate of 15% Initial Investment $50,000 Year 1 Year 2 Year 3 $22,000 $22,000 $22,000 Zero $3,300 Total Cash Flow $66,000 $7,095 $10,395 $22,000 $25,300 $29,095 $76,395 $22,000 $47,300 $76,395 $76,395 $12,000 $12,000 $46,000 $70,000 $3,870 $5,670 $12,000 $13,800 $49,870 $75,670 $12,000 $25,800 $75,670 $75,670 Yearly Cash Flow Cumulative Cash Flow Investmnt B Reinvest. Rate of 15% $50,000 Zero Yearly Cash Flow $1,800 Cumulative Cash Flow Invest Capital in Alternative $50,000 $50,000 $57,500 $66,125 Return @15% $7,500 $8,625 $9,919 Cash Flow at EOY $57,500 $66,125 $76,044 Which is the best decision? Investment A appears best. $76,044 9 Reading 13: Cash Value, Present Value & Multi-period Performance (File024r reference only) Table 3 Exercise for 10% Reinvestment Rate Cash Flows Initial Investment Year 1 Year 2 Year 3 Total Cash Flow Investment A $50,000 $22,000 $22,000 $22,000 $66,000 $50,000 $12,000 $12,000 $46,000 $70,000 $50,000 $50,000 $55,000 $60,500 Reinvest. Rate 10% Yearly Cash Flow Cumulative Cash Flow Investment B Reinvest. Rate of 10% Yearly Cash Flow Cumulative Cash Flow Invest Capital in Alternative Return @10% Cash Flow at EOY The answers are shown below. 10 Reading 13: Cash Value, Present Value & Multi-period Performance (File024r reference only) Table 3: Investment A and B Cash Flow with 10% Reinvestment Rate. Cash Flows Initial Investment Year 1 Year 2 Year 3 Total Cash Flow Investment A $50,000 $22,000 $22,000 $22,000 $66,000 Reinvest. Rate 10% Zero $2,200 $4,620 $6,820 $22,000 $24,200 $26,620 $72,820 $22,000 $46,200 $72,820 $72,820 $12,000 $12,000 $46,000 $70,000 $2,520 $3,720 $12,000 $13,200 $48,520 $73,720 $12,000 $25,200 $73,720 $73,720 Yearly Cash Flow Cumulative Cash Flow Investment B $50,000 Reinvest. Rate of 10% Zero $1,200 Yearly Cash Flow Cumulative Cash Flow Invest Capital in Alternative Return @10% $50,000 $50,000 $55,000 $60,500 $5,000 $5,500 $6,050 $16,550 $55,000 $60,500 $66,550 $66,550 Cash Flow at EOY Which is the best investment? Investment B appears best. 11 Reading 13: Cash Value, Present Value & Multi-period Performance (File024r reference only) Table 4: Recap and Comparison of Three Alternatives - Net Cash Flow. (Incremental Basis) Comparison of All Opportunities Cash Flow @ 15% Less: Original Investment Net Cash Flow Cash Flow @ 10% Less: Original Investment Net Cash Flow Investment A $76,395 Investment B $75,670 Reinvestment Opportunity $76,044 $50,000 $26,395 $50,000 $25,670 $50,000 $26,044 $72,820 $73,720 $66,550 $50,000 $22,820 $50,000 $23,720 $50,000 $16,550 What decision would you make? This method is good for valuing a cash flow stream at the end of the investment. Note that it includes the reinvestment income. However, this method falls short unless the cash flow relative to each investment alternative is equally realized during subsequent time periods over the life of the investment. If the cash flow from the two investments is not equally realized, then this method needs to be supplemented with analysis of the Present Value of the cash flow. Most of you are shuddering right about now because I used the word \"Present Value\". Present Value and Net Present Value: The value of any investment is associated with a \"future\" point in time. Shortterm investments do not have the same issue as long-term investments. We generally do not try to determine the value of any investment in terms of future values. The textbook gives numerous reasons on page 94 and 95, Chapter 7. Review them. What we do try to do is establish a value in terms of present value or value the investment in today dollars. For example: $50,000 invested today at 15% would yield a future value of $76,044 per our previous calculations. In a real sense, the $50,000 is the present value of $76,044. 12 Reading 13: Cash Value, Present Value & Multi-period Performance (File024r reference only) We can essential write the equation $50,000 (PV) = $76,044 (FV) Given a 15% return. These are financial and not mathematical equivalents. In all investment opportunities, we have a balancing point. The balancing point is the equivalent of financial neutrality. Neutrality is defined at the value for which the investor will remain indifferent to taking the present value or wait for the future value to develop. Let's look at an example. Table 5: Determination of the Future Value Factor Using the 15% Alternative. Year 1 1.0000 Beginning Amount 0.15000 Interest at 15% Ending Factor (Sum) 1.1500 Year 2 1.1500 0.1725 * 1.3225 Year 3 1.3225 0.1984** 1.5209 * Find this value by multiplying 0.1500 times 1.15 = 0.1725 for the end of the second year. ** Find this value by multiplying 0.1725 times 1.15 = 0.1984 for the end of the second year. What this tells us is that a $1.00 today will grow to $1.5209 at the end of three years if invested at a return of 15% (assuming annual compounding). In our example, we need to determine the present value and the net present value of two opportunities we are examining - Investment A & B. Remember Investment A returns $22,000 at the end of each of three years, whereas Investment B returns $12,000, $12,000 and $46,000 respectively at the end of years 1 through 3. What we are seeking to do is determine how much the deferred value is worth is today's dollars. In other words, if I wait a year to get my money (say the $22,000 for Investment A at the end of the first year), how much is that money worth in the dollars of today. Said differently how much purchasing power am I giving up by waiting a year to get the $22,000. My current value is directly related to the reinvestment rate. If we set it at 15%, this means that I must divide the deferred income of $22,000 by 1.15 (the factor) to determine what the $22,000 is worth in 13 Reading 13: Cash Value, Present Value & Multi-period Performance (File024r reference only) current dollars ($22,000 1.15 = $19,130.43). So because I have to wait a year, the $22,000 is really only worth $19,130 in today's dollars). I am sure that is about as clear as mud, so let's tackle the entire problem and further muddy the waters. Look at the values under Investment A in the second column of numbers (the third column from the left). The years are on the left, so at the end of the first year the $22,000 is really only worth $19,130 because of the reinvestment rate of 15%. This decreases the value of my cash flow because I am deferring the receipt of money for one year, two years and three years. Table 6: Determination of the Net Present Value at 15% Reinvestment Rate. (Factors Developed In Table 5) Opportunities Invest. A Present Value @ 15% -End Year 1 Present Value @ 15% -End Year 2 Present Value @ 15% -End Year 3 Total Present Value for the Life of the Investment $22,000 1.15 $22,000 1.3225 $22,000 1.5209 Invest. A $19,130 $16,635 $14,465 Invest. B $12,000 1.15 $12,000 1.3225 $46,000 1.5209 Invest. B $10,434 $ 9,074 $30,245 $50,230 (Sum) $49,753 (Sum) $50,000 $50,000 +230 (247) Less: Current Investment Equals Net Present Value (NPV) If the NPV is positive, we have a better investment. If the NPV is negative, we have a worse investment. Here we have a negative net present value for the cash flow from Investment B, but a positive net present value for the cash flow from Investment A. Why do you suppose this happens? Investment B returns more in absolute dollars ($4,000, which is the $70,000 versus the $66,000 determined very early in the solution). However, because so much of the return for Investment B is deferred until the third year, the net present value is negative. This makes some logical sense. The longer I have to wait for my money, the less value it has in today's dollars. 14 Reading 13: Cash Value, Present Value & Multi-period Performance (File024r reference only) This table is very similar to the table previous presented on cash flow alone. Note that the present value of future cash flows is less than the cash flow itself. $50,230 (from Table 6) is less than $76,044 (from Table 2). This is reasonable and logical. If you want $76,044 in the future you must invest $50,230 now at a rate of return of 15%. The future flow ($76,044) has been discounted to account for the time value of money, which is represented by the present value of the cash flow ($50,230). Let's don't overlook the reinvestment rate of 10%. calculations associated with the 10% reinvestment rate. Table 6A makes the Table 6A: Determination of the Net Present Value at 10% reinvestment rate. (Factors Are Developed the Same Way as the 15% Factors in Table 5) Opportunities Invest. A Present Value @ 10% -Year 1 $22,000 1.10 $22,000 1.21 $22,000 1.331 Present Value @ 10% -Year 2 Present Value @ 10% -Year 3. Total Present Value for the Life of the Investment Invest. A $20,000 $18,182 $16,529 Invest. B $12,000 1.10 $12,000 1.21 $46,000 1.331 Invest. B $10,909 $9,917 $34,560 $54,711 (Sum) $55,386 (Sum) $50,000 $50,000 +$4,711 +$5,386 Less: Current Investment Equals Net Present Value (NPV) Here both investments yield a positive net present value, but Investment B yields a higher NPV. At the 10% reinvestment factor, Investment B has a higher NPV. Alternate Way of Thinking about the Same Thing: Sometimes a complicated process such as PV and NPV can be thought of in a different manner. Either way the answers are going to be the same, but I am just presenting the information from a different view point. Let's evaluate Investment A again based on 15% reinvestment rate. 15 Reading 13: Cash Value, Present Value & Multi-period Performance (File024r reference only) Knowing the Present Value and the Future Value, you can develop a different factor, which is the discounting factor usually presented in many present value tables. You would determine the following. Table 7: Development of the Present Value Factor-15% Reinvestment Rate. Present Value $19,130 Future Value $22,000 $16,635 $22,000 $14,465 $22,000 PV FV $19,130 $22,000 $16,635 $22,000 $14,465 $22,000 Factor Which is the Same As 1.0 1.15 = 0.8696 0.8696 0.7561 0.6575 1.0 1.3225 = 0.7561 1.0 1.5209 = 0.6575 The result first presented in Table 6 can now be rewritten in a simplified form in Table 8. It would look like the following: Table 8: Rewritten Cash Flow with 15% Reinvestment Rate. Cash Flow from Times the Present Value Investment A Factor End of Year 1 End of Year 2 End of Year 3 Total $22,000 0.8696 $19,130 $22,000 0.7561 $16,635 $22,000 $66,000 0.6575 $14,465 $50,230 Now look at Investment B using the same 15% reinvestment rate. Notice that the factors remain the same because the reinvestment rate remains the same for both A and B. Table 9: Calculation of the Cash Flow for Investment B Using the 15% Reinvestment Rate Factor. Cash Flow from Times the Present Value Investment B Factor End of Year 1 End of Year 2 End of Year 3 Total $12,000 0.8696 $10,434 $12,000 0.7561 $9,074 $46,000 $70,000 0.6575 $30,245 $49,753 16 Reading 13: Cash Value, Present Value & Multi-period Performance (File024r reference only) Notice that in Tables 8 and 9, the end result is the same as presented in Table 6. Here all we have done is simplify the presentation and calculations using the discounted factor. The present value in Table 6 was $50,730 for Investment A and was $49,753 for Investment B. In Tables 8 and 9, these numbers are the same. We can do the same analysis for Investment A and B for the 10% reinvestment rate. Those results are shown below although I will not make comments on these calculations. The concept is the same. To calculate the Factor you would use the same approach. Table 10: Development of the Factor Using a 10% Reinvestment Rate for Investment B. Present Value $10,909 Future Value $12,000 $ 9,917 $12,000 $34,560 PV FV $46,000 $10,909 $12,000 $9,917 $12,000 Same As Factor 1.0 1.10 = 0.9091 0.9091 1.0 1.21 = 0.8264 0.8264 $34,560 $46,000 0.7513 1.0 1.331 = 0.7513 Rewritten it would look like the following: Table 11: Application of the Factor to the Cash Flow at 10% Reinvestment Rate for Investment B. Cash Flow from Times the Present Value Investment B Factor End of Year 1 End of Year 2 End of Year 3 Total $12,000 0.9091 $10,909 $12,000 0.8264 $ 9,917 $46,000 $66,000 0.7513 $34,560 $55,386 Reading 13: Cash Value, Present Value & Multi-period Performance 17 (File024r reference only) If you are into mathematical formulas, this same approach can be expressed as follows: Formulas for Computations: An = P times (1 + r) n And P = An (1 + r) n Where A is the accumulated value. n is the year (or partial years) in the future. P is the single payment. r is the reinvestment rate (in decimal equivalent) so if I were looking for the accumulated value, my solution An = P times (1 + r) n = $19,130 times (1 + 0.15) 1 = $19,130 times 1.15 = $22,000 for 1 year. Looking for the single payment, my solution would be P = An (1 + r) n = $22,000 (1 + 0.15) 1 = $22,000 1.15 = $19,130. (single payment) Streams in Perpetuity: What happens if the investment yields a continuing cash flow forever? At a reinvestment rate of 15%, an investment of $20,000 per year will yield a cash flow of $3,000 forever, provided the yearly cash flow is taken out each year. The PV is the annual payment ($3,000) divided by the rate (r), which is 15% in this example. $3,000 0.15 = $20,000. This is Cr Where: C is the annual payment and r is the reinvestment rate. For instance: If Investment A yielded a $22,000 perpetuity with a reinvestment rate of 15%, the present value (PV) would be $22,000 0.15 = $146,667. Reading 13: Cash Value, Present Value & Multi-period Performance 18 (File024r reference only) You can see the exponential effect of discounting, when you compare the first three years at $50,230 to the $146,667 perpetuity. Two-thirds of the present value occurs in the first three years. Cash flow in later years has less present value. Makes sense, doesn't it? Pretax versus After Tax Analysis: Use the after tax reinvestment rate whenever possible, since a pretax reinvestment rate can be influenced by depreciation, investment tax incentives or working capital. The Reinvestment Rate: A reinvestment rate must always be used in analyzing any cash flow investment. What that rate is remains open to discussion. The reinvestment rate must be investor neutral. In other words, the investor must have a neutral opinion as to taking the cash flow now versus waiting for it to mature. The PV must equal the FV. Three reinvestment rate guidelines are useful. I. Hurdle Rate II Internal Rate of Return III. Nominal versus Effective Rates of Return I. Hurdle Rate (Three Options): Opportunity Rate (Option I): One concept that enjoys favor is the opportunity rate. This is the marginal rate of return of the pool of investment opportunities available to the firm. If the profile of investment opportunities is complex, the opportunity rate is difficult to ascertain. When this case exists, the alternative is to look for a rate associated with the cost of capital. Reading 13: Cash Value, Present Value & Multi-period Performance 19 (File024r reference only) Market Cost of Capital (WACC Approach) (Option 2): The market cost of capital will be developed by looking at debt and equity cost. Cost of Debt is simply the interests that must be paid, but since interest is an expense, the effective cost of debt is the after tax interest rate. Cost of Shareholders Equity is related to the cost an investor wants as compensation for the use of his money and for the risk associated with the investment. These two costs combine with the capital structure of the firm to build a weighted average cost of capital known as WACC. A firm should only consider those investments whose cash flows will yield at least the WACC. From the viewpoint of the capital markets, the value of the investment is the PV or the cash flows using the WACC. Perfect Environment Market Cost of Capital (Option 3): Assuming perfect information by the investor and the firm, the WACC and the opportunity rate with be the same. The WACC is commonly used as the reinvestment rate. It is called the Hurdle Rate, because investments which have a positive present value at this rate are financially attractive. Conversely investments which have a negative present value are not financially attractive. II. Internal Rate of Return: This rate of return is the reinvestment rate for which the NPV of the investment is zero. This is a break-even reinvestment rate of return which is called the internal rate of return (IRR). Finding this rate is based on trial and error. Textbook examples appear on pages 100 and 101 and we will not cover them here. III. Nominal Versus Effective Rates of Return: If an interest rate is stated as 12%, the effective rate may be more than 12% if the interest is compounded in any manner other than a once per Reading 13: Cash Value, Present Value & Multi-period Performance 20 (File024r reference only) year, year end interest rate. The 12% is considered the nominal rate. If the real rate is compounded monthly, then interest earns interest on interest. The real rate (the effective rate) would be determined by multiplying a $1,000 investment times 1.01 to the 12th power, which would give an effective yield of 12.7%