Accounting Time Money Worksheet
123
The Time Value o f M o n e y 12
C H A P T E R
PURPOSE
The purpose of these computations is to evaluate the use of money. The manager has many options as to where re- sources of the organization should be spent.1 These cal- culations provide guides to assist in evaluating the alternatives.
UNADJUSTED RATE OF RETURN
The unadjusted rate of return is a relatively unsophisti- cated return-on-investment method, and the answer is only an estimate, containing no precision. The computa- tion of the unadjusted rate of return is as follows:
Average Annual Net Income � Rate of Return
Original Investment Amount
OR
Average Annual Net Income � Rate of Return
Average Investment Amount
The original investment amount is a matter of record. The average investment amount is arrived at by taking the total unrecovered asset cost at the beginning of esti- mated useful life plus the unrecovered asset cost at the end of estimated useful life and dividing by two. This method has the advantage of accommodating whatever depreciation method has been chosen by the organiza- tion. This method is sometimes called the accountant’s method because information necessary for the computa- tion is obtained from the financial statements.
After completing this chapter, you should be able to
1. Compute an unadjusted rate of return.
2. Understand how to use a present-value table.
3. Compute an internal rate of return.
4. Understand the payback period theory.
P r o g r e s s N o t e s
124 CHAPTER 12 The Time Value of Money
PRESENT-VALUE ANALYSIS
The concept of present-value analysis is based on the time value of money. Inherent in this concept is the fact that the value of a dollar today is more than the value of a dollar in the future: thus the “present value” terminology. Furthermore, the further in the future the re- ceipt of your dollar occurs, the less it is worth. Think of a dollar bill dwindling in size more and more as its receipt stretches further and further into the future. This is the concept of present-value analysis.
We learned about compound interest in math class. We learned that
$500 invested at the beginning of year 1 .05 earns interest (assumed) at a rate of 5% for one year, $525 and we have a compound amount at the end of year 1 amounting to $525, .05 which earns interest (assumed) at the rate of 5% for another year, $551 and we have a compound amount at the end of year 2 amounting to $551 (rounded), and so on.
Using this concept, it is possible to restate the present values of $1 to be paid out or re- ceived at the end of each of these years. It is possible to use equations, but that is not neces- sary because we have present value tables (also called “look-up tables,” because one can “look-up” the answer). A present value table is included at the end of this chapter in Appendix 12-A. All of the figures on the present value table represent the value of a dollar. The interest rate available on this version of the table is on the horizontal columns and ranges from 1% to 50%. The number of years in the period is on the vertical; in this version of the table, the number of years ranges from 1 to 30. To look up a present value, find the column for the proper interest. Then find the line for the proper number of years. Then trace down the interest column and across the number-of-years line item. The point where the two lines meet is the number (or factor) that represents the value of $1 according to your assumptions. For example, find the year 10 by reading down the left-hand column la- beled “Year.” Then read across that line until you find the column labeled “10%.” The point where the two lines meet is found to be 0.3855. The present value of $1 under these as- sumptions (10 year/10%) is about 38.5 cents (shown as 0.3855 on the table).
Besides using the look-up table, you can also compute this factor on a business analyst calculator. A reference to business analyst calculators is contained in Appendix B at the back of this book. Besides using either the look-up table or the business calculator, you can use a function on your computer spreadsheet to produce the factor. The important point is this: no matter which method you use, you should get the same answer.
Now that you have the present value of $1, by whichever method, it is simple to find the present value of any other number. You merely multiply the other number by the factor you found on the table—or in the calculator or the computer. Say, for example, you want to find the present value of $8,000 under the assumption used above (10 years/10%). You simply multiply $8,000 by the factor of 0.3855 you found in the table. The present value of $8,000 is $3,084 (or $8,000 times 0.3855).
A compound interest table is also included at the end of this chapter in Appendix 12-B, along with a table showing the present value of an annuity of $1.00 in Appendix 12-C, so that you have the tools for computation at your disposal.
INTERNAL RATE OF RETURN
The internal rate of return (IRR) is another return on investment method. It uses a dis- counted cash flow technique. The internal rate of return is the rate of interest that dis- counts future net inflows (from the proposed investment) down to the amount invested. The return for a particular investment can therefore be known. The IRR recognizes the el- ements contained in the previous two methods discussed, but it goes further. It also recog- nizes the time pattern in which the earnings occur. This means more precision in the computation because IRR calculates from period to period, whereas the other two methods rely on an average investment.
The IRR computation is not very complicated. The computation requires two assump- tions and three steps to compute. Assumption 1: find the initial cost of the investment. As- sumption 2: find the estimated annual net cash inflow the investment will generate. Assumption 3: find the useful life of the asset (generally expressed in number of years, known as periods for this computation). Step 1: Divide the initial cost of the investment (as- sumption 1) by the estimated annual net cash inflow it will generate (assumption 2). The answer is a ratio. Step 2: Now use the look-up table. Find the number of periods (assump- tion 3). Step 3: Look across the line for the number of periods and find the column that approximates the ratio computed in Step 1. That column contains the interest rate repre- senting the rate of return.
How is IRR used? It can take the rate of return obtained and restate it. The restated fig- ure represents the maximum rate of interest that can be paid for capital over the entire span of the investment without incurring a loss. (You can think of that restated figure as a kind of break-even point for investment purposes.) The fact that a rate of return can be computed is the benefit of using an IRR method.
PAYBACK PERIOD
The payback period is the length of time required for the cash coming in from an invest- ment to equal the amount of cash originally spent when the investment was acquired. In other words, if we invested $1,000, under a particular set of assumptions, how long would it take to get our $1,000 back? The payback period concept is used extensively in evaluating whether to invest in plant and/or equipment. In that case, the question can be restated as follows: If we invested $1,200,000 in a magnetic resonance imaging machine, under a par- ticular set of assumptions, how long would it take to get the hospital’s $1,200,000 back?
The assumptions are key to the computation of the payback period. In the case of equip- ment, volume of usage is a critical assumption and is sometimes very difficult to predict. Therefore, it is prudent to run more than one payback period computation based on differ- ent circumstances. Generally a “best case” and a “worst case” run are made.
The computation itself is simple, although it has multiple steps. The trick is to break it into segments.
For example, Doctor Green is considering the purchase of a machine for his office laboratory. It will cost $300,000. He wants to find the payback period for this piece of equip- ment. To begin, Dr. Green needs to make the following assumptions: Assumption 1: Pur- chase price of the equipment. Assumption 2: Useful life of the equipment. Assumption 3:
Payback Period 125
126 CHAPTER 12 The Time Value of Money
Revenue the machine will generate per year. Assumption 4: Direct operating costs associ- ated with earning the revenue. Assumption 5: Depreciation expense per year (computed as purchase price per assumption 1 divided by useful life per assumption 2).
Dr. Green’s five assumptions are as follows:
1. Purchase price of equipment � $300,000 2. Useful life of the equipment � 10 years 3. Revenue the machine will generate per year � $10,000 after taxes 4. Direct operating costs associated with earning the revenue � $150,000 5. Depreciation expense per year � $30,000
Now that the assumptions are in place, the payback period computation can be made. It is in three steps, as follows:
Step 1: Find the machine’s expected net income after taxes: Revenue (assumption #3) $200,000 Less Direct operating costs (assumption 4) $150,000 Depreciation (assumption 5) 30,000
180,000 Net income before taxes $20,000 Less income taxes of 50% 10,000 Net income after taxes $10,000
Step 2: Find the net annual cash inflow after taxes the machine is expected to generate (in other words, convert the net income to a cash basis): Net income after taxes $10,000 Add back depreciation (a noncash expenditure) 30,000 Annual net cash inflow after taxes $40,000
Step 3: Compute the payback period:
Investment: $300,000 Machine Cost* � 7.5 year
Net Annual $40,000** Cash Flow after Taxes:
*assumption 1 above **per step 2 above
The machine will pay back its investment under these assumptions in 7.5 years. Payback period computations are very common when equipment purchases are being
evaluated. The evaluation process itself is the final subject we consider in this chapter.
Payback Period
EVALUATIONS
Evaluating the use of resources in healthcare organizations is an important task. There are never enough resources to go around, and it is important to use an objective process to eval- uate which investments will be made by the organization. A uniform use of a chosen method of evaluating return on investment and/or payback period makes the evaluation process more manageable.
It is important to choose a method that is understood by the managers who will be using it. It is equally important to choose a method that can be readily calculated. If a multiple- page worksheet has to be constructed to set up the assumptions for a modestly priced piece of equipment, the evaluation method is probably too complex. This comment actually touches on the cost-benefit of performing the evaluation.
Sometimes a computer program is chosen that performs a uniform computation of in- vestment returns and payback periods. Such a program is a suitable choice if the managers who use it understand the printouts it produces. Understanding both input and output is key for the managers. In summary, evaluations should be objective, the process should not be too cumbersome, and the responsible managers should understand how the computa- tion was achieved.
INFORMATION CHECKPOINT
What Is Needed? Information sufficient to perform these calculations. Where Is It Found? In the files of your supervisor; also in the office of the finan-
cial analyst; probably also in the strategic planning of- fice.
How Is It Used? To measure the time value of money
KEY TERMS
Internal Rate of Return Payback Period Present Value Analysis Time Value of Money Unadjusted Rate of Return
DISCUSSION QUESTIONS
1. Can you compute an unadjusted rate of return now? Would you use it? Why? 2. Are you able to use the present-value look-up table now? Would you prefer a com-
puter to compute it?
Discussion Questions 127
128 CHAPTER 12 The Time Value of Money
3. Have you seen the payback period concept used in your workplace? If not, do you think it ought to be used? What are your reasons?
4. Have you had a chance to participate in an evaluation of an equipment purchase at your workplace? If so, would you have done it differently if you had supervised the evaluation? Why?
129
Year 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 2 0.9803 0.9612 0.9426 0.9246 0.9070 0.8900 0.8734 0.8573 0.8417 0.8264 3 0.9706 0.9423 0.9151 0.8890 0.8638 0.8396 0.8163 0.7938 0.7722 0.7513 4 0.9610 0.9238 0.8885 0.8548 0.8227 0.7921 0.7629 0.7350 0.7084 0.6830 5 0.9515 0.9057 0.8626 0.8219 0.7835 0.7473 0.7130 0.6806 0.6499 0.6209 6 0.9420 0.8880 0.8375 0.7903 0.7462 0.7050 0.6663 0.6302 0.5963 0.5645 7 0.9327 0.8706 0.8131 0.7599 0.7107 0.6651 0.6227 0.5835 0.5470 0.5132 8 0.9235 0.8535 0.7894 0.7307 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665 9 0.9143 0.8368 0.7664 0.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241
10 0.9053 0.8203 0.7441 0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 11 0.8963 0.8043 0.7224 0.6496 0.5847 0.5268 0.4751 0.4289 0.3875 0.3505 12 0.8874 0.7885 0.7014 0.6246 0.5568 0.4970 0.4440 0.3971 0.3555 0.3186 13 0.8787 0.7730 0.6810 0.6006 0.5303 0.4688 0.4150 0.3677 0.3262 0.2987 14 0.8700 0.7579 0.6611 0.5775 0.5051 0.4423 0.3878 0.3405 0.2992 0.2633 15 0.8613 0.7430 0.6419 0.5553 0.4810 0.4173 0.3624 0.3152 0.2745 0.2394 16 0.8528 0.7284 0.6232 0.5339 0.4581 0.3936 0.3387 0.2919 0.2519 0.2176 17 0.8444 0.7142 0.6050 0.5134 0.4363 0.3714 0.3166 0.2703 0.2311 0.1978 18 0.8360 0.7002 0.5874 0.4936 0.4155 0.3503 0.2959 0.2502 0.2120 0.1799 19 0.8277 0.6864 0.5703 0.4746 0.3957 0.3305 0.2765 0.2317. 0.1945 0.1635 20 0.8195 0.6730 0.5537 0.4564 0.3769 0.3118 0.2584 0.2145 0.1784 0.1486 21 0.8114 0.6598 0.5375 0.4388 0.3589 0.2942 0.2415 0.1987 0.1637 0.1351 22 0.8034 0.6468 0.5219 0.4220 0.3418 0.2775 0.2257 0.1839 0.1502 0.1228 23 0.7954 0.6342 0.5067 0.4057 0.3256 0.2618 0.2109 0.1703 0.1378 0.1117 24 0.7876 0.6217 0.4919 0.3901 0.3101 0.2470 0.1971 0.1577 0.1264 0.1015 25 0.7798 0.6095 0.4776 0.3751 0.2953 0.2330 0.1842 0.1460 0.1160 0.0923 26 0.7720 0.5976 0.4637 0.3607 0.2812 0.2198 0.1722 0.1352 0.1064 0.0839 27 0.7644 0.5859 0.4502 0.3468 0.2678 0.2074 0.1609 0.1252 0.0976 0.0763 28 0.7568 0.5744 0.4371 0.3335 0.2552 0.1956 0.1504 0.1159 0.0895 0.0693 29 0.7493 0.5631 0.4243 0.3207 0.2429 0.1846 0.1406 0.1073 0.0822 0.0630 30 0.7419 0.5521 0.4120 0.3083 0.2314 0.1741 0.1314 0.0994 0.0754 0.0573
P resent Value Table (The Present Value of $1.00) 12-A
A P P E N D I X
130 CHAPTER 12 The Time Value of Money
Year 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%
1 0.9009 0.8929 0.8850 0.8772 0.8696 0.8621 0.8547 0.8475 0.8403 0.8333 2 0.8116 0.7972 0.7831 0.7695 0.7561 0.7432 0.7305 0.7182 0.7062 0.6944 3 0.7312 0.7118 0.6913 0.6750 0.6575 0.6407 0.6244 0.6086 0.5934 0.5787 4 0.6587 0.6355 0.6133 0.5921 0.5718 0.5523 0.5337 0.5158 0.4987 0.4823 5 0.5935 0.5674 0.5428 0.5194 0.4972 0.4761 0.4561 0.4371 0.4190 0.4019 6 0.5346 0.5066 0.4803 0.4556 0.4323 0.4104 0.3898 0.3704 0.3521 0.3349 7 0.4817 0.4523 0.4251 0.3996 0.3759 0.3538 0.3332 0.3139 0.2959 0.2791 8 0.4339 0.4039 0.3762 0.3506 0.3269 0.3050 0.2848 0.2660 0.2487 0.2326 9 0.3909 0.3606 0.3329 0.3075 0.2843 0.2630 0.2434 0.2255 0.2090 0.1938
10 0.3522 0.3220 0.2946 0.2697 0.2472 0.2267 0.2080 0.1911 0.1756 0.1615 11 0.3173 0.2875 0.2607 0.2366 0.2149 0.1954 0.1778 0.1619 0.1476 0.1346 12 0.2858 0.2567 0.2307 0.2076 0.1869 0.1685 0.1520 0.1372 0.1240 0.1122 13 0.2575 0.2292 0.2042 0.1821 0.1625 0.1452 0.1299 0.1163 0.1042 0.0935 14 0.2320 0.2046 0.1807 0.1597 0.1413 0.1252 0.1110 0.0985 0.0876 0.0779 15 0.2090 0.1827 0.1599 0.1401 0.1229 0.1079 0.0949 0.0835 0.0736 0.0649 16 0.1883 0.1631 0.1415 0.1229 0.1069 0.0930 0.0811 0.0708 0.0618 0.0541 17 0.1696 0.1456 0.1252 0.1078 0.0929 0.0802 0.0693 0.0600 0.0520 0.0451 18 0.1528 0.1300 0.1108 0.0946 0.0808 0.0691 0.0592 0.0508 0.0437 0.0376 19 0.1377 0.1161 0.0981 0.0829 0.0703 0.0596 0.0506 0.0431 0.0367 0.0313 20 0.1240 0.1037 0.0868 0.0728 0.0611 0.0514 0.0433 0.0365 0.0308 0.0261 21 0.1117 0.0926 0.0768 0.0638 0.0531 0.0443 0.0370 0.0309 0.0259 0.0217 22 0.1007 0.0826 0.0680 0.0560 0.0462 0.0382 0.0316 0.0262 0.0218 0.0181 23 0.0907 0.0738 0.0601 0.0491 0.0402 0.0329 0.0270 0.0222 0.0183 0.0151 24 0.0817 0.0659 0.0532 0.0431 0.0349 0.0284 0.0231 0.0188 0.0154 0.0126 25 0.0736 0.0588 0.0471 0.0378 0.0304 0.0245 0.0197 0.0160 0.0129 0.0105 26 0.0663 0.0525 0.0417 0.0331 0.0264 0.0211 0.0169 0.0135 0.0109 0.0087 27 0.0597 0.0469 0.0369 0.0291 0.0230 0.0182 0.0144 0.0115 0.0091 0.0073 28 0.0538 0.0419 0.0326 0.0255 0.0200 0.0157 0.0123 0.0097 0.0077 0.0061 29 0.0485 0.0374 0.0289 0.0224 0.0174 0.0135 0.0105 0.0082 0.0064 0.0051 30 0.0437 0.0334 0.0256 0.0196 0.0151 0.0116 0.0090 0.0070 0.0054 0.0042
131
Year 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
1 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100 2 1.020 1.040 1.061 1.082 1.102 1.124 1.145 1.166 1.188 1.210 3 1.030 1.061 1.093 1.125 1.156 1.191 1.225 1.260 1.295 1.331 4 1.041 1.082 1.126 1.170 1.216 1.262 1.311 1.360 1.412 1.464 5 1.051 1.104 1.159 1.217 1.276 1.338 1.403 1.469 1.539 1.611 6 1.062 1.120 1.194 1.265 1.340 1.419 1.501 1.587 1.677 1.772 7 1.072 1.149 1.230 1.316 1.407 1.504 1.606 1.714 1.828 1.949 8 1.083 1.172 1.267 1.369 1.477 1.594 1.718 1.851 1.993 2.144 9 1.094 1.195 1.305 1.423 1.551 1.689 1.838 1.999 2.172 2.358
10 1.105 1.219 1.344 1.480 1.629 1.791 1.967 2.159 2.367 2.594 11 1.116 1.243 1.384 1.539 1.710 1.898 2.105 2.332 2.580 2.853 12 1.127 1.268 1.426 1.601 1.796 2.012 2.252 2.518 2.813 3.138 13 1.138 1.294 1.469 1.665 1.886 2.133 2.410 2.720 3.066 3.452 14 1.149 1.319 1.513 1.732 1.980 2.261 2.579 2.937 3.342 3.797 15 1.161 1.346 1.558 1.801 2.079 2.397 2.759 3.172 3.642 4.177 16 1.173 1.373 1.605 1.873 2.183 2.540 2.952 3.426 3.970 4.595 17 1.184 1.400 1.653 1.948 2.292 2.693 3.159 3.700 4.328 5.054 18 1.196 1.428 1.702 2.026 2.407 2.854 3.380 3.996 4.717 5.560 19 1.208 1.457 1.754 2.107 2.527 3.026 3.617 4.316 5.142 6.116 20 1.220 1.486 1.806 2.191 2.653 3.207 3.870 4.661 5.604 6.728 25 1.282 1.641 2.094 2.666 3.386 4.292 5.427 6.848 8.632 10.835 30 1.348 1.811 2.427 3.243 4.322 5.743 7.612 10.063 13.268 17.449
Compound Interest Table
Compound Interest of $1.00 (The Future Amount of $1.00)
12-B A P P E N D I X
132 CHAPTER 12 The Time Value of Money
Year 12% 14% 16% 18% 20% 24% 28% 32% 40% 50%
1 1.120 1.140 1.160 1.180 1.200 1.240 1.280 1.320 1.400 1.500 2 1.254 1.300 1.346 1.392 1.440 1.538 1.638 1.742 1.960 2.250 3 1.405 1.482 1.561 1.643 1.728 1.907 2.067 2.300 2.744 3.375 4 1.574 1.689 1.811 1.939 2.074 2.364 2.684 3.036 3.842 5.062 5 1.762 1.925 2.100 2.288 2.488 2.932 3.436 4.007 5.378 7.594 6 1.974 2.195 2.436 2.700 2.986 3.635 4.398 5.290 7.530 11.391 7 2.211 2.502 2.826 3.185 3.583 4.508 5.629 6.983 10.541 17.086 8 2.476 2.853 3.278 3.759 4.300 5.590 7.206 9.217 14.758 25.629 9 2.773 3.252 3.803 4.435 5.160 6.931 9.223 12.166 20.661 38.443
10 3.106 3.707 4.411 5.234 6.192 8.594 11.806 16.060 28.925 57.665 11 3.479 4.226 5.117 6.176 7.430 10.657 15.112 21.199 40.496 86.498 12 3.896 4.818 5.936 7.288 8.916 13.215 19.343 27.983 56.694 129.746 13 4.363 5.492 6.886 8.599 10.699 16.386 24.759 36.937 79.372 194.619 14 4.887 6.261 7.988 10.147 12.839 20.319 31.691 48.757 111.120 291.929 15 5.474 7.138 9.266 11.074 15.407 25.196 40.565 64.350 155.568 437.894 16 6.130 8.137 10.748 14.129 18.488 31.243 51.923 84.954 217.795 656.840 17 6.866 9.276 12.468 16.672 22.186 38.741 66.461 112.140 304.914 985.260 18 7.690 10.575 14.463 19.673 26.623 48.039 85.071 148.020 426.879 1477.900 19 8.613 12.056 16.777 23.214 31.948 59.568 108.890 195.390 597.630 2216.800 20 9.646 13.743 19.461 27.393 38.338 73.864 139.380 257.920 836.683 3325.300 25 17.000 26.462 40.874 62.669 95.396 216.542 478.900 1033.600 4499.880 25251.000 30 29.960 50.950 85.850 143.371 237.376 634.820 1645.500 4142.100 24201.432 191750.000
133
Periods 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% Periods
1 .980 .962 .943 .926 .909 .893 .877 .862 .848 .833 1 2 1.942 1.886 1.833 1.783 1.736 1.690 1.647 1.605 1.566 1.528 2 3 2.884 2.775 2.673 2.577 2.487 2.402 2.322 2.246 2.174 2.107 3 4 3.808 3.630 3.465 3.312 3.170 3.037 2.914 2.798 2.690 2.589 4 5 4.713 4.452 4.212 3.993 3.791 3.605 3.433 3.274 3.127 2.991 5 6 5.601 5.242 4.917 4.623 4.355 4.111 3.889 3.685 3.498 3.326 6 7 6.472 6.002 5.582 5.206 4.868 4.564 4.288 4.039 3.812 3.605 7 8 7.325 6.733 6.210 5.747 5.335 4.968 4.639 4.344 4.078 3.837 8 9 8.162 7.435 6.802 6.247 5.759 5.328 4.946 4.607 4.303 4.031 9
10 8.983 8.111 7.360 6.710 6.145 5.650 5.216 4.833 4.494 4.193 10 15 12.849 11.118 9.712 8.560 7.606 6.811 6.142 5.576 5.092 4.676 15 20 16.351 13.590 11.470 9.818 8.514 7.469 6.623 5.929 5.353 4.870 20 25 19.523 15.622 12.783 10.675 9.077 7.843 6.873 6.097 5.467 4.948 25
P resent Value of an Annuity of $1.00 12-C
A P P E N D I X