Investment Analysis PDF

Investment Analysis DXP02707 —UN—23FEB11 INTRODUCTION DXP01817 —UN—28SEP10 You should invest surplus funds so they can work fo...

Investment Analysis DXP02707 —UN—23FEB11 INTRODUCTION DXP01817 —UN—28SEP10 You should invest surplus funds so they can work for you. The question is; where do you invest? Continued on next page MM16633,00025C3 -19-24FEB11-1/2 7-1 090117 PN=103  Investment Analysis You need to know how to identify which investments are right for your particular situation. The most practical way to do this is to analyze and compare alternatives (Fig. 1). You need to learn some basic terms and concepts before you can analyze investments effectively. Here is some information to get you started. The first thing you need to know is the amount of capital (funds) required for each investment alternative (Fig. 2). Capital requirements will give you a fast comparison and will eliminate those investment alternatives for which you have insufficient available capital. DXP01772 —19—17SEP10 Fig. 1 — Compare investments directly to each other DXP01773 —19—17SEP10 Fig. 2 — Compare the capital required for each investment MM16633,00025C3 -19-24FEB11-2/2 BENEFIT AND COST ANALYSIS Choose greater benefits over smaller ones. Choose an investment with the overall best return. The second thing you need is a method to measure and evaluate the investments. A good method is to estimate To fully understand estimating benefits and costs, you benefits and costs of the investment. A benefit and cost need to understand the time value of money. analysis will show that you should: Choose early benefits over later benefits. Choose investments that give you the earliest returns. MM61211,00000A8 -19-24FEB11-1/1 7-2 090117 PN=104  Investment Analysis THE TIME VALUE OF MONEY The time value of money is the concept of computing the value of money, either in the present or future, based on a given interest rate and time frame. Anyone prefers a given dollar amount today rather than later if there is no interest to be earned by waiting. Interest is the reward for waiting and becomes a central theme in investment analysis. DXP01778 —UN—17SEP10 The time value of money mathematics includes calculating the future value of a present sum given an interest rate and time frame. This process is referred to as compounding. Alternatively, discounting is the mathematical process of computing present day value based on a future value along with an interest rate and a time frame. Fig. 3 — Compounding tells you value at a future time SIMPLE INTEREST VERSUS COMPOUNDING Simple interest can be thought of as the rent paid on A—Now C—2 Years borrowed money for a certain period of time. For example, B—1 Year D—What Will $1.00 Be Worth in if you borrowed $1,000 at 7% for one year, then the Two Years? interest or rent would be $70. Simple interest is defined as the amount borrowed or principal multiplied by the interest rate. Simple interest in this example would be: For example, what is the future value of $1.00 compounded Equation 1: Interest = $1,000 x.07 or $70 at 5% for one year? The factor (found at the intersection of 5% and one year) is 1.05. The factor is multiplied by Compound interest is when the interest ($70) of the first the amount compounded to find a value of $1.05. time period is added to the original principal and interest What is the value of $250 placed in a savings account is calculated on $1,070 in the second time period. The at 10% interest for 10 years? The factor is 2.5937. The following illustration shows how an original principal would future value is $648.43 and is calculated by multiplying grow over five years with annual compounding. $250 by 2.5937. This is the amount you would have in the savings account after 10 years at 10% interest. Year 1 — $1,000 x.07 = $70 + $1,000 = $1,070 Year 2 — $1,070 x.07 = $74.90 + $1070 = $1,144.90 Year 3 — $1,144.90 x.07 = $80.14 + $1,144.90 = $1,225.04 Year 4 — $1,225.04 x.07 = $85.75 + $1,225.04 = $1,310.79 Year 5 — $1,310.79 x.07 = $91.76 + $1,310.79 = $1,402.54 The compounding formula can be summarized in equation 2: Equation 2: Future Value = Present Value x (1 + I)n Future Value is the computed value ($1,402.54) Present Value is the original principal ($1,000) I is the interest rate (7%) n is the number of time periods (5) Thus, equation 3 summarizes this compounding problem: Equation 3 $1,404.54 = $1,000 x (1 +.07)5 If you compound a sum of money, then you calculate its value at a future date (Fig. 3). Compounding is often accomplished through the use of computed factors in financial tables. The compounding table (Table 1,) gives the factors for compounding $1.00 at different interest rates for various periods of time. To use the table, you locate the factor at the intersection of the appropriate interest rate and time period. Continued on next page FB87413,0000091 -19-24JUL14-1/9 7-3 090117 PN=105  Investment Analysis Table 1 — Future Value Factors Year 4% 5% 6% 7% 8% 9% 10% 11% 1 1.0400 1.0500 1.0600 1.0700 1.0800 1.0900 1.1000 1.1100 2 1.0816 1.1025 1.1236 1.1449 1.1664 1.1881 1.2100 1.2321 3 1.1249 1.1576 1.1910 1.2250 1.2597 1.2950 1.3310 1.3676 4 1.1699 1.2155 1.2625 1.3108 1.3605 1.4116 1.4641 1.5181 5 1.2167 1.2763 1.3382 1.4026 1.4693 1.5386 1.6105 1.6851 6 1.2653 1.3401 1.4185 1.5007 1.5869 1.6771 1.7716 1.8704 7 1.3159 1.4071 1.5036 1.6058 1.7138 1.8280 1.9487 2.0762 8 1.3686 1.4775 1.5938 1.7182 1.8509 1.9926 2.1436 2.3045 9 1.4233 1.5513 1.6895 1.8385 1.9990 2.1719 2.3579 2.5580 10 1.4802 1.6289 1.7908 1.9672 2.1589 2.3674 2.5937 2.8394 11 1.5395 1.7103 1.8983 2.1049 2.3316 2.5804 2.8531 3.1518 12 1.6010 1.7959 2.0122 2.2522 2.5182 2.8127 3.1384 3.4985 13 1.6651 1.8856 2.1329 2.4098 2.7196 3.0658 3.4523 3.8833 14 1.7317 1.9799 2.2609 2.5785 2.9372 3.3417 3.7975 4.3104 15 1.8009 2.0789 2.3966 2.7590 3.1722 3.6425 4.1772 4.7846 16 1.8730 2.1829 2.5404 2.9522 3.4259 3.9703 4.5950 5.3109 17 1.9479 2.2920 2.6928 3.1588 3.7000 4.3276 5.0545 5.8951 18 2.0258 2.4066 2.8543 3.3799 3.9960 4.7171 5.5599 6.5436 19 2.1068 2.5270 3.0256 3.6165 4.3157 5.1417 6.1159 7.2633 20 2.1911 2.6533 3.2071 3.8697 4.6610 5.6044 6.7275 8.0623 21 2.2788 2.7860 3.3996 4.1406 5.0338 6.1088 7.4002 8.9492 22 2.3699 2.9253 3.6035 4.4304 5.4365 6.6586 8.1403 9.9336 23 2.4647 3.0715 3.8197 4.7405 5.8715 7.2579 8.9543 11.0263 24 2.5633 3.2251 4.0489 5.0724 6.3412 7.9111 9.8497 12.2392 25 2.6658 3.3864 4.2919 5.4274 6.8485 8.6231 10.8347 13.5855 26 2.7725 3.5557 4.5494 5.8074 7.3964 9.3992 11.9182 15.0799 27 2.8834 3.7335 4.8223 6.2139 7.9881 10.2451 13.1100 16.7386 28 2.9987 3.9201 5.1117 6.6488 8.6271 11.1671 14.4210 18.5799 29 3.1187 4.1161 5.4184 7.1143 9.3173 12.1722 15.8631 20.6237 30 3.2434 4.3219 5.7435 7.6123 10.0627 13.2677 17.4494 22.8923 31 3.3731 4.5380 6.0881 8.1451 10.8677 14.4618 19.1943 25.4104 32 3.5081 4.7649 6.4534 8.7153 11.7371 15.7633 21.1138 28.2056 33 3.6484 5.0032 6.8406 9.3253 12.6760 17.1820 23.2252 31.3082 34 3.7943 5.2533 7.2510 9.9781 13.6901 18.7284 25.5477 34.7521 35 3.9461 5.5160 7.6861 10.6766 14.7853 20.4140 28.1024 38.5749 36 4.1039 5.7918 8.1473 11.4239 15.9682 22.2512 30.9127 42.8181 37 4.2681 6.0814 8.6361 12.2236 17.2456 24.2538 34.0039 47.5281 38 4.4388 6.3855 9.1543 13.0793 18.6253 26.4367 37.4043 52.7562 39 4.6164 6.7048 9.7035 13.9948 20.1153 28.8160 41.1448 58.5593 40 4.8010 7.0400 10.2857 14.9745 21.7245 31.4094 45.2593 65.0009 Table 1 — Future Value Factors Continued on next page FB87413,0000091 -19-24JUL14-2/9 7-4 090117 PN=106  Investment Analysis DISCOUNTING — COMPUTING PRESENT VALUE Discounting is the opposite of compounding. It is a calculation that tells you the present value or worth of a future sum of money (Fig. 4). Also, if you have a desired amount of money in the future, discounting tells you how much you have to invest at the present. DXP01781 —UN—17SEP10 Referring to the problem stated above, suppose you knew the future value of $1,404.54 at the end of 10 years. Then you would have to invest $1,000 today to reach the $1,404.54 assuming a 7% interest rate and the interest compounded annually. Computing present value, called discounting, can be summarized in equation 4: Equation 4: Present Value = Future Value / (1+i)n Fig. 4 — Discounting is the opposite of compounding Substituting values into equation 4 gives equation 5: Equation 5: $1,000 = $1,404.54 / (1 +.07)5 A—Now C—2 Years B—1 Year The discounting table (Table 2) gives the factors for discounting $1.00 at different interest rates for various time periods. For example, what is the present value of $100 to be received in 5 years at 7%? The factor at the intersection of 7% and 5 years is 0.7130. Multiplying the $100 by 0.7130 gives $71.30. In other words, the $100 you are to receive in 5 years is worth $71.30 today. To illustrate the relationship between compounding and discounting, consider the future value of $648.43 to be received in ten years at 10% interest. The factor (at the intersection of 10 years and 10%) is 0.3855. When you multiply 0.3855 by $648.43, the result is $249.47. The sum does not exactly equal the original $250 (see compounding example) due to a rounding in the factors from the financial tables. Continued on next page FB87413,0000091 -19-24JUL14-3/9 7-5 090117 PN=107  Investment Analysis Table 2 — Present Value Factors Year 4% 5% 6% 7% 8% 9% 10% 11% 1 0.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 0.9009 2 0.9246 0.9070 0.8900 0.8734 0.8573 0.8417 0.8264 0.8116 3 0.8890 0.8638 0.8396 0.8163 0.7938 0.7722 0.7513 0.7312 4 0.8548 0.8227 0.7921 0.7629 0.7350 0.7084 0.6830 0.6587 5 0.8219 0.7835 0.7473 0.7130 0.6806 0.6499 0.6209 0.5935 6 0.7903 0.7462 0.7050 0.6663 0.6302 0.5963 0.5645 0.5346 7 0.7599 0.7107 0.6651 0.6227 0.5835 0.5470 0.5132 0.4817 8 0.7307 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665 0.4339 9 0.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241 0.3909 10 0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 0.3522 11 0.6496 0.5847 0.5268 0.4751 0.4289 0.3875 0.3505 0.3173 12 0.6246 0.5568 0.4970 0.4440 0.3971 0.3555 0.3186 0.2858 13 0.6006 0.5303 0.4688 0.4150 0.3677 0.3262 0.2897 0.2575 14 0.5775 0.5051 0.4423 0.3878 0.3405 0.2992 0.2633 0.2320 15 0.5553 0.4810 0.4173 0.3624 0.3152 0.2745 0.2394 0.2090 16 0.5339 0.4581 0.3936 0.3387 0.2919 0.2519 0.2176 0.1883 17 0.5134 0.4363 0.3714 0.3166 0.2703 0.2311 0.1978 0.1696 18 0.4936 0.4155 0.3503 0.2959 0.2502 0.2120 0.1799 0.1528 19 0.4746 0.3957 0.3305 0.2765 0.2317 0.1945 0.1635 0.1377 20 0.4564 0.3769 0.3118 0.2584 0.2145 0.1784 0.1486 0.1240 21 0.4388 0.3589 0.2942 0.2415 0.1987 0.1637 0.1351 0.1117 22 0.4220 0.3418 0.2775 0.2257 0.1839 0.1502 0.1228 0.1007 23 0.4057 0.3256 0.2618 0.2109 0.1703 0.1378 0.1117 0.0907 24 0.3901 0.3101 0.2470 0.1971 0.1577 0.1264 0.1015 0.0817 25 0.3751 0.2953 0.2330 0.1842 0.1460 0.1160 0.0923 0.0736 26 0.3607 0.2812 0.2198 0.1722 0.1352 0.1064 0.0839 0.0663 27 0.3468 0.2678 0.2074 0.1609 0.1252 0.0976 0.0763 0.0597 28 0.3335 0.2551 0.1956 0.1504 0.1159 0.0895 0.0693 0.0538 29 0.3207 0.2429 0.1846 0.1406 0.1073 0.0822 0.0630 0.0485 30 0.3083 0.2314 0.1741 0.1314 0.0994 0.0754 0.0573 0.0437 31 0.2965 0.2204 0.1643 0.1228 0.0920 0.0691 0.0521 0.0394 32 0.2851 0.2099 0.1550 0.1147 0.0852 0.0634 0.0474 0.0355 33 0.2741 0.1999 0.1462 0.1072 0.0789 0.0582 0.0431 0.0319 34 0.2636 0.1904 0.1379 0.1002 0.0730 0.0534 0.0391 0.0288 35 0.2534 0.1813 0.1301 0.0937 0.0676 0.0490 0.0356 0.0259 36 0.2437 0.1727 0.1227 0.0875 0.0626 0.0449 0.0323 0.0234 37 0.2343 0.1644 0.1158 0.0818 0.0580 0.0412 0.0294 0.0210 38 0.2253 0.1566 0.1092 0.0765 0.0537 0.0378 0.0267 0.0190 39 0.2166 0.1491 0.1031 0.0715 0.0497 0.0347 0.0243 0.0171 40 0.2083 0.1420 0.0972 0.0668 0.0460 0.0318 0.0221 0.0154 Table 2 — Present value factors Continued on next page FB87413,0000091 -19-24JUL14-4/9 7-6 090117 PN=108  Investment Analysis COMPOUNDING ANNUITIES The two examples discussed thus far involve a single sum of money either today (present value) or in the future (future value). Given a time period and an interest rate, a second value can be found by compounding or discounting. In each problem there were no reoccurring values during the specified time period. In contrast to the single sum examples is the concept of an annuity. An annuity is a series of equal payments at equal intervals for a specific period of time. For example, $5,000 per year for ten years would be an annuity. It is important to note that the definition requires an equal sum at the same time each period for a fixed number of periods. There are two different types of annuities based on when the payments are actually made or received. For example, if you were going to save $5,000 per year for the next ten years, then is the first deposit made today or is it made at the end of the first year? Annuities with payments made at the beginning of the time period are called annuities due, whereas annuities with payments made at the end of the time period are referred to as ordinary annuities. An automobile loan with monthly payments for five years, with the first payment due one month from the time of purchase, would be an example of an ordinary annuity. If you started a savings account and planned to deposit $300 per month for five years, and you made the first deposit today, would be an example of an annuity due. Table 3, provides the financial factors of calculating the future value of an ordinary annuity, simply find the interest rate at the top of the table, then the number of time periods from column one. The intersection of the interest rate and time periods gives the factor you will multiply times the amount of the periodic payment. For example, what is the future value of $5,000 per year for 10 years at a 6% interest rate? Table 3 shows a factor of 13.1808 at the intersection of 6% and 10 years. Multiplying $5,000 by 13.1808 equals $65,904. Thus, if you deposited $5,000 per year into an interest bearing account, starting at the end of year one, for 10 years you would have $65,904 at the end of the ten years. Continued on next page FB87413,0000091 -19-24JUL14-5/9 7-7 090117 PN=109  Investment Analysis Table 3 — Future Value Factors for an Ordinary Annuity Year 4% 5% 6% 7% 8% 9% 10% 11% 1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 2 2.0400 2.0500 2.0600 2.0700 2.0800 2.0900 2.1000 2.1100 3 3.1216 3.1525 3.1836 3.2149 3.2464 3.2781 3.3100 3.3421 4 4.2465 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410 4.7097 5 5.4163 5.5256 5.6371 5.7507 5.8666 5.9847 6.1051 6.2278 6 6.6330 6.8019 6.9753 7.1533 7.3359 7.5233 7.7156 7.9129 7 7.8983 8.1420 8.3938 8.6540 8.9228 9.2004 9.4872 9.7833 8 9.2142 9.5491 9.8975 10.2598 10.6366 11.0285 11.4359 11.8594 9 10.5828 11.0266 11.4913 11.9780 12.4876 13.0210 13.5795 14.1640 10 12.0061 12.5779 13.1808 13.8164 14.4866 15.1929 15.9374 16.7220 11 13.4864 14.2068 14.9716 15.7836 16.6455 17.5603 18.5312 19.5614 12 15.0258 15.9171 16.8699 17.8885 18.9771 20.1407 21.3843 22.7132 13 16.6268 17.7130 18.8821 20.1406 21.4953 22.9534 24.5227 26.2116 14 18.2919 19.5986 21.0151 22.5505 24.2149 26.0192 27.9750 30.0949 15 20.0236 21.5786 23.2760 25.1290 27.1521 29.3609 31.7725 34.4054 16 21.8245 23.6575 25.6725 27.8881 30.3243 33.0034 35.9497 39.1899 17 23.6975 25.8404 28.2129 30.8402 33.7502 36.9737 40.5447 44.5008 18 25.6454 28.1324 30.9057 33.9990 37.4502 41.3013 45.5992 50.3959 19 27.6712 30.5390 33.7600 37.3790 41.4463 46.0185 51.1591 56.9395 20 29.7781 33.0660 36.7856 40.9955 45.7620 51.1601 57.2750 64.2028 21 31.9692 35.7193 39.9927 44.8652 50.4229 56.7645 64.0025 72.2651 22 34.2480 38.5052 43.3923 49.0057 55.4568 62.8733 71.4027 81.2143 23 36.6179 41.4305 46.9958 53.4361 60.8933 69.5319 79.5430 91.1479 24 39.0826 44.5020 50.8156 58.1767 66.7648 76.7898 88.4973 102.1742 25 41.6459 47.7271 54.8645 63.2490 73.1059 84.7009 98.3471 114.4133 26 44.3117 51.1135 59.1564 68.6765 79.9544 93.3240 109.1818 127.9988 27 47.0842 54.6691 63.7058 74.4838 87.3508 102.7231 121.0999 143.0786 28 49.9676 58.4026 68.5281 80.6977 95.3388 112.9682 134.2099 159.8173 29 52.9663 62.3227 73.6398 87.3465 103.9659 124.1354 148.6309 178.3972 30 56.0849 66.4388 79.0582 94.4608 113.2832 136.3075 164.4940 199.0209 31 59.3283 70.7608 84.8017 102.0730 123.3459 149.5752 181.9434 221.9132 32 62.7015 75.2988 90.8898 110.2182 134.2135 164.0370 201.1378 247.3236 33 66.2095 80.0638 97.3432 118.9334 145.9506 179.8003 222.2515 275.5292 34 69.8579 85.0670 104.1838 128.2588 158.6267 196.9823 245.4767 306.8374 35 73.6522 90.3203 111.4348 138.2369 172.3168 215.7108 271.0244 341.5896 36 77.5983 95.8363 119.1209 148.9135 187.1021 236.1247 299.1268 380.1644 37 81.7022 101.6281 127.2681 160.3374 203.0703 258.3759 330.0395 422.9825 38 85.9703 107.7095 135.9042 172.5610 220.3159 282.6298 364.0434 470.5106 39 90.4091 114.0950 145.0585 185.6403 238.9412 309.0665 401.4478 523.2667 40 95.0255 120.7998 154.7620 199.6351 259.0565 337.8824 442.5926 581.8261 Table 3 — Future Value Factors for an Ordinary Annuity A relevant example of compounding annuities is retirement funds. If you were 20 years old and started DISCOUNTING ANNUITIESDiscounting or finding a retirement account planning on depositing $2,000 per present value of annuities is the inverse of future value. year into the accounts, what would you have at age 60 (40 Using the tables to calculate present value is relatively years later)? At 4% interest (factor is 95.0255), you would simple; however, the interpretation is a little more complex. have $2,000 times 95.0255 or $190,051. However, at 8% Table 4, provides the factors necessary to calculate the interest (factor is 259.0565), you would have $2,000 times present value of an ordinary annuity. 259.0565 or $518,113. NOTE: The interest rate doubled, but the future value more than doubled. Continued on next page FB87413,0000091 -19-24JUL14-6/9 7-8 090117 PN=110  Investment Analysis Table 4 — Present Value Factors for an Ordinary Annuity Year 4% 5% 6% 7% 8% 9% 10% 11% 1 0.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 0.9009 2 1.8861 1.8594 1.8334 1.8080 1.7833 1.7591 1.7355 1.7125 3 2.7751 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 2.4437 4 3.6299 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 3.1024 5 4.4518 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 3.6959 6 5.2421 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 4.2305 7 6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.7122 8 6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 5.1461 9 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.7590 5.5370 10 8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.8892 11 8.7605 8.3064 7.8869 7.4987 7.1390 6.8052 6.4951 6.2065 12 9.3851 8.8633 8.3838 7.9427 7.5361 7.1607 6.8137 6.4924 13 9.9856 9.3936 8.8527 8.3577 7.9038 7.4869 7.1034 6.7499 14 10.5631 9.8986 9.2950 8.7455 8.2442 7.7862 7.3667 6.9819 15 11.1184 10.3797 9.7122 9.1079 8.5595 8.0607 7.6061 7.1909 16 11.6523 10.8378 10.1059 9.4466 8.8514 8.3126 7.8237 7.3792 17 12.1657 11.2741 10.4773 9.7632 9.1216 8.5436 8.0216 7.5488 18 12.6593 11.6896 10.8276 10.0591 9.3719 8.7556 8.2014 7.7016 19 13.1339 12.0853 11.1581 10.3356 9.6036 8.9501 8.3649 7.8393 20 13.5903 12.4622 11.4699 10.5940 9.8181 9.1285 8.5136 7.9633 21 14.0292 12.8212 11.7641 10.8355 10.0168 9.2922 8.6487 8.0751 22 14.4511 13.1630 12.0416 11.0612 10.2007 9.4424 8.7715 8.1757 23 14.8568 13.4886 12.3034 11.2722 10.3711 9.5802 8.8832 8.2664 24 15.2470 13.7986 12.5504 11.4693 10.5288 9.7066 8.9847 8.3481 25 15.6221 14.0939 12.7834 11.6536 10.6748 9.8226 9.0770 8.4217 26 15.9828 14.3752 13.0032 11.8258 10.8100 9.9290 9.1609 8.4881 27 16.3296 14.6430 13.2105 11.9867 10.9352 10.0266 9.2372 8.5478 28 16.6631 14.8981 13.4062 12.1371 11.0511 10.1161 9.3066 8.6016 29 16.9837 15.1411 13.5907 12.2777 11.1584 10.1983 9.3696 8.6501 30 17.2920 15.3725 13.7648 12.4090 11.2578 10.2737 9.4269 8.6938 31 17.5885 15.5928 13.9291 12.5318 11.3498 10.3428 9.4790 8.7331 32 17.8736 15.8027 14.0840 12.6466 11.4350 10.4062 9.5264 8.7686 33 18.1476 16.0025 14.2302 12.7538 11.5139 10.4644 9.5694 8.8005 34 18.4112 16.1929 14.3681 12.8540 11.5869 10.5178 9.6086 8.8293 35 18.6646 16.3742 14.4982 12.9477 11.6546 10.5668 9.6442 8.8552 36 18.9083 16.5469 14.6210 13.0352 11.7172 10.6118 9.6765 8.8786 37 19.1426 16.7113 14.7368 13.1170 11.7752 10.6530 9.7059 8.8996 38 19.3679 16.8679 14.8460 13.1935 11.8289 10.6908 9.7327 8.9186 39 19.5845 17.0170 14.9491 13.2649 11.8786 10.7255 9.7570 8.9357 40 19.7928 17.1591 15.0463 13.3317 11.9246 10.7574 9.7791 8.9511 Table 4 — Present value factors for an ordinary annuity For example, what is the present value of $2,000 per year this is a very powerful concept and can be the basis for for 15 years at an interest rate of 7%? At the intersections evaluating loans and/or business investments. of 7% and 15 years is the factor of 9.1079. Multiplying $2,000 by 9.1079 results in a present value of $18,215.80. One further example, at age 60 you would like to have But, what does this really mean? If you deposited sufficient funds to withdraw $2,500 per year for 20 years $18,215.80 into an interest bearing account today, and if or until age 80. If the money could earn 4% interest the account paid 7% compounded annually, you could compounded annually, how much would you need at withdraw $2,000 per year (starting at the end of the first age 60? From Table 4, the intersection of 4% and 20 year) for 15 years. When you withdrew the last $2,000 (15 years gives the factor 13.5903. Multiplying 13.5903 times years later), the account balance would be zero. Actually, $2,500 gives $33,975.75, thus the amount you would need to have on hand at age 60 in order to be able to withdraw $2500 per year for 20 years at 4%. Continued on next page FB87413,0000091 -19-24JUL14-7/9 7-9 090117 PN=111  Investment Analysis AMORTIZATION This does not apply to all loan structures, but is generally considered the most popular. For any amortized loan, the Amortization is a particular application of time value of original loan amount (amount borrowed) is the present money applied to loans. Most loans today are based on value of the stream of payments based on the amount of the concept of the present value of an ordinary annuity. the payment, the interest rate, and the time period. Continued on next page FB87413,0000091 -19-24JUL14-8/9 7-10 090117 PN=112  Investment Analysis DXP01782 —UN—17SEP10 Fig. 5 — Future Value at Compound Interest Here is how it works. Fig. 5 is an amortization table the table can be multiplied by any loan amount to give showing different interest rates and time periods, just as the period payments that will be due on that loan at the the previous time value of money tables. The factors in interest rate specified. FB87413,0000091 -19-24JUL14-9/9 7-11 090117 PN=113  Investment Analysis balance after the second payment of $18,870. Continuing For example, what would be the annual payments if you this process for the five-year loan period will completely borrowed $30,000 for five years at 5%? In Fig. 5, the amortize the loan and result in a loan balance of zero intersection of 5 years and 5% interest gives a factor after five years. of.2309 (actual factor is.230975). Multiplying.230975 1 times $30,000 gives an annual payment of $6,929. Thus, Table 5 — An Illustration of an Amortized Loan the annual payments of $6,929 would pay off a loan of Loan $30,000 over five years at 5%. Year Principal Interest P + I Balance The annual payments of $6,929 include the repayment 1 $5,429 $1,500 $6,929 $24,571 of the $30,000 and interest, which is the rent charged 2 $5,701 $1,229 $6,929 $18,870 each year on the portion of the loan that has not been 3 $5,986 $944 $6,929 $12,884 repaid. Over five-years, the entire $30,000 will be repaid 4 $6,285 $644 $6,929 $6,599 plus an amount of interest. Table 5 shows the breakdown of principal, interest, and loan balance over the entire 5 $6,599 $330 $6,929 $0 five-year period. If the $30,000 was borrowed today, Totals $30,000 $4,646 $34,646 then starting one year from today there would be five 1 The loan is based on a principal borrowed of $30,000 for five years at equal payments due of $6,929 (P + I). Since interest is 5% with annual payments. charged on the outstanding loan balance, the interest in Table 5 — An illustration of an amortized loan year one would be 5% multiplied by $30,000 or $1,500. The principal is found by subtracting $1,500 from the The final row in Table 5 shows the totals for principal, annual payment of $6,929 which gives $5,429. After interest, and total payments (P + I). For this loan, the total the first payment, the loan balance is calculated by principal is $30,000, which is the amount borrowed. The subtracting the first principal payment from the $30,000 total interest paid over five years is $4,646 and the total which gives $24,571. In year two, the interest is 5% of amount repaid is $34,646. It is important to note that using $24,571 or $1,229. Subtracting $1,229 from the annual the four-digit factors from the table will give small rounding payment ($6,929) gives a second year principal of $5,701. errors when compared to an electronic spreadsheet or Subtracting the $5,701 principal in year two from the year financial calculator which utilizes more significant digits. one outstanding balance ($24,571) gives an outstanding FB87413,0000091 -19-24JUL14-10/9 7-12 PN=114 090117  Investment Analysis A PARTIAL INVESTMENT ANALYSIS Now let us see how this knowledge can be put to work. First, let's look at a partial analysis of a real investment situation. William Larson must make a decision. His grandmother gives him $1,000. She suggests he place the $1,000 in a savings account at the local bank and let the interest accrue. William is now a freshman in high school and plans to use the money for college tuition. The DXP01780 —UN—17SEP10 money has four years to earn interest. How much money does William have at the end of four years if he gets 9% on a $1000 savings account? To answer, look up the compound rate (1.4115) in the compounding table (see Table 1 — Future Value Factors). It is at the intersection of 4 years and 9%. William will have $1,410 in four years with his $1,000. However, William has hog facilities he is using for an FFA Fig. 6 — William must analyze his possible returns project. With $1,000, he can purchase four hybrid gilts. William has a choice to make (Fig. 6). His enterprise A—Savings Account $1,000.00 budget shows that he would expect to earn $200 each year above all costs with the hogs. This is a very conservative estimate using low market prices and high feed costs. In Table 6 — Williams Investment Analysis for the Hog Alternative addition, at the end of four years, he can sell the sows for End of about $150 each ($600). What is best for William? Year Earnings Factor Future Value 1 $200 1.2950 $259 He must take the $200 annual earnings and compound it to see how much he will have when he goes to college. 2 $200 1.1881 $238 This is William's investment analysis: 3 $200 1.0900 $218 4 $200 1.0000 $200 Total $915 Add Market Value of Sows $600 Total Future Value $1,515 Table 6 — Williams investment analysis for the hog alternative Continued on next page MM61211,00000AF -19-24FEB11-1/2 7-13 090117 PN=115  Investment Analysis William's money, if he puts it in the bank immediately when Grandma gives him the gift, will amount to $1,410 when he goes to college. If William invests in the four sows he will have $188 more dollars ($1,515 – $1410 = $105) at the end of four years if his enterprise goes as planned. The projected $200 profit in year one is compounded DXP01779 —UN—17SEP10 three years since it will be received at the end of the first year, the $200 profit in year two is compounded two years, the $200 profit in year three is compounded for one year, and the $200 in year four is not compounded since it will be realized at the end of the fourth year. The $600 he budgets for the value of the sows is also at the end of the fourth year, thus is not compounded. It is important for William to remember that while the hog alternative Fig. 7— Compare your opportunity cost with your investment projects higher earnings, there is some risk in the hog operation that does not exist in the savings account. B—Borrowed Funds Cost 12% C—Used Savings Cost 10% There are a few more aspects to consider in a partial in Interest per Year Interest LOST per Year investment analysis, as you will see. The compounding rate William uses makes a difference in investment must return enough to repay the loan just to the money he earns. The compounding rate chosen is a break even. If the loan interest rate is 12%, then use a matter of judgment, not a fixed fact. How do you choose 12% or more discount rate in your investment analysis. it? The rate must be your opportunity cost of capital. It is You must earn 12% profit with your investment just to the rate of return you could earn with your best alternative break even. use of the money. If you must borrow the money, the MM61211,00000AF -19-24FEB11-2/2 7-14 090117 PN=116  Investment Analysis FULL INVESTMENT ANALYSIS Now that we have looked at the terms and concepts of investment analysis, we are ready to do a full investment analysis. A full investment analysis will include three techniques: Payback period DXP01789 —UN—17SEP10 Net present value Internal rate of return To illustrate these methods, consider the following scenario. The Don Smith Cattle Company (Fig. 8) makes money by carrying steers through the winter on winter pasture and by selling to feed lots in the spring. Don Smith wants to invest his profits. He narrows his choice to two Fig. 8 — The Don Smith cattle company carries steers through the winter. alternative investments, investment A and investment B. Both investments cost $5,000 with a projected economic life of five years. For ease of calculations, the salvage of recovering the initial investment. Year four shows a value is assumed to be included in year five. Here is what cash inflow of $1,200; however, only $600 is needed to they look like on paper (Table 7). get to $5,000, thus only half of the fourth year cash inflows is needed. Thus, the payback period for Investment B Table 7 — A Comparison of Two Investment Alternatives is 3.5 years. for the Don Smith Cattle Company Year Alternative A Alternative B The payback period technique is simple and widely used. 0 ($5,000) ($5,000) The payback period method is easy to understand and can 1 2300 1900 often be used as a first-glance feasibility analysis. If the payback period is considered too long, then subsequent 2 1400 1400 analyses may not be needed or considered. It has three 3 1300 1100 disadvantages (Table 8): 4 1100 1200 5 800 1500 Benefits of an investment that occur after the cut-off period are ignored. The cash inflows after year 3 for Table 7 — A comparison of two investment investment A and 3.5 years in investment B are not part Year zero is interpreted as the present and shows a of the calculations. negative $5,000 for each investment, which represents The payback period technique doesn't consider the the original investment. The values are negative since time value of money. A dollar received during the first they represent cash outflows. Years 1-5 show the year is given the same weight as a dollar received in net projected cash inflows per year for each of the the later years. investments. Investment A shows net cash inflows of The payback period method does not consider the $2,300 in year one, $1,400 in year two, and so forth. The alternative uses for money. same interpretation applies to investment B. Table 8 — Don Smith Compares Investments Side-by-Side A B PAYBACK PERIOD ANALYSIS (PP) Year *Cash Flow *Cash Flow The payback period analysis technique estimates the 1 500 100 time required for the cash inflows from the investment to 2 400 200 return the initial investment outlay. This method does not 3 **300 300 include any time value of money; rather it is a very simple 4 200 **400 technique that calculates how long it takes an investment 5 100 500 to recover the initial outlay of funds. 6 600 For investment A, $2,300 (year one) plus $1,400 (year *Cash flow is gross income minus variable costs. two) plus $1,300 (year 3) equals $5,000, which is equal to **Indicates year in which initial investment outlay is repaid. the original investment. Therefore, it requires exactly three Table 8 — Don Smith Compares Investments Side-by-Side years for investment A to return the original investment. The payback period for Investment A is 3 years. NET PRESENT VALUE (NPV) Investment B gives a slightly different result. The $1,900 Don needs an investment analysis technique which (year one) plus $1,400 (year two) plus $1,100 (year three) includes all income, discounts for the timing of income, gives a total of $4,400, which is less than the original and allows for alternative uses for the money. investment. The sum of the first three years is $600 short Continued on next page MM61211,00000B0 -19-25FEB11-1/3 7-15 090117 PN=117  Investment Analysis The net present value (NPV) method weighs the present investment A; however, at 15%, investment A had the value of cash inflows (benefits) against the present value of highest net present value. Table 10 summarizes the net cash outflow (costs). The NPV method sums the present present value of both investments at discount rates from value of all future cash inflows and subtracts the sum of 3% to 17%. From 3% to 9%, investment B has the higher the present value of all cash outflows. In Don's case, the net present values, and from 10% and higher, investment only cash outflow is the original cost of the investments, A has the higher net present values. Don realizes that an which is already in present day dollars. Don organizes investment analysis using the net present value method and compares his analysis for investments A and B (Table does not give the same results at all discount rates. 9). To further understand how the discount rate affects his Table 10 — Net Present Value for Investments A & B investment decisions, he performs the calculations at 8% at Different Discount Rate and 15%. He finds the appropriate discount factors in the Rate Invest A Invest B discounting table (Table 9). He discounts the projected 3% $1,410 $1,531 cash inflows for each year separately and adds the results 4% $1,259 $1,358 to arrive at the total present value of the income. Then Don subtracts the original costs of the investments to find 5% $1,115 $1,192 the net present value. A NPV greater than zero indicates 6% $976 $1,033 the investment is actually earning a rate higher than the 7% $843 $881 one chosen for the analysis. 8% $715 $736 Table 9 — A Net Present Value Analysis for Investments 9% $591 $596 A and B at Different Discount Rates 10% $473 $462 Discount Factor and Discount Factor and Computed Computed Present Values 11% $358 $333 Present Values at 8% at 15% 12% $248 $209 Fac- 13% $142 $90 Year tor A B Factor A B 14% $39 ($24) ($5,0 0 ($5,000) ($5,000) 00) ($5,000) 15% ($60) ($134) 0.925 $2,00 16% ($156) ($240) 1 9 $2,130 $1,759 0.8695 0 $1,652 17% ($248) ($342) 0.857 $1,05 Table 10 — Net present value for 2 3 $1,200 $1,200 0.7561 9 $1,059 0.793 INTERNAL RATE OF RETURN (IRR) 3 8 $1,032 $873 0.6575 $855 $723 The internal rate of return (IRR) is a rate that equates 4 0.735 $809 $882 0.5717 $629 $686 the present value of the projected cash inflows to the 0.680 present value of the cash outflow. Thus, the internal rate 5 5 $544 $1,021 0.4971 $398 $746 of return will yield a zero result if used in a net present Totals $715 $735 ($60) ($134) value analysis. What this technique does is to determine Table 9 — A Net Present Value Analysis for Investments the discount rate for you from the cash flow projected for an investment. In Table 9, the discount factors and computed present values are shown for discount rates of 8% and 15%. SUMMARY For the 8% rate, the present value factor for year one is 0.9259 which is multiplied by $2,300 to arrive at a present The Don Smith Cattle Company has used the payback value of $2,130. Present values are computed for each period technique. Don found it helpful, but since the of the five years and summed. The original investment of payback period was short enough to encourage the $5,000 is subtracted from the sum of the present values investments, Don needs the more complete analyses of cash inflows to give a net present value of $715. The produced by net present value and internal rate of return. same process for investment B gives a net present value of $735. Using net present value as a decision criterion, The net present value technique compares discounted Don would choose Investment B since it gives a higher cash inflows to the original cost of the investment. The net present value. Both investments are earning more analysis is performed at a specified rate, and then the than 8% since the net present values are positive. investments can be compared with the highest net present value being the decision criteria. The same analysis at a discount rate of 15% results in net present values of -$60 and -$134 for investments A and The internal rate of return technique is useful because it B, respectively. In this case, Investment A has the highest calculates the exact discount rate or rate of return from net present value; however, neither investment is actually an investment. This is a time-consuming task without a earning 15% since the net present values are negative. computer. Don realizes that neither investment has higher net present values, at all discount rates, than the other investment. At 8%, investment B had a higher net present value than Continued on next page MM61211,00000B0 -19-25FEB11-2/3 7-16 090117 PN=118  Investment Analysis Since the cash inflows are projected into the future, there should be some inclusion of inflation rates for both input FINAL NOTE and output prices which would affect the net inflows. Likewise, since the projected cash inflows are future The examples in this chapter are presented as an amounts, the decision must consider risk associated with introduction to the methods and techniques for evaluating the accuracy of the projections. Some of these factors can investments. A more thorough analysis would require be addressed by conducting sensitivity analysis, which consideration of income taxes, inflation, and risk. The is evaluating net present values at different discount or projected investment and the projected cash inflows interest rates. When analyzing alternative investments, it would need to be adjusted for income tax considerations. is always a good idea to consult a financial advisor. For example, if the original investment is depreciable and funded with borrowed money, then there would be tax implications. Furthermore, the projected cash inflows, if profits, would be subject to income tax. MM61211,00000B0 -19-25FEB11-3/3 7-17 090117 PN=119