Waterways puts much emphasis on cash flow when it plans for capital investments. The company chose its discount rate of 8% based on the rate
Waterways puts much emphasis on cash flow when it plans for capital investments. The company chose its discount rate of 8% based on the rate of return it must pay its owners and creditors. Using that rate, Waterways then uses different methods to determine the best decisions for making capital outlays. This year Waterways is considering buying five new backhoes to replace the backhoes it now has. The new backhoes are faster, cost less to run, provide for more accurate trench digging, have comfort features for the operators, and have 1-year maintenance agreements to go with them. The old backhoes are working just fine, but they do require considerable maintenance. The backhoe operators are very familiar with the old backhoes and would need to learn some new skills to use the new backhoes. The following information is available to use in deciding whether to purchase the new backhoes.
| | | Old Backhoes | | New Backhoes |
| Purchase cost when new | | $89,700 | | $201,044 |
| Salvage value now | | $42,900 | | |
| Investment in major overhaul needed in next year | | $54,000 | | |
| Salvage value in 8 years | | $15,100 | | $89,000 |
| Remaining life | | 8 years | | 8 years |
| Net cash flow generated each year | | $30,000 | | $44,800 |
Click here to view PV table. (a) Evaluate in the following ways whether to purchase the new equipment or overhaul the old equipment. (Hint: For the old machine, the initial investment is the cost of the overhaul. For the new machine, subtract the salvage value of the old machine to determine the initial cost of the investment.) (1) Using the net present value method for buying new or keeping the old. (For calculation purposes, use 5 decimal places as displayed in the factor table provided. If the net present value is negative, use either a negative sign preceding the number eg -45 or parentheses eg (45). Round final answer to 0 decimal places, e.g. 5,275.)
| | | New Backhoes | | Old Backhoes |
| Net Present Value | | $ | | $ |
| Waterways should buy New Backhoesretain Old Backhoes equipment. |
(2) Using the payback method for each choice. (Hint: For the old machine, evaluate the payback of an overhaul.) (Round answers to 2 decimal places, e.g. 1.25)
| | | New Backhoes | | Old Backhoes |
| Payback Period | | years | | years |
| Waterways should buy New Backhoesretain Old Backhoes equipment. |
(3) Comparing the profitability index for each choice. (Round answers to 2 decimal places, e.g. 1.25)
| | | New Backhoes | | Old Backhoes |
| Profitability Index | | | | |
| Waterways should buy New Backhoesretain Old Backhoes equipment. |
Calculate the internal rate of return factor for the new and old blackhoes. (Round answers to 5 decimal places, e.g. 5.27647.)
| | | New Backhoes | | Old Backhoes |
| IRR Factor | | | | |
(4) Comparing the internal rate of return for each choice to the required 8% discount rate.
| Waterways should buy New Backhoesretain Old Backhoes equipment. |
$
ILLUSTRATION G.4 Time diagram Another method used to compute the future value of a single amount involves a compound interest table. This table shows the future value of 1 for n periods. Table 1 is such a table. (n) Periods 4% 5% 6% 7% 8% 9% 10% 11% 12% 15% 0 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1 1.04000 1.05000 1.06000 1.07000 1.08000 1.09000 1.10000 1.11000 1.12000 1.15000 2 1.08160 1.10250 1.12360 1.14490 1.16640 1.18810 1.21000 1.23210 1.25440 1.32250 3 1.12486 1.15763 1.19102 1.22504 1.25971 1.29503 1.33100 1.36763 1.40493 1.52088 4 1.16986 1.21551 1.26248 1.31080 1.36049 1.41158 1.46410 1.51807 1.57352 1.74901 5 1.21665 1.27628 1.33823 1.40255 1.46933 1.53862 1.61051 1.68506 1.76234 2.01136 6 1.26532 1.34010 1.41852 1.50073 1.58687 1.67710 1.77156 1.87041 1.97382 2.31306 7 1.31593 1.40710 1.50363 1.60578 1.71382 1.82804 1.94872 2.07616 2.21068 2.66002 8 1.36857 1.47746 1.59385 1.71819 1.85093 1.99256 2.14359 2.30454 2.47596 3.05902 9 1.42331 1.55133 1.68948 1.83846 1.99900 2.17189 2.35795 2.55803 2.77308 3.51788 10 1.48024 1.62889 1.79085 1.96715 2.15892 2.36736 2.59374 2.83942 3.10585 4.04556 11 1.53945 1.71034 1.89830 2.10485 2.33164 2.58043 2.85312 3.15176 3.47855 4.65239 12 1.60103 1.79586 2.01220 2.25219 2.51817 2.81267 3.13843 3.49845 3.89598 5.35025 13 1.66507 1.88565 2.13293 2.40985 2.71962 3.06581 3.45227 3.88328 4.36349 6.15279 14 1.73168 1.97993 2.26090 2.57853 2.93719 3.34173 3.79750 4.31044 4.88711 7.07571 15 1.80094 2.07893 2.39656 2.75903 3.17217 3.64248 4.17725 4.78459 5.47357 8.13706 16 1.87298 2.18287 2.54035 2.95216 3.42594 3.97031 4.59497 5.31089 6.13039 9.35762 17 1.94790 2.29202 2.69277 3.15882 3.70002 4.32763 5.05447 5.89509 6.86604 10.76126 18 2.02582 2.40662 2.85434 3.37993 3.99602 4.71712 5.55992 6.54355 7.68997 12.37545 19 2.10685 2.52695 3.02560 3.61653 4.31570 5.14166 6.11591 7.26334 8.61276 14.23177 20 219112265330 3 20714 3 86968 4 66096 5 60441 672750 8 06231 9.64629 16 36654 ILLUSTRATION G.7 Future value of periodic payment computation The first $2,000 investment is multiplied by the future value factor for two periods (1.1025) because two years' interest will accumulate on it (in years 2 and 3). The second $2,000 investment will earn only one year's interest in year 3) and therefore is multiplied by the future value factor for one year (1.0500). The final $2,000 investment is made at the end of the third year and will not earn any interest. Thus, n= 0 and the future value factor is 1.00000. Consequently, the future value of the last $2,000 invested is only $2,000 since it does not accumulate any interest. Calculating the future value of each individual cash flow is required when the periodic payments or receipts are not equal in each period. However, when the periodic payments (receipts) are the same in each period, the future value can be computed by using a future value of an annuity of 1 table. Table 2 is such a table. (n) Payments 4% 5% 6% 7% 8% 9% 10% 11% 12% 15% 1 1.00000 1.00000 1.00000 1.0000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 2 2.04000 2.05000 2.06000 2.0700 2.08000 2.09000 2.10000 2.11000 2.12000 2.15000 3 3.12160 3.15250 3.18360 3.2149 3.24640 3.27810 3.31000 3.34210 3.37440 3.47250 4 4.24646 4.31013 4.37462 4.4399 4.50611 4.57313 4.64100 4.70973 4.77933 4.99338 5 5.41632 5.52563 5.63709 5.7507 5.86660 5.98471 6.10510 6.22780 6.35285 6.74238 6 6.63298 6.80191 6.97532 7.1533 7.33592 7.52334 7.71561 7.91286 8.11519 8.75374 7 7.89829 8.14201 8.39384 8.6540 8.92280 9.20044 9.48717 9.78327 10.08901 11.06680 8 9.21423 9.54911 9.89747 10.2598 10.63663 11.02847 11.43589 11.85943 12.29969 13.72682 9 10.58280 11.02656 11.49132 11.9780 12.48756 13.02104 13.57948 14.16397 14.77566 16.78584 10 12.00611 12.57789 13.18079 13.8164 14.48656 15.19293 15.93743 16.72201 17.54874 20.30372 11 13.48635 14.20679 14.97164 15.7836 16.64549 17.56029 18.53117 19.56143 20.65458 24.34928 12 15.02581 15.91713 16.86994 17.8885 18.97713 20.14072 21.38428 22.71319 24.13313 29.00167 13 16.62684 17.71298 18.88214 20.1406 21.49530 22.95339 24.52271 26.21164 28.02911 34.35192 14 18.29191 19.59863 21.01507 22.5505 24.21492 26.01919 27.97498 30.09492 32.39260 40.50471 15 20.02359 21.57856 23.27597 25.1290 27.15211 29.36092 31.77248 34.40536 37.27972 47.58041 16 21.82453 23.65749 25.67253 27.8881 30.32428 33.00340 35.94973 39.18995 42.75328 55.71747 17 23.69751 25.84037 28.21288 30.8402 33.75023 36.97351 40.54470 44.50084 48.88367 65.07509 18 25.64541 28.13238 30.90565 33.9990 37.45024 41.30134 45.59917 50.39593 55.74972 75.83636 19 27.67123 30.53900 33.75999 37.3790 41.44626 46.01846 51.15909 56.93949 63.43968 88.21181 20 29.77808 33.06595 36.78559 40.9955 45.76196 51.16012 57.27500 64.20283 72.05244 102.44358 ILLUSTRATION G.11 Finding present value if discounted for two periods The present value of 1 may also be determined through tables that show the present value of 1 for n periods. In Table 3, n is the number of discounting periods involved. The percentages are the periodic interest rates or discount rates, and the 5-digit decimal numbers in the respective columns are the present value of 1 factors. When using Table 3, the future value is multiplied by the present value factor specified at the intersection of the number of periods and the discount rate. (n) Periods 4% 5% 6% 7% 8% 9% 10% 11% 12% 15% 1 .96154.95238.94340 .93458 .92593 .91743 .90909.90090 .89286 .86957 2 .92456 .90703 .89000 .87344 .85734 .84168 .82645 .81162.79719.75614 3 .88900 .86384 .83962 .81630 .79383 .77218.75132.73119 .71178 .65752 4 .85480 .82270 .79209.76290 .73503.70843 .68301 .65873 .63552 .57175 5 .82193 .78353 .74726.71299 .68058 .64993 .62092.59345 .56743 .49718 6 .79031 .74622.70496 .66634.63017 .59627 .56447 .53464 .50663 .43233 7 .75992 .71068.66506.62275 .58349.54703 .51316.48166 45235 .37594 8 .73069 .67684 .62741 .58201 .54027 .50187 46651 .43393 40388 .32690 9 .70259 .64461 .59190 .54393 .50025 .46043 .42410 .39092.36061 .28426 10 .67556 .61391 .55839.50835 .46319.42241 .38554 .35218 .32197 .24719 11 .64958 .58468 .52679 47509.42888 .38753 .35049 .31728 .28748 .21494 12 .62460 .55684 49697 44401 .39711.35554 .31863 .28584 .25668 18691 13 .60057 .53032.46884 .41496 .36770.32618 .28966 .25751 .22917 .16253 14 .57748 .50507 44230 .38782.34046.29925 .26333 .23199 .20462 14133 15 .55526.48102 .41727 .36245 .31524 .27454 .23939 .20900 18270 12289 16 .53391 .45811 .39365.33873.29189.25187 .21763 18829.1631210687 17 .51337 43630 .37136.31657 .27027 .23107 19785 16963.14564 .09293 18 49363.41552 .35034 .29586 .25025 .21199 17986.15282 .13004 .08081 19 47464 .39573.33051 .27615.23171.19449.16351 .13768 11611 .07027 20 .45639.37689 .31180 .25842.21455 . 17843.14864 12403 10367 .06110 ILLUSTRATION G.15 Present value of a series of future amounts computation This method of calculation is required when the periodic cash flows are not uniform in each period. However, when the future receipts are the same in each period, an annuity table can be used. As illustrated in Table 4, an annuity table shows the present value of 1 to be received periodically for a given number of payments. It assumes that each payment is made at the end of each period. (n) Payments 4% 5% 6% 7% 8% 9% 10% 11% 12% 15% 1 .96154 .95238 .94340 .93458 .92593.91743.90909.90090.89286 .86957 2 1.88609 1.85941 1.83339 1.80802 1.78326 1.75911 1.73554 1.71252 1.69005 1.62571 3 2.77509 2.72325 2.67301 2.62432 2.57710 2.53130 2.48685 2.44371 2.40183 2.28323 4 3.62990 3.54595 3.46511 3.38721 3.31213 3.23972 3.16986 3.10245 3.03735 2.85498 5 4.45182 4.32948 4.21236 4.10020 3.99271 3.88965 3.79079 3.69590 3.60478 3.35216 6 5.24214 5.07569 4.91732 4.76654 4.62288 4.48592 4.35526 4.23054 4.11141 3.78448 7 6.00205 5.78637 5.58238 5.38929 5.20637 5.03295 4.86842 4.71220 4.56376 4.16042 8 6.73274 6.46321 6.20979 5.97130 5.74664 5.53482 5.33493 5.14612 4.96764 4.48732 9 7.43533 7.10782 6.80169 6.51523 6.24689 5.99525 5.75902 5.53705 5.32825 4.77158 10 8.11090 7.72173 7.36009 7.02358 6.71008 6.41766 6.14457 5.88923 5.65022 5.01877 11 8.76048 8.30641 7.88687 7.49867 7.13896 6.80519 6.49506 6.20652 5.93770 5.23371 12 9.38507 8.86325 8.38384 7.94269 7.53608 7.16073 6.81369 6.49236 6.19437 5.42062 13 9.98565 9.39357 8.85268 8.35765 7.90378 7.48690 7.10336 6.74987 6.42355 5.58315 14 10.56312 9.89864 9.29498 8.74547 8.24424 7.78615 7.36669 6.98187 6.62817 5.72448 15 11.11839 10.37966 9.71225 9.10791 8.55948 8.06069 7.60608 7.19087 6.81086 5.84737 16 11.65230 10.83777 10.10590 9.44665 8.85137 8.31256 7.82371 7.37916 6.97399 5.95424 17 12.16567 11.27407 10.47726 9.76322 9.12164 8.54363 8.02155 7.54879 7.11963 6.04716 18 12.65930 11.68959 10.82760 10.05909 9.37189 8.75563 8.20141 7.70162 7.24967 6.12797 19 13.13394 12.08532 11.15812 10.33560 9.60360 8.95012 8.36492 7.83929 7.36578 6.19823 20 13.59033 12.46221 11.46992 10.59401 9.81815 9.12855 8.51356 7.96333 7.46944 6.25933
