Conference on Fishing Vessel Construction Materials
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328 CONFERENCE ON FISHING VESSEL CONSTRUCTION MATERIALS concentrate our analysis on the life-cycle costs of the Boats of Unequal Capability systems. In this, we must recognize invested costs as well as operating costs, and we also must recognize taxes and the The preceding section deals with cost studies in which time-value of money. Two widely accepted (and practically competing designs promise equal incomes. There will be equivalent) economic criteria are used for this purpose: cases, however, where we must recognize differences in average annual cost, AAC, and present value, PV. If we annual income. We then consider each proposed boat as an assume uniform annual costs of operation, Y, then finding investment and aim our study at finding the one that the average annual cost simply involves adding those costs promises the highest yield. By "yield", we refer to the to the annual cost of capital recovery: profitability of the operation, expressed as an equivalent rate of interest. This is a widely-used concept, which goes AAC = Y + (CR)P under many other names, such as discounted cash flow rate where P = initial investment of retum, DCF; profitability index PI; and equated interest and CR = capital recovery factor based on expected life rate of retum, EiRR. In those cases where after-tax returns of the boat, owner's stipulated yield, and tax. are uniform (as they may be with straight-line deprecia- In calculating annual operating costs, we specifically tion), finding yield is very simple in principle — if we are exclude depreciation allocations and any interest paid to a also willing to assume that the entire investment is made in bank; both are recognized, however, in arriving at the a lump sum upon delivery of the boat. First we divide the capital recovery factor (as explained in the section on after-tax returns, A', by the initial investment, P. This gives taxes). Establishing a suitable yield, is an important first us the venture's after-tax capital recovery factor, CR': step and one that deserves elaboration. It involves some CR' = matters of opinion and its value has a strong bearing on the final outcome. Reference (8) discusses the question of We then go to Table 5 and find the yield, i', that reasonable levels of yield. This requires business judgement corresponds to the derived value of CR' and number of and would normally be set by management. Considering the years, N. If, in addition, all alternatives have equal lives, we risks of the fishing industry, I should judge that the can skip the last step; the alternative with the highest CR' stipulated level would normally fall between 12% and 20%, will automatically have the highest i'. Indeed, to make the the latter figure being appropriate to countries where task even simpler, we need only find the capital recovery investment capital is relatively scarce. factor before tax, CR: A The present value criterion, as its name implies, is found CR = by taking the present value of all projected costs discounted in which A = annual retum before tax. This shortcut is valid to the present. To simplify our work, we may define "the under our assumptions of equal lives and uniform after-tax present" as the time of delivery of the ship. Thus, the initial returns. The alternative promising highest CR then also investment, P, occurs at time zero and is used without promises highest CR' , which in turn promises highest i'. discounting. All other costs are discounted, however, in a degree commensurate with their time of occurrence and There will, of course, be many cases where after-tax with some appropriate interest rate. If we again assume retums are not uniform. Finding yield then requires trial uniform annual costs, we would have this expression for and error to determine that interest rate that will bring the present value, PV: present value of all cash flows (including the investment) to zero. Figure 2 and Table PV = P + (SPW)Y 6 (columns 1 and 2) show an imaginary cash flow forecast for a proposed fish boat. The where Y = uniform annual costs of operation investment is spread over two years and the annual after-tax and SPW = series present worth factor. returns vary because of such factors as declining-balance depreciation, non-uniform trends in revenue or operating As before, the operating costs are exclusive of any costs, occasional major rehabilitation costs, and income allocations for depreciation or interest. The series present from disposal after 15 years of operation. Let us assume worth factor is simply the reciprocal of the capital recovery that we want to find the resulting yield for comparison factor, the derivation of which has already been explained. with other proposed designs. As shown in Table 6, columns Again, the numerical value of these factors must recognize 4 and 5, we first guess at an interest rate (in this case 10%) the owner's need for reasonable profits after tax. and use Table 3 to find the corresponding present worth Harry Benford 329 factors for entry into column 4. The individual present values in column 5 (which equal column 2 times column 4) soo add up to a positive net amount. This indicates that the 400 initially guessed-at interest rate of 10% was too low. So we 300 4/../ next try a higher figure: 12% (columns 6 and 7). The net 0 present value is still positive, so we try yet higher: 13% S 2004. (columns 8 and 9). Now the net present value is negative, so AR we know that the yield must fall between 12% 100 and 13%. DOLL The interpolated value is 12.1%. We are now ready to OF I 2 i Er repeat the process with the next alternative design, seeking 4 5 6 e 8 9 10 11 12 13 14 15 16 17 S YEARS that which promises the highest yield. ND (100) SA U (200) The dashed line in Figure 2 shows the cumulative cash THO **'..`"" PAYBACK PERIOD 7.7 YEARS flow. Its intersection with the baseline indicates the (300 ) payback period, or time required to regain the investment. i 01 Payback period is a crude measure of merit at best, but it (400) \ I deserves consideration when future conditions are particu- (500) V larly unsettled. Another popular economic criterion is the net present value, NPV. If you will refer back to Table 6, you will FIGURE 2 CASH FLOW DIAGRAM notice that we found the net present value of the projected cash flow for each of three arbitrary interest rates. In normal use, NPV involves the use of an assigned interest Table 6 Cash Flow Summary for a Proposed Fishing Vessel (1) (2) (3) (4) (5) (6) (7) (8) (9) ./ .1 j 1 = 10% i = 12% i' = 13% Cumulative Present • Present Cash Cash . (' -N) Year Flow Flow (PW--N) Value (PW-e-N) Value Value $ $ $ $ $ 1 (190,000) (190,000) 0.909 (172,710) 0.893 (169,670) 0.885 (168,150) 2 (320,000) (510,000) .826 (264,320) .797 (255,040) .783 (250,560) 3 140,000 (370,000) .751 105,140 .712 99,680 .693 97,020 4 120,000 (250,000) .683 81,960 .635 76,200 .613 73,560 5 110,000 (140,000) .621 68,310 .567 62,370 .543 59,730 6 85,000 ( 55,000) .564 47,940 .507 40,560 .480 40,800 7 70,000 15,000 .513 35,910 .452 31,640 .425 29,750 8 20,000 35,000 .467 9,340 .404 8,080 .376 7,520 9 60,000 95,000 .424 25,440 .361 21,660 .333 19,980 10 55,000 150,000 .385 21,175 .322 17,710 .295 16,225 11 50,000 200,000 .351 17,550 .287 14,350 .261 13,050 12 45,000 245,000 .319 14,355 .257 11,565 .231 10,395 13 45,000 290,000 .290 13,050 .229 10,305 .204 9,180 14 40,000 330,000 .263 10,520 .205 8,200 .181 7,240 15 40,000 370,000 .239 9,560 .183 7,320 .160 6,400 16 35,000 405,000 .218 7,630 .163 5,705 .142 4,970 17 75,000 480,000 .198 14,850 .146 10,950 .125 9,375 Net Present Value 45,700 1,585 (13,515) Note: Parentheses indicate cash outflows. 330 CONFERENCE ON FISHING VESSEL CONSTRUCTION MATERIALS rate that represents management's opinion of what con- Miscellaneous Considerations stitutes a minimum acceptable level of profitability. This is often called the cut-off rate. Its value is somewhat There are several important comments that apply to any arbitrary. As a minimum, it will be at least as high as the ofthe aforementioned methods of economic analysis: organization's cost of capital. Some managers will set it perhaps 2% higher. Cost of capital is simply the weighted 1. A most important calculation is that of the initial average of interest paid for debt capital (bank loans) and cost. You will, however, find surprisingly little help equity capital (from sale of stock). Typical figures for the in the literature. References (17 and 18) are of some cut-off rate in Canada and the United States range from 8% benefit, but leave many questions unanswered. If we to 11%. are to malce meaningful progress in systems analysis, we must persuade cost estimators to publish the Solving for NPV is not difficult. If the assigned cut-off contents of their little black books. We must also rate is 10%, for example, we need only go through the carry out research in new ways to estimate costs.