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Question & Answer: EXHIBIT 8B-1 Present Value of $1 Periods 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 0.962 0.952 0.943…..

ardinal Company is considering a five-year project that would require a $2,975,000 investment in equipment with a useful life of five years and no salvage value. The company’s discount rate is 14%. The project would provide net operating income in each of five years as follows:

Sales $ 2,735,000
Variable expenses 1,000,000
Contribution margin 1,735,000
Fixed expenses:
Advertising, salaries, and other
fixed out-of-pocket costs		 $ 735,000
Depreciation 595,000
Total fixed expenses 1,330,000
Net operating income $ 405,000

See Appropriate Discount Tables below:

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Question & Answer: EXHIBIT 8B-1 Present Value of $1 Periods 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 0.962 0.952 0.943…..
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EXHIBIT 8B-1 Present Value of $1 Periods 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 0.826 0.820 0.813 0.806 0.800 925 0.907 0.890 0.873 0.857 0.842 0.826 0.812 0.797 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694 0.683 0.672 0.661 0.650 0.640 0.889 0.864 0.840 0.816 0.794 0.772 0.751 0.731 0.712 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579 0.564 0.551 0.537 0.524 0.512 0.855 0.823 0.792 0.763 0.735 0.708 0.683 0.659 0.636 0.613 0.592 0.572 0.552 0.534 0.516 0.499 0.482 0.467 0.451 0.437 0.423 0.410 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.593 0.567 0.543 0.519 0497 0476 0.456 0.437 0419 402 0.388 300355 0.341 328 2 4 6 .370 0.352 0.335 0.319 0.303 0.289 0.275 0.2 790 0.746 0.705 0.666 0.630 0.596 0.564 0.535 0.507 0.480 0.456 0.432 0.410 0.390 0 7 0.583 0.547 0.513 0.482 0.452 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279 0.263 0.249 0.235 0.222 0.210 731 0.677 0.627 0.582 0.540 0.502 0.467 0.434 0.404 0.376 0.351 0.327 0.305 0.285 0.266 0.249 0.233 0.218 0.204 0.191 0.179 0.168 60 0.711 0.6 703 0.645 0.592 0.544 0. 500 0.460 0.424 0.391 0.361 0.333 0.308 0.284 0.263 0.243 0.225 0.209 0.194 0.180 0.167 0.155 0.144 0.1 0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.352 0.322 0.295 0.270 0.247 0.227 0.208 0.191 0.176 0.162 0.149 0.137 0.126 0.116 0.107 0.650 0.585 0.527 0.475 0.429 0.388 0.350 0.317 0.287 0.261 0.237 0.215 0.195 0.178 0.162 0.148 0.135 0.123 0.112 0.103 0.094 0.086 0.625 0.557 0.497 0.444 0.397 0.356 0.319 0.286 0.257 0.231 0.208 0.187 0.168 0.152 0.137 0.124 0.112 0.102 0.092 0.083 0.076 0.069 0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.258 0.229 0.204 0.182 0.163 0.145 0.130 0.116 0.104 0.093 0.084 0.075 0.068 0.061 0.055 0.577 0.505 0.442 0.388 0.340 0.299 0.263 0.232 0.205 0.181 0.160 0.141 0.125 0.111 0.099 0.088 0.078 0.069 0.062 0.055 0.049 0.044 0.555 0.481 0.417 0.362 0.315 0.275 0.239 0.209 0.183 0.160 0.140 0.123 0.108 0.095 0.084 0.074 0.065 0.057 0.051 0.045 0.040 0.035 12 0.218 0.188 0.163 0.141 0.123 0.534 0.458 0.394 0.339 0.292 0.252 0.513 0.4 0.107 0.093 0.081 0.071 0.062 0.054 0.047 0.042 0.036 0.032 0.028 0.371 0.317 0.270 0.231 0.198 0.170 0.146 0.125 0.108 0.093 0.080 0.069 0.060 0.052 0.045 0.039 0.034 0.030 0.026 0.023 0.350 0.296 0.250 0.212 0.180 0.153 0.130 0.111 0.095 0.081 0.069 0.059 0.051 0.044 0.038 0.032 0.028 0.024 0.021 0.018 0.475 0.396 0.331 0.277 0.232 0.194 0.164 0.138 0.116 0.098 0.083 0.070 0.060 0.051 0.043 0.037 0.031 0.027 0.023 0.020 0.017 0.014 0.456 0.377 0.312 0.258 0.215 0.178 0.149 0.124 0.104 0.087 0.073 0.061 0.051 0.043 0.037 0.031 0.026 0.022 0.019 0.016 0.014 0.012 17 36 0.416 20 21 23 24 25 0.439 0.359 0.294 0.242 0.199 0.164 0.135 0.112 0.093 0.077 0.064 0.053 0.044 0.037 0.031 0.026 0.022 0.018 0.015 0.013 0.011 0.009 0.422 0.342 0.278 0.226 0.184 0.150 0.123 0.101 0.083 0.068 0.056 0.046 0.038 0.032 0.026 0.022 0.018 0.015 0.013 0.011 0.009 0.007 0.406 0.326 0.262 0.211 0.170 0.138 0.112 0.091 0.074 0.060 0.049 0.040 0.033 0.027 0.022 0.018 0.015 0.012 0.010 0.009 0.007 0.006 0.390 0.310 0.247 0.197 0.158 0.126 0.102 0.082 0.066 0.053 0.043 0.035 0.028 0.023 0.019 0.015 0.013 0.010 0.008 0.007 0.006 0.005 0.375 0.295 0.233 0.184 0.146 0.116 0.092 0.074 0.059 0.047 0.038 0.030 0.024 0.020 0.016 0.013 0.010 0.009 0.007 0.006 0.005 0.004 0.361 0.281 0.220 0.172 0.135 0.106 0.084 0.066 0.053 0.042 0.033 0.026 0.021 0.017 0.014 0.011 27 28 29 30 0.009 0.007 0.006 0.005 0.004 0.003 0.347 0.268 0.207 0.161 0.125 0.098 0.076 0.060 0.047 0.037 0.029 0.023 0.018 0.014 0.011 0.009 0.007 0.006 0.005 0.004 0.003 0.002 0.333 0.255 0.196 0.150 0.116 0.090 0.069 0.054 0.042 0.033 0.026 0.020 0.016 0.012 0.010 0.008 0.006 0.005 0.004 0.003 0.002 0.002 0.107 0.082 0.063 0.048 0.037 0.029 0.022 0.017 0.014 0.011 0.008 0.006 0.005 0.004 0.003 0.002 0.002 0.002 0.308 0.231 0.174 0.131 0.099 0.075 0.057 0.044 0.033 0.026 0.020 0.015 0.012 0.009 0.007 0.005 0.004 0.003 0.003 0.002 0.002 0.001 0.321 0.243 0.185 0.1 41 40 0.208 0.142 0.097 0.067 0.046 0.032 0.022 0.015 0.011 0.008 0.005 0.004 0.003 0.002 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000

Question & Answer: EXHIBIT 8B-1 Present Value of $1 Periods 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 0.962 0.952 0.943..... 1

Please answer the following:

Required:

10.  If the equipment had a salvage value of $300,000 at the end of five years, would you expect the project’s net present value to be higher, lower, or the same?

11.  If the equipment had a salvage value of $300,000 at the end of five years, would you expect the project’s simple rate of return to be higher, lower, or the same?

12. Assume a postaudit showed that all estimates (including total sales) were exactly correct except for the variable expense ratio, which actually turned out to be 45%. What was the project’s actual net present value? (Negative amount should be indicated by a minus sign. Round discount factor(s) to 3 decimal places and intermediate calculations to nearest whole dollar amount.)

13. Assume a postaudit showed that all estimates (including total sales) were exactly correct except for the variable expense ratio, which actually turned out to be 45%. What was the project’s actual payback period? (Round your answer to 2 decimal places.)

14. Assume a postaudit showed that all estimates (including total sales) were exactly correct except for the variable expense ratio, which actually turned out to be 45%. What was the project’s actual simple rate of return? (Round your answer to 2 decimal places. i.e. 0.12342 should be considered as 12.34%.)

EXHIBIT 8B-1 Present Value of $1 Periods 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 0.826 0.820 0.813 0.806 0.800 925 0.907 0.890 0.873 0.857 0.842 0.826 0.812 0.797 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694 0.683 0.672 0.661 0.650 0.640 0.889 0.864 0.840 0.816 0.794 0.772 0.751 0.731 0.712 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579 0.564 0.551 0.537 0.524 0.512 0.855 0.823 0.792 0.763 0.735 0.708 0.683 0.659 0.636 0.613 0.592 0.572 0.552 0.534 0.516 0.499 0.482 0.467 0.451 0.437 0.423 0.410 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.593 0.567 0.543 0.519 0497 0476 0.456 0.437 0419 402 0.388 300355 0.341 328 2 4 6 .370 0.352 0.335 0.319 0.303 0.289 0.275 0.2 790 0.746 0.705 0.666 0.630 0.596 0.564 0.535 0.507 0.480 0.456 0.432 0.410 0.390 0 7 0.583 0.547 0.513 0.482 0.452 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279 0.263 0.249 0.235 0.222 0.210 731 0.677 0.627 0.582 0.540 0.502 0.467 0.434 0.404 0.376 0.351 0.327 0.305 0.285 0.266 0.249 0.233 0.218 0.204 0.191 0.179 0.168 60 0.711 0.6 703 0.645 0.592 0.544 0. 500 0.460 0.424 0.391 0.361 0.333 0.308 0.284 0.263 0.243 0.225 0.209 0.194 0.180 0.167 0.155 0.144 0.1 0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.352 0.322 0.295 0.270 0.247 0.227 0.208 0.191 0.176 0.162 0.149 0.137 0.126 0.116 0.107 0.650 0.585 0.527 0.475 0.429 0.388 0.350 0.317 0.287 0.261 0.237 0.215 0.195 0.178 0.162 0.148 0.135 0.123 0.112 0.103 0.094 0.086 0.625 0.557 0.497 0.444 0.397 0.356 0.319 0.286 0.257 0.231 0.208 0.187 0.168 0.152 0.137 0.124 0.112 0.102 0.092 0.083 0.076 0.069 0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.258 0.229 0.204 0.182 0.163 0.145 0.130 0.116 0.104 0.093 0.084 0.075 0.068 0.061 0.055 0.577 0.505 0.442 0.388 0.340 0.299 0.263 0.232 0.205 0.181 0.160 0.141 0.125 0.111 0.099 0.088 0.078 0.069 0.062 0.055 0.049 0.044 0.555 0.481 0.417 0.362 0.315 0.275 0.239 0.209 0.183 0.160 0.140 0.123 0.108 0.095 0.084 0.074 0.065 0.057 0.051 0.045 0.040 0.035 12 0.218 0.188 0.163 0.141 0.123 0.534 0.458 0.394 0.339 0.292 0.252 0.513 0.4 0.107 0.093 0.081 0.071 0.062 0.054 0.047 0.042 0.036 0.032 0.028 0.371 0.317 0.270 0.231 0.198 0.170 0.146 0.125 0.108 0.093 0.080 0.069 0.060 0.052 0.045 0.039 0.034 0.030 0.026 0.023 0.350 0.296 0.250 0.212 0.180 0.153 0.130 0.111 0.095 0.081 0.069 0.059 0.051 0.044 0.038 0.032 0.028 0.024 0.021 0.018 0.475 0.396 0.331 0.277 0.232 0.194 0.164 0.138 0.116 0.098 0.083 0.070 0.060 0.051 0.043 0.037 0.031 0.027 0.023 0.020 0.017 0.014 0.456 0.377 0.312 0.258 0.215 0.178 0.149 0.124 0.104 0.087 0.073 0.061 0.051 0.043 0.037 0.031 0.026 0.022 0.019 0.016 0.014 0.012 17 36 0.416 20 21 23 24 25 0.439 0.359 0.294 0.242 0.199 0.164 0.135 0.112 0.093 0.077 0.064 0.053 0.044 0.037 0.031 0.026 0.022 0.018 0.015 0.013 0.011 0.009 0.422 0.342 0.278 0.226 0.184 0.150 0.123 0.101 0.083 0.068 0.056 0.046 0.038 0.032 0.026 0.022 0.018 0.015 0.013 0.011 0.009 0.007 0.406 0.326 0.262 0.211 0.170 0.138 0.112 0.091 0.074 0.060 0.049 0.040 0.033 0.027 0.022 0.018 0.015 0.012 0.010 0.009 0.007 0.006 0.390 0.310 0.247 0.197 0.158 0.126 0.102 0.082 0.066 0.053 0.043 0.035 0.028 0.023 0.019 0.015 0.013 0.010 0.008 0.007 0.006 0.005 0.375 0.295 0.233 0.184 0.146 0.116 0.092 0.074 0.059 0.047 0.038 0.030 0.024 0.020 0.016 0.013 0.010 0.009 0.007 0.006 0.005 0.004 0.361 0.281 0.220 0.172 0.135 0.106 0.084 0.066 0.053 0.042 0.033 0.026 0.021 0.017 0.014 0.011 27 28 29 30 0.009 0.007 0.006 0.005 0.004 0.003 0.347 0.268 0.207 0.161 0.125 0.098 0.076 0.060 0.047 0.037 0.029 0.023 0.018 0.014 0.011 0.009 0.007 0.006 0.005 0.004 0.003 0.002 0.333 0.255 0.196 0.150 0.116 0.090 0.069 0.054 0.042 0.033 0.026 0.020 0.016 0.012 0.010 0.008 0.006 0.005 0.004 0.003 0.002 0.002 0.107 0.082 0.063 0.048 0.037 0.029 0.022 0.017 0.014 0.011 0.008 0.006 0.005 0.004 0.003 0.002 0.002 0.002 0.308 0.231 0.174 0.131 0.099 0.075 0.057 0.044 0.033 0.026 0.020 0.015 0.012 0.009 0.007 0.005 0.004 0.003 0.003 0.002 0.002 0.001 0.321 0.243 0.185 0.1 41 40 0.208 0.142 0.097 0.067 0.046 0.032 0.022 0.015 0.011 0.008 0.005 0.004 0.003 0.002 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000

Expert Answer

Question & Answer: EXHIBIT 8B-1 Present Value of $1 Periods 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 0.962 0.952 0.943..... 2Question & Answer: EXHIBIT 8B-1 Present Value of $1 Periods 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 0.962 0.952 0.943..... 3Question & Answer: EXHIBIT 8B-1 Present Value of $1 Periods 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 0.962 0.952 0.943..... 4Formula sheet

A B C D E F G H I J
2 10)
3 First free cash flow needs to be calculated using the following formula:
4 Free Cash Flow = Operating Cash Flow – Capex – Change in working capital
5 Operating Cash Flow = EBIT*(1-T)+Depreciation
6
7 Step 1: Calculation of depreciation
8 Initial investment 2975000
9 Life of Project 5 years
10 Salvage 300000
11 Depreciation per year =(Investment – Salvage Value)/Expected life of Project
12 =(D8-D10)/D9
13
14 Step 2: Calculation of free cash flow:
15 Using the following data:
16 Project cost =D8
17 Depreciation per year =D12
18 Sales 2735000
19 Variable Expenses 1000000
20 Contribution margin =D18-D19
21 Fixed Costs other than depreciation 735000
22 Operating income =D20-D21-D17
23 Salvage Value =D10
24 Tax Rate 0
25 Opportunity cost of capital 0.14
26 Free Cash Flow can be calculated as follows:
27 Year 0 =D27+1 =E27+1 =F27+1 =G27+1 =H27+1
28 Investment =-D8
29 Operating income (EBIT) =$D$22 =$D$22 =$D$22 =$D$22 =$D$22
30 Tax expense =-E29*$D$24 =-F29*$D$24 =-G29*$D$24 =-H29*$D$24 =-I29*$D$24
31 EBIT*(1-T) =SUM(E29:E30) =SUM(F29:F30) =SUM(G29:G30) =SUM(H29:H30) =SUM(I29:I30)
32 Depreciation =$D$17 =$D$17 =$D$17 =$D$17 =$D$17
33 Operating Cash Flow = EBIT*(1-T)+depreciation =E31+E32 =F31+F32 =G31+G32 =H31+H32 =I31+I32
34 Salvage Value =D23
35 Free Cash Flow =D28 =E33+E34 =F33+F34 =G33+G34 =H33+H34 =I33+I34
36
37
38 NPV Calculation:
39
40 NPV of the project is present value of future cash flows discounted at required rate of return less the initial investment.
41
42 Year 0 =D42+1 =E42+1 =F42+1 =G42+1 =H42+1
43 Free cash flow =D35 =E35 =F35 =G35 =H35 =I35
44
45 To find the present value of cash flows, there will be annuity for 19 years and Salvage value at the end of the period.
46 Assuming annuity with A amount and n period S is salvage value at end of the period i.e. n.
47
48 A =E43
49 S =I43-H43
50 n 5
51 MARR (i) =D25
52 Present value of annuity =A*(P/A,i,n) =D48*PV(D51,D50,-1,0) =D48*PV(D51,D50,-1,0)
53 Present value of Salvage Value =S*(P/F,i,n) =D49/((1+D51)^D50) =D49/((1+D51)^D50)
54
55 Present value of future cash flows =E54+E52 =E54+E52
56
57 Net Present Value =Present Value of future cash flows – Initial investment
58 Net Present Value =E55+D43 =E55+D43
59
60 Hence NPV for the project with salvage value is =D58
61
62 11)
63
64 Simple rate of return can be calculated as follows:
65
66 Simple rate of return = Incremental income from investment / Investment amount
67
68 Using the following data
69 Incremental incom from investment =D22
70 Investment amount =D16
71
72 Simple rate of return = Incremental income from investment / Investment amount
73 =$465000 / 2,975,000
74 =D69/D70
75
76 Hence Simple rate of return with salvage value of $300,0000 =D74
77
78
79 12)
80
81 Project cost =D16
82 Depreciation per year 595000
83 Sales =D18
84 Variable Expenses (45%) =D83*45% =D83*45%
85 Contribution margin =D83-D84
86 Fixed Costs other than depreciation =D21
87 Operating income =D85-D86-D82
88 Salvage Value 0
89 Tax Rate =D24
90 Opportunity cost of capital =D25
91 Free Cash Flow can be calculated as follows:
92 Year 0 =D92+1 =E92+1 =F92+1 =G92+1 =H92+1
93 Investment =-D81
94 Operating income (EBIT) =$D$87 =$D$87 =$D$87 =$D$87 =$D$87
95 Tax expense =-E94*$D$89 =-F94*$D$24 =-G94*$D$24 =-H94*$D$24 =-I94*$D$24
96 EBIT*(1-T) =SUM(E94:E95) =SUM(F94:F95) =SUM(G94:G95) =SUM(H94:H95) =SUM(I94:I95)
97 Depreciation =$D$82 =$D$17 =$D$17 =$D$17 =$D$17
98 Operating Cash Flow = EBIT*(1-T)+depreciation =E96+E97 =F96+F97 =G96+G97 =H96+H97 =I96+I97
99 Salvage Value =D88
100 Free Cash Flow =D93 =E98+E99 =F98+F99 =G98+G99 =H98+H99 =I98+I99
101
102
103 NPV Calculation:
104
105 NPV of the project is present value of future cash flows discounted at required rate of return less the initial investment.
106
107 Year 0 =D107+1 =E107+1 =F107+1 =G107+1 =H107+1
108 Free cash flow =D100 =E100 =F100 =G100 =H100 =I100
109
110 To find the present value of cash flows, there will be annuity for 19 years and Salvage value at the end of the period.
111 Assuming annuity with A amount and n period S is salvage value at end of the period i.e. n.
112
113 A =E108
114 S =I108-H108
115 n 5
116 MARR (i) =D90
117 Present value of annuity =A*(P/A,i,n) =D113*PV(D116,D115,-1,0) =D113*PV(D116,D115,-1,0)
118 Present value of Salvage Value =S*(P/F,i,n) =D114/((1+D116)^D115)
119
120 Present value of future cash flows =E119+E117 =E119+E117
121
122 Net Present Value =Present Value of future cash flows – Initial investment
123 Net Present Value =E120+D108 =E120+D108
124
125 Hence Actual NPV for the project is =D123
126
127
128 13)
129 Calculation of Payback period:
130 Payback period is the period when investment amount is recovered.
131 Year 0 =D131+1 =E131+1 =F131+1 =G131+1 =H131+1
132 Free Cash Flow =D108 =E108 =F108 =G108 =H108 =I108
133 Cumulative cash flow =D132 =D133+E132 =E133+F132 =F133+G132 =G133+H132 =H133+I132
134
135 Payback period is when cumulative free cash flow becomes zero.
136 It can be seen from above that cumulative cash flow becomes zero between year 4 and year 5.
137
138 To estimate the exact payback period cumulative free cash flow can be proprated over the years as follows:
139 Payback period =E131+(0-E133)/(F133-E133) =E131+(0-E133)/(F133-E133)
140
141 Hence Actual Payback period is =D139 Years

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