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:

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

Formula 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 |