Question

The Present Value of $1 table:

Reference Periods 1% 0.990 0.980 0.971 0.961 0.951 6% | 0.943 0.890 | 0.840 | 0.792 0.747 15% 0.870 0.756 0.658 0.572 0.497 0.579 0.386 0.942 0.933 0.923 0.914 0.905 0.896 0.887 0.879 0.870 0.861 2% 3% | 0.980 0.971 0.961 0.943 0.942 0.915 0.924 0.888 0.906 0.863 0.888 0.837 0.871 0.813 0.853 0.789 0.837 0.766 0.820 0.744 0.8040.722 0.788 0.701 0.773 0.681 0.758 0.661 0.743 0.642 0.7280.623 0.714 0.605 0.700 0.587 0.686 0.570 0.673 0.554 0.660 0.538 0.647 0.634 0.507 0.622 0.492 0.610 0.478 0.598 0.464 0.586 0.450 0.574 0.437 0.563 0.424 0.552 0.412 0.453 0.307 0.372 0.228 4% 5% 0.962 0.952 0.925 0.907 0.889 0.864 0.855 0.823 0.822 0.784 | 0.790 0.746 0.760 0.711 0.731 0.677 0.703 0.645 0.676 | 0.614 0.650 0.585 0.625 0.557 0.601 0.530 0.577 0.505 0.555 0.481 0.534 0.458 0.513 0.436 0.494 0.416 0.475 0.396 0.456 0.377 0.439 0.359 0.422 0.342 0.406 0.326 0.390 0.310 0.375 0.295 0.361 0.281 0.347 0.268 0.333 0.255 0.321 0.308 | 0.231 0.208 0.142 0.141 0.087 0.853 0.844 0.836 0.828 0.820 0.811 0.803 0.795 0.788 0.780 0.772 0.764 0.757 0.749 Present Value of $1 7% 8% 9% 10% 0.935 0.926 0.917 0.909 | 0.873 0.857 0.842 0.826 0.816 0.794 0.772 0.751 | 0.763 0.735 0.708 0.683 0.713 0.681 0.650 0.621 0.6660.630 0.596 0.564 0.623 0.583 0.547 0.513 0.582 0.540 0.502 0.467 0.544 0.500 0.460 0.424 0.508 0.463 0.422 0.475 0.429 0.388 0.350 | 0.444 0.397 | 0.356 0.319 | 0.415 0.368 0.326 0.290 | 0.388 0.340 0.299 0.263 0.362 0.315 0.275 0.239 0.3390.292 0.252 0.218 0.317 0.270 0.231 0.198 0.296 0.250 0.212 0.180 0.277 0.232 0.194 0.164 0.258 0.215 0.178 0.149 0.242 0.199 0.164 0.135 | 0.226 0.184 0.150 0.123 | 0.211 0.170 0.138 0.112 0.197 0.158 0.126 0.102 0.184 0.146 0.116 0.092 0.172 0.135 0.106 0.084 0.161 0.125 0.098 0.076 0.150 0.116 0.090 0.069 0.141 0.107 0.082 0.063 0.131 0.099 0.075 0.057 0.067 0.046 0.032 | 0.022 0.034 0.021 0.013 0.009 0.705 0.665 0.627 0.592 0.558 0.527 0.497 0.469 0.442 0.417 0.394 0.371 0.350 0.331 0.312 0.294 0.278 0.262 0.247 0.233 0.220 0.207 0.196 0.185 0.174 0.097 0.054 12% 14% 0.893 0.877 0.797 0.769 0.712 0.675 0.636 0.592 0.567 0.519 0.507 | 0.456 0.452 0.400 | 0.404 0.351 0.361 | 0.308 0.322 0.270 0.287 0.237 0.257 0.208 0.229 0.182 0.205 0.160 0.183 0.140 0.163 0.123 0.146 0.108 0.130 0.095 0.116 0.083 0.104 0.073 0.093 0.064 0.083 0.056 0.074 0.049 0.066 0.043 0.059 0.038 0.053 0.033 0.047 0.029 0.042 0.026 0.037 0.022 0.033 0.020 0.011 0.005 0.003 0.001 0.432 0.376 0.327 0.284 0.247 0.215 0.187 0.163 | 0.141 0.123 0.107 0.093 0.081 0.070 0.061 0.053 0.046 0.040 0.035 0.030 0.026 0.023 0.020 0.017 0.015 0.004 0.001 16% 18% 20% 0.862 0.847 0.833 0.743 0.7180.694 0.641 0.609 0.552 0.516 0.482 0.476 0.437 0.402 0.410 0.370 0.335 0.354 0.314 0.279 0.305 0.266 0.233 0.263 0.225 0.194 0.227 0.191 0.162 0.195 0.162 0.135 0.168 0.137 0.112 0.145 0.116 0.093 0.125 0.099 0.078 0.108 0.084 | 0.065 0.093 0.071 0.054 0.080 0.060 0.045 0.069 0.051 0.038 0.060 0.043 0.031 0.051 0.037 0.026 0.044 0.031 0.022 0.038 0.026 0.018 0.033 0.022 0.015 0.028 0.019 0.013 0.024 0.016 0.010 0.021 0.014 0.009 0.0180.011 0.0160.010 0.006 0.014 0.008 0.012 0.007 0.004 0.003 0.001 0.001 0.001 0.522 0.007 0.243 0.005 0.742 0.672 Print Done

The Present Value of Ordinary Annuity of $1 table:

The Future Value of $1 table:

The Future Value of Ordinary Annuity of $1:

​Recommendation: Water City ▼ (SHOULD/SHOULD NOT) invest in the project because the payback period is ▼(GREATER THAN/ LESS THAN) the operating​ life, the NPV is ▼(NEGATIVE/POSITIVE) ​, the profitability index is ▼(GREATER THAN/ LESS THAN) ​one, and the ARR and IRR are ▼(GREATER THAN/ LESS THAN) the​ company's required rate of return.

Answer 1

Solution

Before making the solution, following calculations are required to be made,

Amount Invested = $ 1,870,000

Average Amount Invested = (Initial Investment + Residual Value) / 2, where
Initial Investment = $ 1,870,000
Residual Value = NIL
Therefore, Average Amount Invested = (1870000 + 0) / 2 = $ 935,000

Expected Annual Net Cash Inflow = $ 475,000

Present Value of Net Cash Inflow = Expected Annual Net Cash Inflow X Present Value Annuity Factor
Here, Present Value Annuity Factor for 8 years @ 10% = 5.335
Therefore, Present Value of Net Cash Inflow = 475000 X 5.335 = $ 2,534,125

Now, let's make our solutions.

Requirement 1:
(A) Payback Period = Amount Invested / Expected Annual Net Cash Inflow
Or, Payback Period = 1,870,000 / 475,000 = 3.9 Years (Approx)

(B) Accounting Rate of Return (ARR) = Expected Annual Net Cash Inflow / Average Amount Invested
Or, ARR = 475000 / 935000 = 50.8% (Approx)

(C) Net Present Value

Years		Net Cash Inflow	Annuity PV Factor (i=10%, n=8)	Present Value
1 - 8	Present Value of Annuity	$ 4,75,000.00	5.335	$   25,34,125.000
0	Investment			$ -18,70,000.000
	Net Present Value of the investment			$     6,64,125.000

(D) Internal Rate of Return is between 19 - 20 %
Workings:
Using Excel calculations as below, we get,

	Year	Amount ($)
Initial Investment	0	$             -18,70,000.00
Net Cash Inflow	1	$                 4,75,000.00
	2	$                 4,75,000.00
	3	$                 4,75,000.00
	4	$                 4,75,000.00
	5	$                 4,75,000.00
	6	$                 4,75,000.00
	7	$                 4,75,000.00
	8	$                 4,75,000.00
Internal Rate of Return
[ = IRR (Total Cash Flow, Guess Rate) ]
[ = IRR (C2:C10, 10%) ]		19.15%

Therefore, IRR should be 19.15%, or less specifically, within 19% to 20%.

(E) Profitability Index = Present Value of Net Cash Inflow / Amount Invested
Or, Profitability Index = 2534125 / 1870000 = 1.36 (Approx)

Requirement 2:

Recommendation: Water City SHOULD invest in the project because the payback period is LESS THAN the operating life, the NPV is POSITIVE, the profitability index is GREATER THAN one, and the ARR and IRR are GREATER THAN the company's required rate of return.