The Present Value of $1 table: The Present Value of Ordinary Annuity of $1 table: The…
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Question “The Present Value of $1 table: The Present Value of Ordinary Annuity of $1 table: The…”
The Present Value of $1 table:
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 â–¼(GREATER THAN/ LESS THAN)
​one, and the ARR and IRR are ▼(GREATER THAN/ LESS
THAN) the​ company’s required rate of return.
Answer
Solution
The following calculations must be done before you can solve the problem.
Invested Amount = $ 1,870,000
Average Amount Invested = Initial Investment + Residual Valuation / 2.
Initial Investment: $ 1,870,000
Residual value = NIL
The Average Investment = (1870000 + 0.) / 2 = $ 9355,000
Expected Annual Cash Inflow = $475,000
Present Value of Net cash Inflow = Expected Annual Cash Inflow X Current Value Annuity Factor
Here is the Present Value Annuity Factor 8 Years @ 10% = 5.335
Present Value of Net Cash Inflow = 475000 * 5.335 = $ 2,534,125
Let’s now find 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 Ratio of Return (ARR = Expected Annual Cash Inflow/Average Investment)
Or, ARR = 475000/935000 = 50.8% (Approx.)
(C). Net Present Value
Years | Net Cash Inflow | Annuity PV Factor, i=10%, and n=8 | Current Value | |
1 – 8 | Current Value of Annuity | $ 4,75,000.00 | 5.335 | $ 25,34,125.000 |
0 | Invest | $ -18,70,000.000 | ||
The investment’s net present value | $ 6,64,125.000 |
(D) Internal Rate of Return is between 19 – 20 %
Workings:
We can get the following results by using Excel calculations:
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% | |
The IRR should therefore be between 19.15% and 20%.
(E) Profitability Index = Present Value of Net Cash
Inflow / Amount Invested
Or, Profitability Index = 2534125 / 1870000 = 1.36
(Approx)
Requirement 2:
Recommendation to Water City: Water City SHOULD invest because the payback period, the operating life, and the NPV are POSITIVE and GREATER THAN one. The profitability index is GREATER THAN and the ARR is GREATER THAN the company’s required rate.
Conclusion
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