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# ADMS 3530 Lecture Notes - Capital Requirement, Tax Rate, Scenario Analysis

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Course Code
Professor
Lois King

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Assignment #2
Fall 2012 Solutions
Question 1 - NPV and Other Investment Criteria (20 marks)
Parts (a) and (b) below are related, but they are not related to parts (c).
Consider the following project in parts (a) and (b).
Cost: C0 = \$10,000,000.
Annual net cash inflows: \$3,000,000.
Project life: N = 5 years.
Annual required rate of return: 12%.
Maximum payback: 4 years.
(a) Compute the NPV, Profitability Index and Payback for the above project. Indicate
whether the project should be accepted based on each of these three criteria and briefly
NPV: -\$10,000,000 + \$3,000,000 PV of a 5 year annuity at 12% = -\$10,000,000 +
\$10,814,328.61 = \$814,328.61.
Accept the project since the NPV is positive.
Profitability Index: \$814,328.61 / \$10,000,000 = 0.081433.
Accept the project since the PI is above zero.
Payback: \$10,000,000 / \$3,000,000 = 3 1/3 years.
Accept the project since the payback is less than the maximum payback of 4 years.
2 marks each for calculation, 1 mark for the conclusion
(b) Suppose that you later discover that at the end of the project it will cost \$1,500,000 to
shut down the project. How would this affect the decision to accept or reject the project
based on the NPV and payback criteria? Briefly discuss your results. (6 marks)
NPV: -\$1,500,000 / (1.12)5 = -\$851,140.28
New NPV = \$814,328.61 \$851,140.28 = -\$36,811.67 < 0, so reject the project.
Payback: Since this shut down cost occurs after the maximum payback period of 4 years,
it would be ignored and the project would still be deemed acceptable according to the

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payback criterion. This example illustrates the weakness of using the payback criterion.
Specifically, the project is now unacceptable, yet because the additional cash flow
happens after the payback period the payback rule still suggests that the project be
undertaken.
3 marks for each
(c) You have an annual required rate of return of 13%. To fund your project, Mr.
VC is going to give you \$10,000 if you agree to pay him \$15,000 in 3 years from today.
What is your annual rate of return on this investment? What is the IRR on this investment?
Should you agree to this investment? Why or why not? (5 marks)
The annual rate of return is: (\$15,000 / \$10,000)1/3 -1 = 0.144714 or 14.4714%, which is
also the IRR on this investment. (3 marks)
You should not agree to this investment since this is a loan (from Mr. VC) and your
required rate of return (13%) is lower than the IRR (14.4714%). (2 marks)
Question 2- DCF Analysis (20 marks)
Discount Smartphones Inc. is about to launch a new Smartphone to compete with Apple’s
iPhone 5. The phone will be priced at \$110 per unit and the unit cost is \$60. The firm
expects it can sell the phone over the next 5 years. The company estimates an initial
investment in equipment of \$400,000 which will fall into a CCA class that has a 20%
declining balance rate. The equipment will have no salvage value at the end of year 5.
Sales projections of the new phone are as follows:
Year
Unit Sales
1
3000
2
3500
3
4000
4
5000
5
5000
The net working capital (including the initial working capital needed in year 0) is expected
to be 20% of the following year’s sales. All the working capital is expected to be recovered
at the end of year 5. Incremental fixed costs are estimated to be \$20,000 per year and the
accounting department is allocating \$5,000 each year of existing plant operating expenses
to the project. If the firm’s tax rate is 35% and the project’s discount rate is 12%, should
Discount Smartphones go ahead with the project? (Note: You may submit an Excel
Solution:

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Project NPV = \$63,859. The company should accept the project.
Year:
0
1
2
3
4
5
Sales Units
3000
3500
4000
5000
5000
Sales revenue
330,000
385,000
440,000
550,000
550,000
Less: Variable cost
-180,000
-210,000
-240,000
-
300,000
-
300,000
Less: Fixed costs
-20,000
-20,000
-20,000
-20,000
-20,000
Revenues - cash expenses
130,000
155,000
180,000
230,000
230,000
Taxes (35 percent)
-45,500
-54,250
-63,000
-80,500
-80,500
84,500
100,750
117,000
149,500
149,500
Working capital requirement
66,000
77,000
88,000
110,000
110,000
0
Change in NWC requirement
-66,000
-11,000
-11,000
-22,000
0
110,000
Initial Investment
-400,000
Total cash flow (excl CCA)
(lines 19 + 22 +23)
-466,000
73,500
89,750
95,000
149,500
259,500
PV of total cash flow (excl
CCA)
-466,000
65,625
71,548
67,619
95,010
147,247
NPV of line 27
-18,951
Present value of CCA Tax Shield (PVTS), given a zero salvage value:
=
87,500 x 0.9464
=
82,810
Total Project NPV =
-18,951 +82,810 =
63,859
Question 3- Scenario Analysis (20 marks)
12.01
)12.05.0(1
20.012.0
35.020.0000,400