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York University

Administrative Studies

ADMS 3530

Lois King

Winter

Description

AP/ADMS3530 3.0
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: C 0 $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
justify your answers. (9 marks)
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)
5
NPV: -$1,500,000 / (1.12) = -$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 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/-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
spreadsheet for the solution and please ignore any terminal loss/recaptured depreciation)
Solution: 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
Cash flow operations (excl CCA) 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:
400,000 0.20 0.35 1 (0.5 0.12)
0.12 0.20 1 0.12
= 87,500 x 0.9464
= 82,810
Total Project NPV = -18,951 +82,810 = 63,859
Question 3- Scenario Analysis (20 marks) Suppose you are analyzing the cash flows on a manufacturing plant that will produce a
new type of digital camera. The plant will cost $10,000,000 to build and will have the
capacity to sell 25,000 digital cameras per year for five years. Each digital camera is
expected to sell for $250 and the variable cost of making each digital camera is expected
to be $100. The fixed costs are expected to be $500,000 per year, not including
depreciation, which is assumed to be straight-line on the initial investment of $10,000,000,
with no salvage value. The firm’s cost of capital is 15% and its tax rate is 36%.
(a) Assume that the expected unit sales, selling price, variable cost and the fixed costs
given above are accurate to within ± 12 percent. Estimate the net present value for the
base, optimistic and pessimistic scenarios. (9 marks)
In the optimistic scenario, unit sales and selling price increase, while costs
decrease. In the pessimistic scenario, unit sales and selling price decrease, and costs
increase.
Scenario Sales (units) Selling Price ($) Variable Cost ($) Fixed Costs ($)
Base 25,000 250 100 500,000
Optimistic 28,000 280 88 440,000
Pessimistic 22,000 220 112 560,000
Base scenario
Using the tax shield approach,
OCF expected[($250 – 100) (25,000) – $500,000] (0.64) + 0.36($10,000,000/5)
OCF expected$2,800,000
NPV expected –$10,000,000 + $2,800,000(PVIFA 15%,5
NPV expected -$613,966
Optimistic scenario
OCF optimistic$280 – 88) (28,000) – $440,000] (0.64) + 0.36($10,000,000/5)
OCF optimistic3,879,040
NPV = –$10,000,000 + $3,879,040(3.352155)
optimistic
NPV optimistic$3,003,144
Pessimistic scenario
OCF = [($220 – 112) (22,000) – $560,000] (0.64) + 0.36($10,000,000/5)
pessimistic
OCF pessimistic1,882,240
NPV pessimistic$10,000,000 + $1,882,240(3.352155)
NPV pessimistic-$3,690,440 2 marks for each OCF and 1 mark for each NPV
(b) Calculate the degree of operating leverage (DOL) for the base scenario?
(5 marks)
Pre-tax profits = Revenues – Variable Costs – Fixed Costs – Depreciation
= 25,000 (250 – 100) – 500,000 – 2,000,000
= $1,250,000 (3 marks)
DOL = 1 + (Fixed costs + depreciation/Pretax profits)
DOL = 1 + ($500,000 + $2,000,000/$1,250,000)
DOL = 3 (2 marks)
(c) What is the optimistic NPV break-even sales level for this plant? (6 marks)
Profit per $1 of extra sales = 1 – (88/280) = $0.685714 (1 mark)
Depreciation per year = $2,000,000
(PVIFA 15%,5 =3.352155
NPV equals zero: PV (CF) – Investment = 0
CF = (Sales – Costs) (1 – T) + (T Depreciation)
= (0.685714 Sales – 440,000) (0.64) + (0.36 2,000,000)
= 0.438857 Sales + 438,400 (3 marks)
3.352155 (0.438857 Sales + 438,400) – 10,000,000 = 0
1.471117 Sales = 8,530,415
Sales = $5,798,597 (2 marks)
Question 4- Risk and CAPM (20 marks)
You believe in digital demographic revolution (people adopting technology at a faster pace
and they want to be connected to the world on the go) and are looking to invest in
companies that will benefit from this secular shift. After doing rigorous research, you ha

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