Need Answers To The Questions And Problems Below
Need Answers To The Below Questions And Problems Prepare The Answers
This set of questions and problems involves various aspects of capital budgeting, net present value (NPV), internal rate of return (IRR), cash flows, and project evaluation techniques. Each problem requires evaluating the financial viability of projects, including calculating NPVs at different discount rates, understanding incremental cash flows, and assessing operational cash flows. The tasks also involve analyzing specific scenarios such as a proposed nuclear power plant, computer system installation, new product introduction, valuation of charitable donations, and operational cost assessments for business expansion.
Paper For Above instruction
This paper provides detailed solutions to the set of financial evaluation problems presented above, focusing on capital budgeting principles and cash flow analysis. It demonstrates how to calculate the net present value (NPV) for a proposed nuclear power plant at different discount rates, evaluates the feasibility of a computer system based on different required returns, analyzes the proper cash flows for a new product introduction, discusses the concept of incremental cash flows in the context of charitable donations, and assesses the appropriateness of cost allocation and operational cash flows in a business expansion scenario. Each problem is approached methodically, utilizing standard financial formulas and valuation techniques rooted in corporate finance theory, with references to reputable sources to support the calculations and conceptual explanations.
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Problem 1: NPV of a proposed nuclear power plant
The project has an initial cost of $2.2 billion, cash flows of $300 million annually for 15 years, and a decommissioning cost of $900 million at year 15.
a. Calculation of project NPV at a 5% discount rate
The NPV is computed as the sum of the discounted cash inflows minus the initial investment and the decommissioning cost, with cash flows occurring over 15 years:
\[
NPV = \sum_{t=1}^{15} \frac{\text{Cash flow}}{(1 + r)^t} - \text{Initial investment} - \frac{\text{Decommissioning cost}}{(1 + r)^{15}}
\]
Using the Present Value of an Annuity formula for cash flows:
\[
PV_{annuity} = C \times \frac{1 - (1 + r)^{-n}}{r}
\]
Where:
- \(C = 300\, \text{million}\),
- \(r = 0.05\),
- \(n=15\).
Calculating:
\[
PV_{cash flows} = 300 \times \frac{1 - (1 + 0.05)^{-15}}{0.05}
\]
Similarly, discount the decommissioning cost at year 15:
\[
PV_{decommission} = 900 \times (1 + 0.05)^{-15}
\]
NPV then becomes:
\[
NPV = PV_{cash flows} - 2,200 + PV_{decommission}
\]
(Note: Since the decommissioning cost is an outflow, it is subtracted. Because it happens at year 15, discounted appropriately, it acts as a negative cash flow occurring at that point.)
Calculations yield approximately:
- \(PV_{cash flows} \approx \$3,927\) million.
- \(PV_{decommission} \approx \$277\) million.
- NPV ≈ \$3,927 - \$2,200 - \$900 + \$277 = approximately \$1,104 million.
b. NPV at an 18% discount rate
Repeat the same process with \(r = 0.18\):
\[
PV_{cash flows} = 300 \times \frac{1 - (1 + 0.18)^{-15}}{0.18}
\]
\[
PV_{decommission} = 900 \times (1 + 0.18)^{-15}
\]
Resulting in a much lower present value, leading to a negative NPV, indicating the project would not be viable at this higher discount rate.
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Problem 2: NPV/IRR of a computer system
Initial outlay: \$20,000; annual cash flows: \$4,000 for 8 years; required return: 9% and 14%.
a. NPV at 9%
\[
PV_{cash flows} = 4000 \times \frac{1 - (1 + 0.09)^{-8}}{0.09}
\]
Calculations suggest:
\[
PV_{cash flows} \approx \$26,794
\]
NPV:
\[
NPV = PV_{cash flows} - 20,000 \approx \$6,794
\]
Since NPV > 0, the project is acceptable at 9%.
b. NPV at 14%
\[
PV_{cash flows} = 4000 \times \frac{1 - (1 + 0.14)^{-8}}{0.14} \approx \$23,128
\]
NPV:
\[
NPV = 23,128 - 20,000 = \$3,128
\]
Still positive, so acceptable at 14%.
c. Max discount rate before rejection
Determine the IRR where NPV = 0:
\[
0 = 4000 \times \frac{1 - (1 + IRR)^{-8}}{IRR} - 20,000
\]
Solving numerically (via trial or financial calculator), IRR is approximately 19.5%. The project would be rejected if the discount rate exceeds this.
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Problem 3: Proper cash flow analysis for new chip introduction
Initial sales estimates: Old chip sales 10 million at \$20, revenue \$200 million; new chip sales 12 million at \$25, revenue \$300 million; decreased old chip sales to 3 million, costs for old: \$6 per unit; costs for new: \$8 per unit.
Proper cash flow:
Incremental revenue: \(\$300M + \$200M - \$25 \times 12\, \text{million} - \$6 \times 3\, \text{million}\).
Plus, subtract incremental costs. The proper evaluation considers only the incremental cash flows resulting from the introduction, including changes in revenues, costs, and any avoidable expenses.
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Problem 4: Incremental cash flows from donation
Options:
- (a) The original purchase price does not impact cash flows; irrelevant.
- (b) The current market value reflects opportunity cost.
- (c) Tax deduction affects subsequent cash flows.
- (d) The tax deduction leads to tax savings, an actual cash flow, so is an incremental cash flow.
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Problem 5: Cost allocation for office expansion
Allocating one-eighth of rent costs for capacity use isn't appropriate because costs like rent are fixed and unavoidable. Better to consider variable or avoidable costs, such as the additional rent for the extra space.
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Problem 6: Operating cash flows for tubing company
Sales: \$7M, Costs: \$4M, Depreciation: \$1M, Tax rate: 25%.
EBIT:
\[
EBIT = Revenue - Operating\, Costs - Depreciation = 7M - 4M - 1M = 2M
\]
Taxes:
\[
Tax = 0.25 \times 2M = 0.5M
\]
Net income:
\[
NI = EBIT - Tax = 2M - 0.5M = 1.5M
\]
Operating cash flow (using the direct approach):
\[
OCF = NI + Depreciation = 1.5M + 1M = \$2.5\,\text{million}
\]
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Problem 7: True/False questions
a. False. Depreciation tax shields depend on tax laws and depreciation schedule, not inflation.
b. False. Project cash flows exclude financing effects like interest; focus on operating cash flows.
c. True. Accelerated depreciation affects taxable income and taxes but primarily impacts cash in the near term.
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Problem 8: Cash flow statement for bicycle shop
Revenues: \$160,000; variable costs: \$50,000; rent: \$30,000; depreciation: \$10,000; tax rate: 20%.
a. Income statement
- Revenue: \$160,000
- Operating expenses:
- Variable costs: \$50,000
- Rent: \$30,000
- Depreciation: \$10,000
- EBIT:
\[
160,000 - (50,000 + 30,000 + 10,000)= \$70,000
\]
- Tax:
\[
0.20 \times 70,000= \$14,000
\]
- Net income:
\[
\$70,000 - \$14,000= \$56,000
\]
b. Operating cash flow (OCF)
- Using direct method: Net income + depreciation:
\[
OCF = \$56,000 + \$10,000 = \$66,000
\]
- Alternatively, from operating profit:
\[
EBIT = \$70,000
\]
Add back depreciation:
\[
OCF = EBIT \times (1 - T) + Depreciation = \$70,000 \times (1 - 0.20) + \$10,000 = \$56,000 + \$10,000= \$66,000
\]
This confirms the consistency among different methods.
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References
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