Please see attached instructions and project.
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> Instructions 22
022
of 1, 00 invested at an interest rate of 4. 5%?
years .1%?
,000
. The present value of a payment is $4000. The future value of that payment in five years will be $4800. What is the annual rate of return?
years FV Time value of money (TVM) exercises —regular payments
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Instructions
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3
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Answer all questions in this workbook. Be sure to read the introductory text on tabs 1 and 3 as well as these instructions.
Keep in mind that the focus of this project is corporate finance. The information generated by the accounting system is important; but in finance, decisions are driven by an analysis of cash flows rather than profits.
Tab 1 contains a series of exercises on the concept of the time value of money. These exercises do not relate directly to the issues facing LGI.
Tab 2 focuses on the concept of annuities. The first few questions do not pertain specifically to LGI; the latter questions do.
Tab 3 pertains to whether LGI should acquire new assets that may enhance the company’s productivity and thus improve financial performance.
Tab 1 – TVM
0
11
1. Briefly explain the meaning of the term “present value” in your own words.
2. Briefly explain the meaning of the term “future value” in your own words.
3. What is the future value in five
years
$
5
9
4. What is the future value of a single payment with the following characteristics?
PV
$950
NPER
6
RATE
5.4%
5. What is the present value of $65,000 in six years, if the relevant interest rate is
8
6. What is the present value of a single payment with the following characteristics?
NPER
11
years
RATE
5.05%
FV
$
10
7
8. What is the annual rate of return of a single payment with the following characteristics?
PV
$1,000
NPER
15
$10,000
There are five variables in TVM calculations: present value, number of periods, rate of return, regular payments, and future value. If four of the variables are known, then the fifth can be calculated using algebra, a financial calculator, or a computer program such as Excel.
Excel functions for the five variables are as follows:
PV—present value
NPER—number of periods
RATE—rate of return
PMT
FV—future valueTab 2 – Annuities
| 011022 | |||||||||||||||||
| 1. How many years would be required to pay off a loan with the following characteristics? | |||||||||||||||||
| $11,500 | |||||||||||||||||
| 10.6% | |||||||||||||||||
| $1,600 | (annual payments) | ||||||||||||||||
| 2. What is the annual payment required to pay off a loan with the following characteristics? | |||||||||||||||||
| $14,700 | |||||||||||||||||
| 10.0% | |||||||||||||||||
| 3. Why is FV not part of the calculations for either question 1 or question 2? | |||||||||||||||||
| 4. At what annual rate of interest is a loan with the following characteristics? | |||||||||||||||||
| 17 | |||||||||||||||||
| $100,000 | |||||||||||||||||
| $1,000,000 | |||||||||||||||||
| For questions 5-8, LGI’s cost of capital is | 8.11% | ||||||||||||||||
| 5. LGI projects the following after-tax cash flows from operations from | |||||||||||||||||
| its aging Bowie, Maryland distribution facility (which first went on line in 1953) | |||||||||||||||||
| over the next five years. What is the PV of these cash flows? | |||||||||||||||||
| Projected after-tax cash flows | |||||||||||||||||
| Year | (in $ | million | |||||||||||||||
| (40) | |||||||||||||||||
| 6. LGI extended the analysis out for an additional 7 years, and generated the | |||||||||||||||||
| following projections. What is the PV of these cash flows? | |||||||||||||||||
| 12 | |||||||||||||||||
| 7. The CFO asked you to undertake a more detailed analysis of the plant’s costs, noting that while | |||||||||||||||||
| it is convenient for making calculations when projections result in data that can be treated like an annuity, | |||||||||||||||||
| this does not always represent the most accurate estimate of future results. What is the PV of these cash flows? | |||||||||||||||||
| (50) | |||||||||||||||||
| (55) | |||||||||||||||||
| (60) | |||||||||||||||||
| (70) | |||||||||||||||||
| 8. As part of a larger plan to sell off underperforming assets, LGI is considering selling the Bowie property | |||||||||||||||||
| and using other existing facilities more efficiently. LGI received four preliminary offers from potential buyers for the Bowie | |||||||||||||||||
| property. What is the PV of each offer? | |||||||||||||||||
| PV of each offer (in $ millions) | |||||||||||||||||
| Offer A | $102.17 million, paid today | ||||||||||||||||
| Offer B | $19.85 million per year, to be paid over the next 8 years | ||||||||||||||||
| Offer C | $201.88 million, to be paid in year 8 | ||||||||||||||||
| Offer D | $18.09 million per year, to be paid over the next 7 years and | ||||||||||||||||
| a $53.05 million payment in year 8 | |||||||||||||||||
| 9. From a profit maximizing point of view, which offer should LGI accept? | |||||||||||||||||
| 10. Define the term annuity in your own words. How might the concept of an annuity impact the process of | |||||||||||||||||
| capital budgeting and new asset acquisition? |
Tab 2 – Annuities
Tab 3 – Capital Budgeting
| Table 1 – Data | |||||||||||||||||||
| Cost of the new manfactoring equipment (at year=0) | 191.1 | ||||||||||||||||||
| Corporate income tax rate – Federal | 26.0% | ||||||||||||||||||
| Corporate income tax rate – State | 8.0% | ||||||||||||||||||
| Discount rate for the project | 5.98% | ||||||||||||||||||
| Table 2 – After-tax Cash Flow Timeline | |||||||||||||||||||
| (all figures in $ millions) | |||||||||||||||||||
| Projected Cash Inflows from Operations | Projected Cash Outflows from Operations | Depreciation Expense | Projected Taxable Income | Projected Federal Income Taxes | Projected State Income Taxes | Projected After-tax Cash Flows | |||||||||||||
| 850.0 | 840.0 | ||||||||||||||||||
| 900.0 | 810.0 | ||||||||||||||||||
| 990.0 | 870.0 | ||||||||||||||||||
| 1,005.0 | |||||||||||||||||||
| 1,200.0 | 1,100.0 | ||||||||||||||||||
| 1,300.0 | 1,150.0 | ||||||||||||||||||
| 1,350.0 | |||||||||||||||||||
| 1,320.0 | |||||||||||||||||||
| Table 3 – Example – Computing Projected After-tax Cash Flows | |||||||||||||||||||
| For Year 4 | |||||||||||||||||||
| 1005.0 | |||||||||||||||||||
| minus | (900.0) | ||||||||||||||||||
| (23.9) | ( | 21.1 | |||||||||||||||||
| equals | 81.1 | ( | 6.5 | ||||||||||||||||
| 77.4 | |||||||||||||||||||
| times | |||||||||||||||||||
| 1. Complete Table 2. Compute the projected after tax cash flows for each of years 1-8. | |||||||||||||||||||
| 2. Compute the total present value (PV) of the projected after tax cash flows for years 1-8. | |||||||||||||||||||
| 3. Compute the net present value (NPV) of the projected after tax cash flows for years 0-8. | |||||||||||||||||||
| 4. Compute the internal rate of return (IRR) of the project. | |||||||||||||||||||
| 5. The CFO believes that it is possible that the next few years will bring a very low interest rate environment. | |||||||||||||||||||
| Therefore, she has asked that you repeat the NPV calculation in question 3 showing the case where the | |||||||||||||||||||
| discount rate for the project is | 5.02% |
Robotics-based equipment proposal
If the Bowie plant is sold, those operations will need to shift to the main Largo facility. The CEO is proposing to acquire robotics-based sorting and distribution equipment to facilitate more cost-effective operations (and be able to handle the increased workload) at Largo.
The CFO has asked you to evaluate the cash flow projections associated with the equipment purchase proposal and recommend whether the purchase should go forward. Table 2 shows projections of the cash inflows and outflows that would occur during the first eight years using the new equipment.
Keep the following in mind:
Depreciation. The equipment will be depreciated using the straight-line method over eight years. The projected salvage value is $0.
Taxes. The CFO estimates that company operations as a whole will be profitable on an ongoing basis. As a result, any accounting loss on this specific project will provide a tax benefit in the year of the loss.
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