Instructions
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.
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Time value of money (TVM) exercises
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:
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PV—present value
NPER—number of periods
RATE—rate of return
PMT—regular payments
FV—future value
1. Briefly explain the meaning of the term “present value” in your own words.
Is the current worth of a sum that is to be received in the future, discounted to reflect the time value of money and
2. Briefly explain the meaning of the term “future value” in your own words.
Is the amount of money that an investment made today will grow to at a specific future date, given a certain intere
3. What is the future value in five years of $1,500 invested at an interest rate of 4.95%?
$1,909.87
4. What is the future value of a single payment with the following characteristics?
PV
$950
NPER
6 years
RATE
5.4%
$1,302.47
5. What is the present value of $65,000 in six years, if the relevant interest rate is 8.1%?
$40,734.20
6. What is the present value of a single payment with the following characteristics?
NPER
11 years
RATE
5.05%
FV
$10,000
$5,816.25
7. The present value of a payment is $4000. The future value of that payment in five years will be $4800. What is
3.71%
8. What is the annual rate of return of a single payment with the following characteristics?
PV
$1,000
NPER
15 years
FV
$10,000
16.59%
t the time value of money and other factors like investment risk.
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Tab 2 – Annuities
1. How many years would be required to pay off a loan with the following characteristics?
PV
$11,500
RATE
10.6%
PMT
$1,600 (annual payments)
14.24
2. What is the annual payment required to pay off a loan with the following characteristics?
PV
$14,700
RATE
9.95%
NPER
10 years
$2,387.22
3. Why is FV not part of the calculations for either question 1 or question 2?
Because in both scenarios, we are calculating payments based on paying off a loan. In question 1, the goal is to det
4. At what annual rate of interest is a loan with the following characteristics?
NPER
PMT
PV
17 years
$100,000
$1,000,000
6.66%
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?
Year
Projected after-tax cash flows
(in $ millions)
1
(40)
$40.00
2
(40)
$37.00
3
(40)
$34.22
4
(40)
$31.66
5
(40)
$29.28
$172.16
6. LGI extended the analysis out for an additional 7 years, and generated the
following projections. What is the PV of these cash flows?
Year
Projected after-tax cash flows
(in $ millions)
1
(40)
40.00
2
(40)
37.00
3
(40)
34.22
4
(40)
31.66
5
(40)
29.28
6
(40)
27.09
7
(40)
25.05
8
(40)
23.17
9
(40)
21.44
10
(40)
19.83
11
(40)
18.34
12
(40)
16.96
324.04
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?
Year
Projected after-tax cash flows
(in $ millions)
1
(40)
$37.00
2
(50)
$42.78
3
(55)
$43.53
4
(60)
$43.92
5
(70)
$47.40
$214.63
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 th
property. What is the PV of each offer?
Offer A
Offer B
Offer C
Offer D
$102.17 million, paid today
$19.85 million per year, to be paid over the next 8 years
$201.88 million, to be paid in year 8
$18.09 million per year, to be paid over the next 7 years and
a $53.05 million payment in year 8
PV of each offer (in $ millions)
$102.17 million
$113.60
$108.18
$122.26
$28.43
9. From a profit maximizing point of view, which offer should LGI accept?
Offer D has the highest present value when summing both components, which are $93.83 million for the annuity p
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?
An annuity in finance is a series of fixed payments made at regular intervals. In capital budgeting, the concept of an annuity is
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question 1, the goal is to determine how many years it will take to pay off the loan with a fixed annual payment, so the Future
3.83 million for the annuity part and $28.43 million for the lump sum part in year 8, resulting in a total of $122.26 million. Ther
ng, the concept of an annuity is used to calculate the present value of consistent cash flows from an investment over time, which aids in c
al payment, so the Future Value will be zero as the loan is expected to be fully paid off. In question 2, we are calculating the an
al of $122.26 million. Therefore, from a profit-maximizing point of view, LGI should accept Offer D.
n 2, we are calculating the annual payment required to pay off the existing loan within a certain period, so again, the Future V
od, so again, the Future Value is zero as the loan is expected to be fully paid by the end of the term. In essence, for loan paym
In essence, for loan payments, the FV is typically considered to be zero because the final goal is to pay off the loan completely
pay off the loan completely.
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 acq
based sorting and distribution equipment to facilitate more cost-effective operations (and be able to handle the in
workload) at Largo.
The CFO has asked you to evaluate the cash flow projections associated with the equipment purchase proposal an
whether the purchase should go forward. Table 2 shows projections of the cash inflows and outflows that would o
first eight years using the new equipment.
Keep the following in mind:
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Depreciation. The equipment will be depreciated using the straight-line method over eight years. The projec
value is $0.
Taxes. The CFO estimates that company operations as a whole will be profitable on an ongoing basis. As a re
accounting loss on this specific project will provide a tax benefit in the year of the loss.
Table 1 – Data
Cost of the new manfactoring equipment (at year=0)
$
Corporate income tax rate – Federal
Corporate income tax rate – State of Maryland
Discount rate for the project
191.1
26.0%
8.0%
5.98%
5.02%
Table 2 – After-tax Cash Flow Timeline
Year
minus
minus
equals
(all figures in $ millions)
Projected Cash
Projected Cash
Depreciation
Projected Taxable
0
(191.1)
1
850.0
840.0
23.9
(13.9)
2
900.0
810.0
23.9
66.1
3
990.0
870.0
23.9
96.1
4
1,005.0
900.0
23.9
81.1
5
1,200.0
1,100.0
23.9
76.1
6
1,300.0
1,150.0
23.9
126.1
7
1,350.0
1,300.0
23.9
26.1
8
1,320.0
1,300.0
23.9
(3.9)
Table 3 – Example – Computing Projected After-tax Cash Flows
For Year 4
(all figures in $ millions)
Projected Cash Inflows from Operations
1005.0
Projected Cash Outflows from Operations
(900.0)
Depreciation Expense
(23.9)
Projected Taxable Income
81.1
Projected Taxable Income
81.1
times
equals
Corporate income tax rate – Federal
Projected Federal Income Taxes
26.0%
21.1
times
equals
Projected Taxable Income
Corporate income tax rate – State
Projected State Income Taxes
81.1
8.0%
6.5
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.
$214.79
3. Compute the net present value (NPV) of the projected after tax cash flows for years 0-8.
$23.69
4. Compute the internal rate of return (IRR) of the project.
29.01%
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%
$39.32
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acility. The CEO is proposing to acquire roboticstions (and be able to handle the increased
e equipment purchase proposal and recommend
inflows and outflows that would occur during the
ethod over eight years. The projected salvage
itable on an ongoing basis. As a result, any
r of the loss.
million
Projected Federal
Projected State
0.0
(17.2)
25.0
21.1
19.8
32.8
6.8
0.0
$0.00
5.3
7.7
6.5
6.1
10.1
2.1
0.0
Projected After-tax PV
(191.1)
10.0
101.9
87.3
77.4
74.1
107.1
41.1
20.0
Total
NPV
($191.10)
$9.44
$90.73
$73.36
$61.37
$55.44
$75.60
$27.38
$12.57
$214.79
g Projected After-tax Cash Flows
minus
minus
equals
Projected Cash Inflows from Operations
Projected Cash Outflows from Operations
Projected Federal Income Taxes
Projected State Income Taxes
Projected After-tax Cash Flows
1005.0
(900.0)
(21.1)
(6.5)
77.4
$214.79
$214.79
$214.79
$214.79
$214.79
$214.79
$214.79
$214.79
PV
($191.10)
$9.52
$92.39
$75.39
$63.65
$58.02
$79.84
$29.19
$13.52
$230.42
