Number 4

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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 assets that may enhance the company's productivity and thus improve financial performance.

Tab 1 - TVM

1. Briefly explain the meaning of the term "present value" in your own words.
Present value is the sum of money that must be put in place to ensure that a future goal is attained.
2. Briefly explain the meaning of the term "future value" in your own words.
Future value is future date of an investment at an assumed growth rate
3. What is the future value in five years of $1,500 invested at an interest rate of 4.75%?
$ 1,891.74
4. What is the future value of a single payment with the following characteristics?
PV	$950
NPER	6	years
RATE	5.5%
$ 1,309.90
5. What is the present value of $62,000 in six years, if the relevant interest rate is 8.1%?
$ 38,854.16
6. What is the present value of a single payment with the following characteristics?
NPER	11	years
RATE	7.7%
FV	$10,000
$ 4,422.09
7. The present value of a payment is $4000. The future value of that payment in four years will be $4800. What is the annual rate of return?
4.66%
8. What is the annual rate of return of a single payment with the following characteristics?
PV	$1,000
NPER	12	years
FV	$10,000
21%

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:  PV—present value  NPER—number of periods  RATE—rate of return  PMT—regular payments  FV—future value

Tab 2 - Annuities

1. How many years would be required to pay off a loan with the following characteristics?
PV	$11,500
RATE	8.8%
PMT	$1,600	(annual payments)
	11.8688443176
2. What is the annual payment required to pay off a loan with the following characteristics?
PV	$14,700
RATE	9.9%
NPER	10	years
	$ 2,382.09
3. Why is FV not part of the calculations for either question 1 or question 2?
Question 1 & 2 cannot use the future value as the annual payments have been provided in the questions.
4. At what annual rate of interest is a loan with the following characteristics?
NPER	12	years
PMT	$100,000
PV	$1,000,000
	2.92%
For questions 5-8, LGI's cost of capital is			8.15%
5. LGI projects the following after-tax cash flows from operations from
its aging Bowie, Maryland plant (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 $ millions)
1	(45)	$ 41.61
2	(45)	$ 38.47
3	(45)	$ 35.57
4	(45)	$ 32.89
5	(45)	$ 30.41
		$ 178.96
6. LGI extended the analysis out for an additional 7 years, and generated the
following projections. What is the PV of these cash flows?
	Projected after-tax cash flows
Year	(in $ millions)
1	(45)	$ 41.61
2	(45)	$ 38.47
3	(45)	$ 35.57
4	(45)	$ 32.89
5	(45)	$ 30.41
6	(45)	$ 28.12
7	(45)	$ 26.00
8	(45)	$ 24.04
9	(45)	$ 22.23
10	(45)	$ 20.56
11	(45)	$ 19.01
12	(45)	$ 17.57
		$ 336.50
7. The CFO asked the team 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?
	Projected after-tax cash flows
Year	(in $ millions)
1	(45)	$ 41.61
2	(50)	$ 42.75
3	(55)	$ 43.48
4	(60)	$ 43.86
5	(70)	$ 47.31
		$ 219.01
8. Because the estimates of the cash flows in Qs5-7 are all negative, 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? From a profit maximizing point of view, which offer should LGI accept?
		Present Value
Offer A	$101.9 million, paid today	101.9
Offer B	$19.9 million per year, to be paid over the next 8 years	$ 113.71
Offer C	$201.9 million, to be paid in year 8	107.8758246673
Offer D	$17.9 million per year, to be paid over the next 7 years	$ 120.45
	plus a $51.9 million payment in year 8
	Offer D
9. 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?
Annuity can be referred to as a fixed number of payments paid to someone each year.
By assessing the annuity, one can know the value of an asset as well as identifying the
value needed to purchase an asset. Moreover, management can know when to purchase
an asset either in the short term or in the long-term.

Tab 2 - Annuities

Tab 3 - Capital Budgeting

			Table 1 - Data
Cost of the new manfactoring equipment (at year=0)			$	191.1	million
Corporate income tax rate - Federal				26.0%
Corporate income tax rate - State of Maryland				8.0%
Discount rate for the project				6.0%
			Table 2 - After-tax Cash Flow Timeline
	(all figures in $ millions)
Year	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	Present Value
0
1	850.0	840.0	23.9	(13.9)	(3.6)	(1.1)	14.7	$13.89	$14.03
2	900.0	810.0	23.9	66.1	17.2	5.3	67.5	$123.79	$125.64
3	990.0	870.0	23.9	96.1	25.0	7.7	87.3	$233.41	$238.02
4	1,005.0	900.0	23.9	81.1	21.1	6.5	77.4	$268.27	$274.85
5	1,200.0	1,100.0	23.9	76.1	19.8	6.1	74.1	$312.23	$321.35
6	1,300.0	1,150.0	23.9	126.1	32.8	10.1	107.1	$526.75	$544.59
7	1,350.0	1,300.0	23.9	26.1	6.8	2.1	41.1	$229.56	$238.38
8	1,320.0	1,300.0	23.9	(3.9)	(1.0)	(0.3)	21.3	$132.40	$138.09
			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 Inflows from Operations		1005.0
minus	Projected Cash Outflows from Operations		(900.0)		minus	Projected Cash Outflows from Operations		(900.0)
minus	Depreciation Expense		(23.9)		minus	Depreciation Exp - (Depreciation is not a cash flow)		0.0
equals	Projected Taxable Income		81.1		minus	Projected Federal Income Taxes		(21.1)
					equals	Projected State Income Taxes		(6.5)
	Projected Taxable Income		81.1			Projected After-tax Cash Flows		77.4
times	Corporate income tax rate - Federal		26.0%
equals	Projected Federal Income Taxes		21.1
	Projected Taxable Income		81.1
times	Corporate income tax rate - State		8.0%
equals	Projected State Income Taxes		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.
	$ 1,894.95
3. Compute the net present value (NPV) of the projected after tax cash flows for years 0-8.
	1,649.21
4. Compute the internal rate of return (IRR) of the project.
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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		4.95%
	npv	$ 1,703.95

Technologically advanced manufacturing equipment proposal LGI has decided to divest itself of some unproductive factory assets. The vice president of production is proposing to acquire robotics-based manufacturing equipment to enable more cost-effective production. 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.