Finance 445

Practice Exam

Chapters 1, 2, 5, and part of Chapter 6

Part One. Multiple Choice Questions.

  1. Similar to the example given in class, assume that a corporation has $500 of cash revenue and $300 of cash expenses. Therefore the corporation has $200 of taxable income. The corporation pays taxes at the 40% income tax rate (i.e., all of the $200 of taxable income will be taxed at 40%). The corporation plans to pay any cash left over after the payment of income taxes to the stockholders. If the stockholders pay taxes at the 20% tax rate (i.e., any dividends they receive will be taxed at 20%), how much income tax (both corporate and individual) will be paid?
  1. $82
  2. $104
  3. $112
  4. $116
  5. $120
  6. $140
  1. A project requires an initial investment of $10 million and produces a single positive cash flow in one year. The opportunity cost of capital for the project is 8%. The expected return for the project is X%. Which of the following statements is true?
  1. The project will create value for the owner only if the expected return for the project is greater than 8%.
  2. The project will create value for the owner if the expected return for the project is greater than 0% (even if the expected return is less than 8%)
  1. A project requires an initial investment of $1000 and produces one of two cash flows in one year: $1300 or $900. The probability of the $1300 cash flow is 40%. The probability of the $900 cash flow is 60%. Using a 10% discount rate, what is the NPV of the project?
  1. -$140.00
  2. -$60.00
  3. -36.36
  4. $36.36
  5. $60.00
  6. $140.00
  1. Today is January 1, 2000. A newly formed corporation raises $10 million through a stock issue and uses the money to purchase $10 million of land, buildings, and equipment in order to undertake a new project. The corporation has no other assets. Therefore, the January 1, 2000 book value (accounting value) for the assets is $10,000,000. Managers of the corporation and outside investors know that the project NPV is negative. Based on this, the market value of the firm’s assets is ______the book value of its assets.
  1. Greater than
  2. The same as
  3. Less than
  1. The internal rate of return for Project A is 6%. Using an opportunity cost of capital of 8%, the NPV for Project A is +$250. Based on this information:
  1. The modified internal rate of return will be greater than 8%.
  2. The modified internal rate of return will be greater than 6%, but less than 8%.
  3. The modified internal rate of return will be less than 6%.
  4. There are not enough facts to answer this question.
  1. The internal rate of return for the following project is 14.80%. Using a 5% opportunity cost of capital, compare the project’s internal rate of return with its modified internal rate of return.

0 / 1 / 2 / 3 / 4 / 5 / 6
$100 / $100 / $100 / $100 / $100 / $100 / -$1000
  1. The internal rate of return is greater than the modified internal rate of return.
  2. The internal rate of return is less than the modified internal rate of return.
  1. A project has a negative cash flow at time zero, a positive cash flow at time one, and a negative cash flow at time two. Because the project has two sign changes, there could be two internal rates of return. (Assume that there are two internal rates of return in this case.) With two sign changes:
  1. There will be one net present value.
  2. There will be two net present values.
  3. There could either be one or two net present values. (More information is needed to determine the exact number of net present values.)
  1. Using a 5% opportunity cost of capital, what is the modified internal rate of return of the following cash flow stream?

0 / 1
+$100 / -$120
  1. –10.750%
  2. –9.500%
  3. –8.125%
  4. 6.667%
  5. 15.83%
  6. 20.00%
  1. A firm is considering a ten-year project that will require the purchase of one of two different depreciable assets. Both will cost $100,000 and both will be worthless at the end of the project. Either asset could be used on the project with no difference in the project’s incremental cash flows (other than possible depreciation effects). Since the firm uses straight-line depreciation for financial statement reporting purposes, the accounting depreciation is $10,000 per year for both assets. However for tax purposes, the first depreciable asset is classified as five-year MACRS property and the second as seven-year MACRS property. Assuming that the firm is in the 34% income tax bracket for each of the years of the analysis, and using a 5% opportunity cost of capital, which of the two depreciable assets will produce the highest project NPV? (Hint: The follow table gives the yearly MACRS tax-depreciation rates.)

1 / 2 / 3 / 4 / 5 / 6 / 7 / 8
5-year / 20.00% / 32.00% / 19.20% / 11.52% / 11.52% / 5.76%
7-year / 14.29% / 24.49% / 17.49% / 12.49% / 8.93% / 8.93% / 8.93% / 4.45%
  1. The project NPV is the same using either of the two depreciable assets.
  2. The first depreciable asset (the five-year MACRS asset).
  3. The second depreciable asset (the seven-year MACRS asset).
  1. A firm is considering a five-year project that will require the purchase of inventory. The firm will purchase 1000 units of inventory for $1 per unit once a month for the next 60 months. (Assume no inflation in the purchase price.) Using a 5% opportunity cost of capital, the NPV of the project is $5000 if the firm will make payment for the inventory one month after purchase. Assume that the supplier will allow the firm to make payment two months after purchase without any penalty. Continuing to use the 5% opportunity cost of capital, what effect will this change in assumption have on the project NPV?
  1. The NPV will be higher than $5000.
  2. The NPV will be equal to $5000.
  3. The NPV will be lower than $5000.
  1. A firm is considering two possible projects. The first project will require an initial investment of $100,000 and produces positive cash flows of $20,000 a year for the next 10 years. In addition to these cash flows, this project will increase cash flows on the firm’s existing projects by $5000 per year. The second project also requires an initial investment of $100,000 and produces positive cash flows of $20,000 a year for the next 10 years. In addition, it also affects the cash flows of the firm’s existing projects. However, unlike the first project, this second project will decrease cash flows on the firm’s existing projects by $5000 per year. Using a 5% opportunity cost of capital, which of the projects have the higher NPV?
  1. The first project.
  2. The second project.
  3. Both projects have the same NPV. (The effects on the cash flows of the firm’s other existing projects should be ignored in the analysis.)
  1. A project requires an initial investment of $5000 and produces positive cash flows of $X per year for five years. Using a 7% opportunity cost of capital, the equivalent annual cash flow (EAC) for the project is $780.55. Which of the two cash flow streams will have the higher NPV using a 7% discount rate?

0 / 1 / 2 / 3 / 4 / 5
Cash Flow #1 / -$5000 / $X / $X / $X / $X / $X
Cash Flow #2 / $780.55 / $780.55 / $780.55 / $780.55 / $780.55 / $780.55
  1. Cash Flow #1
  2. Cash Flow #2
  3. Both cash flows have the same NPV.
  1. You are trying to decide whether you should replace an old machine with a new machine this year or wait until next year. One part of the NPV calculation in this machine replacement analysis is the estimated cash flows associated with the salvage value of the old machine. Assume that your company has a marginal income tax rate of 34%. You originally estimate the salvage value of the old machine as $50,000 if sold today and $35,000 if sold in one year. Based on this (and your analysis of the other cash flows from replacing the old machine), and using a 5% discount rate, you determine that the NPV associated with replacing the old machine with a new machine this year (t = 0), instead of next year (t = 1), is $0. After thinking about it more, you now think that the salvage value of the old machine if it is sold in one year is $36,000 (instead of $35,000). Keeping all of the other assumptions the same, this single change in assumptions will:
  1. Make the NPV positive (i.e., you should replace the old machine with a new machine at t = 0).
  2. Make the NPV negative (i.e., you should not replace the old machine with a new machine at t = 0).
  3. Have no effect on the NPV (i.e., the NPV remains equal to zero).

Problem Questions.

  1. The U.S. Government is offering the ability to rent forest service land with the following terms:

Rental period = Perpetual

Rental payments = Once a year (skip every seventh payment, i.e., no payment due in year 7, 14, 21, 28, etc.)

Rental payments = $10,000 (no inflation)

Use a real discount rate = 3%

For example, the cash flows through year 10 look like this:

0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
$0 / $10000 / $10000 / $10000 / $10000 / $10000 / $10000 / $0 / $10000 / $10000 / And so on

What is the present value of the rent cash flows?

  1. It is January 1, 2000 and ABC Inc. (a calendar year taxpayer) is considering a project. If the project is not accepted, ABC Inc. will have $102,000 of state taxable income. If the project is accepted, ABC Inc. will have $122,000 of state taxable income. As in class, assume that the corporation accurately estimates the Kentucky state income tax and pays this amount to the State of Kentucky during the year 2000. Using the Federal and Kentucky corporate income tax rate schedules on the next page, calculate the amount of additional federal and state income tax ABC Inc. will need to pay in the year 2000 if it accepts the project.
  1. The nominal discount rate is 7% per year, the expected inflation rate is 2.8846154% per year, and the real discount rate is 4% per year. The following project cash flows are presented using nominal dollars. Repeat the analysis using “method one” discussed in class. (Method one uses constant dollar, i.e., real cash flows, for revenues and associated taxes. It uses nominal dollars for tax depreciation and associated cash flows resulting from the depreciation deduction on the tax return.)

Analysis Using Nominal Figures
0 / 1 / 2 / 3 / 4
Unit sales / 1000 / 1000 / 1000 / 1000
Price per unit / 1.02885 / 1.05852 / 1.08906 / 1.12047
Revenue / 1,028.85 / 1,058.52 / 1,089.06 / 1,120.47
Depreciation / (583.28) / (777.88) / (259.18) / (129.68)
Taxable Income / 445.57 / 280.65 / 829.88 / 990.80
Income Tax at 34% / (151.49) / (95.42) / (282.16) / (336.87)
Subtotal / 294.08 / 185.23 / 547.72 / 653.93
Adjustments
Add: Depreciation / 583.28 / 777.88 / 259.18 / 129.68
Subtract: Initial Investment / (1,750.00)
Cash Flow / (1,750.00) / 877.35 / 963.10 / 806.90 / 783.60
NPV at 7% = 1,167.64
Tax depreciation rates / 33.33% / 44.45% / 14.81% / 7.41%
  1. Your firm is considering a project that requires an initial investment of $112,000 and will produce positive cash flows of $2,400 per year in perpetuity (starting in one year). In addition to these cash flows, you must consider the following: Assume that undertaking this project requires the use of an existing machine. If the project is rejected, this old machine will last 9 more years before it needs to be replaced with a new machine. However, if the project is accepted, the old machine will need to be replaced in 6 years with a new machine. This new machine has more than enough capacity to handle the new project and all other existing projects, will cost $45000 to purchase (either at t = 9 or t = 6) and will cost $8600 per year to operate for the next 12 years (until t = 21 or t = 18). At the end of this 12-year period, an identical machine with the same cash flows will be purchased. This will continue forever. Assume that the figures presented are real cash flows. Therefore, the cash flows are the same if the replacement machine is purchased at time 9 or time 6. Use a 3% real discount rate. As in the example discussed in class, ignore the cash flows associated with maintaining and operating the existing machine.

A)Initially ignore the “cost of using the excess capacity” of the old machine. Using the 3% real discount rate, the initial investment of $112,000, and the expected cash flows of $2,400 per year in perpetuity (starting in one year), what is the NPV of the project?

B)What is the equivalent annual cash flow (EAC) for the new replacement machine? Make sure you indicate whether the EAC is negative or positive.

C)What is the NPV of the project (after taking into account the additional costs associated with having to buy the new machine at the end of the 6th year instead of the end of the 9th year)?

Corporate Income Tax Rates (Federal)

Bracket / Tax Rate
$0 - $50,000 / 15%
$50,000 - $75,000 / 25%
$75,000 - $100,000 / 34%
$100,000 - $335,000 / 39%
$335,000 - $10,000,000 / 34%
$10,000,000 - $15,000,000 / 35%
$15,000,000 - $18,333,333 / 38%
Above $18,333,333 / 35%

Corporate Income Tax Rates (Kentucky)

Bracket / Tax Rate
$0 - $25,000 / 4%
$25,000 - $50,000 / 5%
$50,000 - $100,000 / 6%
$100,000 - $250,000 / 7%
Above $250,000 / 8.25%

.
Finance 445

Practice Exam

Chapters 1, 2, 5, and part of Chapter 6

Multiple Choice Solutions

1.______

2.______

3.______

4.______

5.______

6.______

7.______

8.______

9.______

10.______

11.______

12.______

13.______

Problem Questions:

  1. PV = ______

Your work

  1. Kentucky state income tax (with project)= ______

Kentucky state income tax (without project)= ______

Addition state income tax = ______

Federal income tax (with project)= ______

Federal income tax (without project)= ______

Addition Federal income tax = ______

Your work

  1. Fill out the following table with your solution to problem 3.

0 / 1 / 2 / 3 / 4
Unit sales
Price per unit
Revenue
Income Tax (at 34%)
Cash Flow
PV @ ___% =
Depreciation income tax deduction
Cash flow from depreciation tax deduction (at 34%)
PV @ ___% =
NPV of project =

Your work

  1. Preliminary calculation of the project NPV= ______

EAC= ______

Final calculation of the project NPV= ______

(The preliminary calculation of the Project NPV does not include the ‘cost of using the excess capacity’ of the old machine. The final calculation of the project NPV includes this cost.)

Your work

Finance 445

Practice Exam Answers

Multiple Choice Solutions

1.B

2.A

3.C

4.C

5.A

6.A

7.A

8.C

9.B

10.A

11.A

12.B

13.B

Problem Questions:

  1. PV = $289,831.22

Solution hints: (A) calculate the EAC over the seven-year period, (B) calculate the PV of a perpetuity of cash flows equal to the EAC

  1. Kentucky state income tax (with project)= $6,790.00

Kentucky state income tax (without project)= $5,390.00

Addition state income tax = $1,400.00

Federal income tax (with project)= $28,181.90

Federal income tax (without project)= $21,097.40

Addition Federal income tax = $7,084.50

  1. Fill out the following table with your solution to problem 3.

0 / 1 / 2 / 3 / 4
Unit sales / 1000 / 1000 / 1000 / 1000
Price per unit / $1 / $1 / $1 / $1
Revenue / $1,000.00 / $1,000.00 / $1,000.00 / $1,000.00
Income Tax (at 34%) / $ (340.00) / $ (340.00) / $ (340.00) / $ (340.00)
Cash Flow / $ 660.00 / $ 660.00 / $ 660.00 / $ 660.00
PV @ 4% = $2395.73
Depreciation income tax deduction / $ (583.28) / $ (777.88) / $ (259.18) / $ (129.68)
Cash flow from depreciation tax deduction (at 34%) / $ 198.31 / $ 264.48 / $ 88.12 / $ 44.09
PV @ 7% = $521.91

NPV of project = -$1750 + $2395.73 + $521.91 = $1,167.64

  1. Preliminary calculation of the project NPV= -$32,000.00

EAC= -$13,120.79

Final calculation of the project NPV= -$63,082.08

Solution hints for problem 4

  • Preliminary calculate of project NPV = -$112,000 + ($2400 / 0.03) = -$32,000
  • The EAC is calculated by first calculating the NPV of a single purchase of the new replacement machine. The cash flows are:

-$45,000 (purchase price)

-$8,600 (per year for 12 years)

NPV = -$130,604.43

EAC = -$13,120.79

  • Take a PV of the EAC at time 7, 8, and 9 using the 3% real rate and add this answer to -$32,000 to determine the final NPV

PV of EAC at time 7, 8, and 9 = -$31,082.08

Preliminary NPV = -$32,000

Final NPV = -$63,082.08