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# IRR Given After Tax Cash FlowsEven Cash Flows, No Present Value Table

1. Valentine Company is considering investing in a new project. The project will need an initial investment of
\$1,200,000 and will generate \$600,000 (after-tax) cash flows for three years. Calculate the IRR for the project. (E)
A. 14.5% C. 23.4%
B. 18.6% D. 20.2% B & M
2. Elephant company is investing in a giant crane. It is expected to cost 2.2 million in initial investment and it is
expected to generate an end of year cash flow of 1.0 million each year for three years. Calculate the IRR
approximately. (E)
A. 14.6 C. 22.1
B. 16.4 D. 17.3 B & M
106
. The capital budgeting director of Sparrow Corporation is evaluating a project which costs \$200,000, is expected to
last for 10 years and produce after-tax cash flows, including depreciation, of \$44,503 per year. If the firm’s cost of
capital is 14 percent and its tax rate is 40 percent, what is the project’s IRR? (E)
a. 8% d. -5%
b. 14% e. 12%
c. 18% Brigham
Even Cash Flow, With Present Value Table
107
. A project has a cost of \$5,000 and is expected to produce a cash flow of \$1,220 a year for five years. Using the
table given, what is the internal rate of return? (Note: Annuity factors are rounded to two places.) (E)
Future Value of an Annuity of \$1
per Period for 5 Periods
Present Value of an Annuity of \$1
per Period for 5 Periods
7% 5.75 4.10
8% 5.87 3.99
9% 5.98 3.89
10% 6.11 3.79
A. 9% C. 7%
B. 10% D. 8% CIA adapted
*. Progressive Corporation acquired an equipment at a cost of P40,500. It had an estimated life of ten years. Annual
after tax net cash benefits are estimated to be P10,000 at the end of each year. The following amounts appear in
the interest table for present value of an annuity of P1 at year end for ten years:
20% 4.19
22% 3.92
24% 3.68
What is the maximum rate that could be paid for the capital employed over the life of this asset without loss on this
project? (M)
a. 20% c. 22%
b. 21% d. 23% RPCPA 1080
*. Jeroig, Inc. placed P300,000 in a ten-year project. The annual cash inflow after income taxes from this project was
estimated to be P58,500. The company’s cut-off rate on investments of this type was 14%. Information on the
present value factors is:
at 14% at 15%
Present value of P1 for ten periods 0.270 0.247
Present value of an annuity of P1 for ten periods 5.216 5.019
The company’s expected rate of return on this investment is (M) RPCPA 0583
a. 14% c. Less than 14% but more than 0%
b. 15% d. Less than 15% but more than 14%
*. Scott, Inc. is planning to invest \$120,000 in a 10-year project. Scott estimates that the annual cash inflow, net of
income taxes, from this project will be \$20,000. Scott’s desired rate of return on investments of this type is 10%.
Information on present value factors is as follows:
at 10% at 12%
Present value of \$1 for ten periods 0.386 0.322
Present value of an annuity of \$1 for ten periods 6.145 5.650
Scott’s expected rate of return on this investment is
a. Less than 10% but more than 0% c. Less than 12% but more than 10%
b. 10% d. 12% AICPA 1180 I-26
Uneven Cash Flow, No Present Value Table
3. Given the following cash flows for Project M: C0
= -2,000, C1
= +500, C2
= +1,500, C3
= +1455, calculate the IRR
for the project. (E)
A. 10% C. 28%
B. 18% D. None of the above B & M
Multiple IRRs
108
. Two fellow financial analysts are evaluating a project with the following net cash flows:
Year Cash Flow
0 -\$ 10,000
1 100,000
2 -100,000
One analyst says that the project has an IRR of between 12 and 13 percent. The other analyst calculates an IRR of
just under 800 percent, but fears his calculator’s battery is low and may have caused an error. You agree to settle
the dispute by analyzing the project cash flows. Which statement best describes the IRR for this project? (D)
a. There is a single IRR of approximately 12.7 percent.
b. This project has no IRR, because the NPV profile does not cross the X axis.
c. There are multiple IRRs of approximately 12.7 percent and 787 percent.
d. This project has two imaginary IRRs.
e. There are an infinite number of IRRs between 12.5 percent and 790 percent that can define the IRR for this
project. Brigham
Comprehensive
Questions 73 and 74 are based on the following information. Barfield
Fordem Co. is considering an investment in a machine that would reduce annual labor costs by \$30,000. The machine
has an expected life of 10 years with no salvage value. The machine would be depreciated according to the straight-line
method over its useful life. The company’s marginal tax rate is 30 percent.
4. Assume that the company will invest in the machine if it generates an internal rate of return of 16 percent. What is
the maximum amount the company can pay for the machine and still meet the internal rate of return criterion?
a. \$180,000 c. \$187,500
b. \$210,000 d. \$144,996
5. Assume the company pays \$250,000 for the machine. What is the expected internal rate of return on the machine?
a. between 8 and 9 percent c. between 17 and 18 percent
b. between 3 and 4 percent d. less than 1 percent
MODIFIED IRR
6. Valentine Company is considering investing in a new project. The project will need an initial investment of
\$1,200,000 and will generate \$600,000 (after-tax) cash flows for three years. Calculate the MIRR (modified internal
rate of return) for the project if the cost of capital is 15%. (E)
A. 14.5% C. 23.4%
B. 18.6% D. 20.2% B & M
7. Elephant company is investing in a giant crane. It is expected to cost 2.2 million in initial investment and it is
expected to generate an end of year cash flow of 1.0 million each year for three years. Calculate the MIRR for the
project if the cost of capital is approximately 12% APA. (E)
A. 15.3% C. 23.8%
B. 17.3% D. 22.1% B & M
109
. A project requires an initial cash investment at its inception of \$10,000, and no other cash outflows are necessary.
Cash inflows from the project over its 3-year life are \$6,000 at the end of the first year, \$5,000 at the end of the
second year, and \$2,000 at the end of the third year. The future value interest factors for an amount of \$1 at the
cost of capital of 8% are
Period
1 2 3 4
1.080 1.166 1.26 1.36
The present value interest factors for an amount of \$1 for three periods are as follows:
Interest Rate
8% 9% 10% 12% 14%
.794 .772 .751 .712 .675
The modified IRR (MIRR) for the project is closes to
a. 8% c. 10%
b. 9% d. 12% Gleim
110
. Alyeska Salmon Inc., a large salmon canning firm operating out of Valdez, Alaska, has a new automated production
line project it is considering. The project has a cost of \$275,000 and is expected to provide after-tax annual cash
flows of \$73,306 for eight years. The firm’s management is uncomfortable with the IRR reinvestment assumption
and prefers the modified IRR approach. You have calculated a cost of capital for the firm of 12 percent. What is the
project’s MIRR? (M)
a. 15.0% d. 16.0%
b. 14.0% e. 17.0%
c. 12.0% Brigham
111
. Below are the returns of Nulook Cosmetics and “the market” over a three-year period:
Year Nulook Market
1 8% 6%
2 9 9
3 32 22
Nulook finances internally using only retained earnings, and it uses the Capital Asset Pricing Model with a historical
beta to determine its cost of equity. Currently, the risk-free rate is 7 percent, and the estimated market risk premium
is 6 percent. Nulook is evaluating a project which has a cost today of \$2,028 and will provide estimated cash
inflows of \$1,000 at the end of the next 3 years. What is this project’s MIRR? (M)
a. 12.4% d. 20.0%
b. 16.0% e. 22.9%
c. 17.5% Brigham
INFLATIONARY ENVIRONMENT
Rate of Return
Minimum Desired Rate of Return
112
. You just passed the CPA licensure examination and took your oath. As you started your practice, Kon Fuse, Inc.
came to you for help in establishing a minimum desired rate of return to be used in the evaluation of a capital project
with a five year life. The following data were provided: (D)
Inflation rate for the past 5 years 13%
Expected inflation rate for the next five years 9%
“Risk-free” element 5%
“Risk” premium demanded for the project 7%
You will advice the client to consider a minimum desired rate of return of
a. 20% c. 16%
b. 21% d. 25% RPCPA 0596
Nominal Rate of Interest
8. The real rate of interest is 3 % and the inflation is 4%. What is the nominal rate of interest?
A. 3% C. 7.12%
B. 4% D. 1% B & M
9. The real interest rate is 3% and the inflation rate is 6%. What is the nominal interest rate?
A. 3% C. 9.2%
B. 4% D. 1% B & M
Real Interest Rate
10. If the nominal interest rate is 8.1% and the inflation rate is 4%, what is the real interest rate?
A. 3.85% C. 4%
B. 8% D. None of the above B & M
Cash Flow
Real Cash Flow
11. A cash flow received in two years is expected to be \$11,236. If the real rate of interest is 4% and the inflation rate is
6%, what is the real cash flow for year 2?
A. \$11,236 C. \$10,000
B. \$10,388 D. \$9,246 B & M
Nominal Cash Flow
12. Real cash flow occurring in year 2 is 50,000. If the inflation rate is 10% per year, calculate nominal cash flow for
year 2.
A. 60,500 C. 55,000
B. 50,000 D. None of the above B & M
Net Present Value – Infinite Life
13. You have been asked to evaluate a project with infinite life. Sales and costs are projected to be \$1000 and \$500
respectively. There is no depreciation and the tax rate is 30%. The real required rate of return is 10% The inflation
rate is 4% and is expected to be 4% forever. Sales and costs will increase at the rate of inflation. If the project
costs \$3000, what is the NPV?
A. \$240.74 C. \$500.00
B. \$1629.62 D. None of the above B & M
14. A project costs \$100 today. It has sales of \$100 per year forever. Costs will be \$50 the first year and increase by
19% per year. Ignoring taxes calculate the NPV of the project at the discount rate of 10%.
A. \$11.62 C. \$100.00
B. \$65.00 D. Cannot be calculated as g > g B & M
Investment Decision
15. You own 100 acres of timberland, with young timber worth \$20,000 if logged today. This represents 500 cords of
wood at \$40 per cord. After logging, the land can be sold today for \$10,000 (\$100 per acre). The opportunity cost
of capital is 10%. You have made the following estimates:
i) The price of a cord of wood will increase by 5% per year.
ii) The price of land will increase by 3% per year.
iii) The yearly growth rate of the mutual cords of wood on your land are: years 1-2: 15%; years 3-4: 10%; years 5-
8: 5%; years thereafter: 2%.
The present value of the optimal decision is approximately:
A. \$30,000 C. \$34,250
B. \$32,800 D. \$34,315 B & M
16. You own 100 acres of timberland, with young timber worth \$20,000 if logged today. This represents 500 cords of
wood at \$40 per cord. After logging, the land can be sold today for \$10,000 (\$100 per acre). The opportunity cost
of capital is 10%. You have made the following estimates:
i) The price of a cord of wood will increase by 5% per year.
ii) The price of land will increase by 3% per year.
iii) The yearly growth rate of the mutual cords of wood on your land are: years 1-2: 15%; years 3-4: 10%; years 5-
8: 5%; years thereafter: 2%.
The optimal decision is to sell after:
A. 8 years C. 4 years
B. 5 years D. 3 years B & M
POINT OF INDIFFERENCE – COST OF CAPITAL
Required Investment
113
. Athey Airlines is considering two mutually exclusive projects, Project A and Project B. The projects have the
following cash flows (in millions of dollars):
Year Project A Cash Flow Project B Cash Flow
0 -\$4.0 ?
1 2.0 \$1.7
2 3.0 3.2
3 5.0 5.8
The crossover rate of the two projects’ NPV profiles is 9 percent. Consequently, when the WACC is 9 percent the
projects have the same NPV. What is the cash flow for Project B at t = 0? (M)
a. -\$4.22 d. +\$4.22
b. -\$3.49 e. -\$4.51
c. -\$8.73 Brigham
Even Cash Flow
17. PDLT Investment which has a weighted average cost of capital of 12% is evaluating two mutually exclusive projects
(X and Y), which have the following projections:
Project X Project Y
Investment P48,000 P83,225
After-tax cash inflow 12,000 15,200
Asset life 6 years 10 years
The fisher rate for the two projects is
A. 12.64% C. 16.01%
B. 12.00% D. 19.33% Pol Bobadilla
114
. Suzie owns a computer reselling business and is expanding her business. Suzie is presented with one proposal,
Proposal A, such that the estimated investment for the expansion project is \$85,000, and it is expected to produce
cash flows after taxes of \$25,000 for each of the next 6 years. An alternate proposal, Proposal B, involves an
investment of \$32,000 and after-tax cash flows of \$10,000 for each of the next 6 years. The cost of capital that
would make Suzie indifferent between these two proposals lies between
a. 10% and 12% c. 16% and 18%
b. 14% and 16% d. 18% and 20% Gleim
18. Berry Products is considering two pieces of machinery. The first machine costs P50,000 more than the second
machine. During the two-year life of these two alternatives, the first machine has P155,000 more cash flow in year
one and a P110,000 less cash flow in year two than the second machine. All cash flows occur at year-end. The
present value of 1 at 15% end of 1 period and 2 periods are 0.86957 and 0.75614, respectively. The present value
of 1 at 8% end of period 1 is 0.92593 and period 2 is 0.85734.
At what discount rate would Machine 1 equally acceptable as machine 2? (D)
A. 9% C. 11%
B. 10% D. 12% RPCPA 0503
Questions 75 and 76 are based on the following information. Barfield
The net after-tax cash flows associated with two projects under consideration by Novelle Co. follow:
Project 1 Project 2
Initial investment \$(300,000) \$(100,000)
Cash flows years 1-5 80,000 30,000
19. What is the Fisher rate for these two projects? (D)
a. less than 1 percent c. between 4 and 5 percent
b. between 7 and 8 percent d. between 6 and 7 percent
20. Assume that the company can potentially accept both projects, one project, or neither project. Which project(s)
would the company accept if it estimates its weighted average cost of capital is 9 percent?
a. both projects c. Project 2
b. Project 1 d. neither project
Uneven Cash Flow
115
. Two projects being considered are mutually exclusive and have the following projected cash flows:
Year Project A Cash Flow Project B Cash Flow
0 -\$50,000 -\$ 50,000
1 15,990 0
2 15,990 0
3 15,990 0
4 15,990 0
5 15,990 100,560
At what rate (approximately) do the NPV profiles of Projects A and B cross? (D)
a. 6.5%
b. 11.5%
c. 16.5%
d. 20.0%
e. The NPV profiles of these two projects do not cross. Brigham
EVALUATION OF INVESTMENT ALTERNATIVES
Net Present Value
116
. The U.S. Postal Service is looking for a new machine to help sort the mail. Two companies have submitted bids to
Cliff Kraven, the postal inspector responsible for choosing a machine. A cash flow analysis of the two machines
indicates the following:
Year Machine A Machine B
0 -\$30,000 -\$30,000
1 0 13,000
2 0 13,000
3 0 13,000
4 60,000 13,000
If the cost of capital for the Postal Service is 8%, which of the two mail sorters should Cliff choose and why? (M)
A. Machine A, because NPVA > NPVB, by \$1,044.
B. Machine B, because NPVA < NPVB, by \$22,000. C. Machine A, because NPVA > NPVB, by \$8,000.
D. Machine B, because IRRA < IRRB. Gleim
117
. Rohan Transport is considering two alternative buses to transport people between cities that are in the Southeastern
U.S., such as Baton Rouge and Gainesville. A gas-powered bus has a cost of \$55,000, and will produce end-of-year
net cash flows of \$22,000 per year for 4 years. A new electric bus will cost \$90,000, and will produce cash flows of
\$28,000 per year for 8 years. The company must provide bus service for 8 years, after which it plans to give up its
franchise and to cease operating the route. Inflation is not expected to affect either costs or revenues during the
next 8 years. If Rohan Transport’s cost of capital is 17 percent, by what amount will the better project increase the
company’s value? (D)
A. \$5,350 C. \$10,701
B. -\$17,441 D. \$27,801 Gleim
Present Value of Costs
118
. Union Electric Company must clean up the water released from its generating plant. The company’s cost of capital
is 11 percent for average projects, and that rate is normally adjusted up or down by 2 percentage points for highand low-risk projects. Clean-Up Plan A, which is of average risk, has an initial cost of \$10 million, and its operating
cost will be \$1 million per year for its 10-year life. Plan B, which is a high-risk project, has an initial cost of \$5 million,
and its annual operating cost over Years 1 to 10 will be \$2 million. What is the approximate PV of costs for the better
project? (VD)
A. -\$5.9 million. C. -\$16.8 million.
B. -\$15.9 million. D. -\$17.8 million. Gleim
Weighted-Average Cost of Capital (WACC)
119
. Mulva Inc. is considering the following five independent projects:
Project Required Amount of Capital IRR
A \$300,000 25.35%
B 500,000 23.22%
C 400,000 19.10%
D 550,000 9.25%
E 650,000 8.50%
The company has a target capital structure which is 40 percent debt and 60 percent equity. The company can issue
bonds with a yield to maturity of 10 percent. The company has \$900,000 in retained earnings, and the current stock
price is \$40 per share. The flotation costs associated with issuing new equity are \$2 per share. Mulva’s earnings are
expected to continue to grow at 5 percent per year. Next year’s dividend (D1) is forecasted to be \$2.50. The firm
faces a 40 percent tax rate. What is the size of Mulva’s capital budget? (D)
A. \$1,200,000 C. \$2,400,000
B. \$1,750,000 D. \$800,000 Glei

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