The preferred technique for evaluating most capital investments is
net present value
Gamma Electronics is considering the purchase of testing equipment that will cost $500,000 to replace old equipment. Assume the new machine will generate after-tax savings of $250,000 per year over the next four years.
What’s the payback period for the investment?
2.0 years
The investment requires $500,000. In its first two years, this investment generates $500,000.
Gamma Electronics is considering the purchase of testing equipment that will cost $500,000 to replace old equipment. Assume the new machine will generate after-tax savings of $250,000 per year over the next four years.
Refer to Gamma Electronics. If the firm has a 15% cost of capital, what’s the discount payback period of the investment?
2.6 years
PV of Year 1 = 250,000/1.15 = 217,391
PV of Year 2 = 250,000/1.152 = 189,036
PV of Year 3 = 250,000/1.153 = 164,379
By the end of year 3, the project produces a cumulative cash flow that’s greater than $500,000. Thus the project earns back the initial $500,000 at some point during the third year.
Gamma Electronics is considering the purchase of testing equipment that will cost $500,000 to replace old equipment. Assume the new machine will generate after-tax savings of $250,000 per year over the next four years.
If Gamma Electronics has a 15% cost of capital, what’s the NPV of the investment?
Gamma Electronics is considering the purchase of testing equipment that will cost $500,000 to replace old equipment. Assume the new machine will generate after-tax savings of $250,000 per year over the next four years.
If Gamma Electronics has a 15% cost of capital, what’s the IRR of the investment?
Gamma Electronics is considering the purchase of testing equipment that will cost $500,000 to replace old equipment. Assume the new machine will generate after-tax savings of $250,000 per year over the next four years.
If Gamma Electronics has a 15% cost of capital, what’s the profitability index of the investment?
The cash flows associated with an investment project are as follows:
Cash Flows
Initial Outflow -$70,000
Year 1 $20,000
Year 2 $30,000
Year 3 $30,000
Year 4 $30,000
What’s the payback period of the project? If a firm’s cutoff payback period is 3 years, should it accept the project?
-By the end of year 3, the project produces a cumulative cash flow of $80,000. Thus the project earns back the initial $70,000 at some point during the third year.
-(70,000 - 20,000 - 30,000)/ 30,000 = 0.67
-The project’s payback period is 2.7 years.
-The firm should invest in the project.
The cash flows associated with an investment project are as follows:
Cash Flows
Initial Outflow -$70,000
Year 1 $20,000
Year 2 $30,000
Year 3 $30,000
Year 4 $30,000
If a firm uses discounted payback with a 15% discount rate and a 3-year cutoff period, what’s the discount payback period of the project? Should the firm accept the project?
Cumulative PV at end of year 3 = 20,000/1.15 +30,000/1.152 + 30,000/1.153 = 59,801
Cumulative PV at end of year 4 = 20,000/1.15 +30,000/1.152 + 30,000/1.153 + 30,000/1.154 = 76,954
By the end of year 4, the project produces a cumulative discounted cash flow of $76,954. Thus the project earns back the initial $70,000 at some point during the fourth year.
(70,000 - 59,801)/(76,954 - 59,801) = 0.6
The discount payback period is 3.6 years.
Flaws of the accounting rate of return method include:
D. all of the above
A piece of equipment costs $1.2m. The equipment has a useful life of 4 years. In each of the four years, the investment generates a cash inflow of $0.5m. The impact of the investment project on net income is derived by subtracting depreciation from cash flow each year.
Assume the equipment is depreciated on a straight-line basis over 4 years, what is the average contribution to net income across all four years?
Depreciation charge per year = 1.2m/4 = 0.3m
Net income per year = 0.5m - 0.3m = 0.2m
A piece of equipment costs $1.2m. The equipment has a useful life of 4 years. In each of the four years, the investment generates a cash inflow of $0.5m. The impact of the investment project on net income is derived by subtracting depreciation from cash flow each year.
The project’s average accounting rate of return equals the average contribution to net income divided by the average book value of the investment.
Assume the equipment is depreciated on a straight-line basis over 4 years, what is the average accounting rate of return?
Depreciation charge per year = 1.2m/4 = 0.3m
Net income per year = 0.5m - 0.3m = 0.2m
Average book value = 0.6m
Average accounting rate of return = 0.2m/0.6m = 33.3%
Suppose a particular investment project will generate an immediate cash inflow of $1,000,000 followed by cash outflows of $500,000 in each of the next three years. What is the project’s IRR? Suppose a company’s hurdle rate is 15%, should it accept the project?
The project has an initial cash inflow and subsequent cash outflows, and its IRR is higher than the hurdle rate, should reject the project.
Suppose a particular investment project will require an initial cash outlay of $1,000,000 and will generate a cash inflow of $500,000 in each of the next three years. What is the project’s IRR? Suppose a company’s hurdle rate is 15%, should it accept the project?
IRR is higher than the hurdle rate, should accept the project.
Future Semiconductors is evaluating a new etching tool. The equipment costs $1.0m and will generate after-tax cash inflows of $0.4m per year for six years. Assume the firm has a 15% cost of capital. What’s the NPV of the investment?
The firm is indifferent between accepting or rejecting projects with zero NPVs
A firm has 10 million shares outstanding with a current market price of $20 per share. There is one investment project available to the firm. The initial investment of the project is $20 million, and the NPV of the project is $10 million. What will be the firm’s stock price if capital markets fully reflect the value of undertaking the project?
=$21
The stock price will increase by $1 per share (= $10m/10m shares)
Kelley Industries has 100 million shares of common stock outstanding with a current market price of $50. The firm is contemplating to take an investment project which requires an initial cash outflow of $100 million. The IRR of the project is equal to the firm’s cost of capital. What will be the firm’s stock price if capital markets fully reflect the value of undertaking the project?
=$50
The NPV of the project is zero since the project’s IRR equals the cost of capital. So there is no change in stock price
Consider a project with the following cash flows.
Year Cash Flow
0 -$16,000
1 42,000
2 -27,000
What’s the IRR of the project? If a firm’s cost of capital is 15%, should the firm accept the project?
Let r represent the IRR of the investment.
-16,000 + 42,000/(1+r) - 27,000/(1+r)2 = 0
r1 = 12.5%, r2 = 50%
When r = 15%, the NPV of the project is greater than 0, should accept the project
Consider a project with the following stream of cash flows.
Year Cash Flow ($ in millions)
0 +80
1 -388
2 +700
3 -557
4 +165
What’s the IRR of the project? If a firm’s cost of capital is 15%, should the firm accept the project?
0%, 10%, 25%, 50%; accept the project
A simple way to solve this problem is to take all the IRRs given in the answer choices and to see whether the IRRs will make the NPV of the project equal to zero.
The NPV of the cash flow at discount rate of 15% is has a positive value of $0.01m, should accept the project.
A firm is evaluating two investment proposals. The following data is provided for the two investment alternatives.
Initial cash outflow IRR NPV(@18%)
Project 1 $250m 28% $80m
Project 2 $ 50m 36% $20m
If the two projects are independent, which project should the firm choose based on the IRR rule?
The hurdle rate is equal to the discount rate in the NPV calculation, which is 18%. Both projects pass the hurdle rate.
A firm is evaluating two investment proposals. The following data is provided for the two investment alternatives.
Initial cash outflow IRR NPV(@18%)
Project 1 $250m 28% $80m
Project 2 $ 50m 36% $20m
If the two projects are mutually exclusive, which project should the firm choose? What is the problem that the firm should be concerned with in making this decision?
Both projects pass the hurdle rate of 18%, and project 1 has higher NPV. The firm should be concerned with the scale problem that occurs when using IRR as a decision rule.
Kelley Industries is evaluating two investment proposals. The scale of Project 1 is roughly 4 times that of the Project 2. The following data is provided for the two investment alternatives.
IRR
Project 1 28%
Project 2 50%
Incremental project 26%
If the two projects are mutually exclusive, and the firm’s hurdle rate is 18%, which project should the firm choose?
Both projects and the incremental project pass the hurdle rate of 18%, and project 1 is of bigger scale, should invest in project 1.
A project may have multiple IRRs when
the project generates an alternating series of net cash inflows and outflows
The IRR method assumes that the reinvestment rate of cash flows is
the IRR
Potential problems in using the IRR as a capital budgeting technique include:
D. all of the above
Thompson Manufacturing is considering two investment proposals. The first involves a quality improvement project, and the second is about an advertising campaign. The cash flows associated with each project appear below.
QualityImprovement AdvertisingCampaign
Initial cash outflow $100,000 $100,000
Cash Inflows
Year 1 10,000 80,000
Year 2 30,000 45,000
Year 3 125,000 10,000
Refer to Tompson Manufacturing. Suppose the hurdle rate of the firm is 10%. Calculate the cash flows of the “incremental project” by subtracting the cash flows of the second project from the cash flows of the first project. What is the IRR of the incremental project?
Cash flow of the incremental project:
Year 0 0
Year 1 -70,000
Year 2 -15,000
Year 3 115,000
Let r represent the IRR of the incremental project.
-70,000/(1+r) -15,000/(1+r)2 + 115,000/(1+r)3 = 0
r = 17.9%
Incremental project IRR passes the hurdle rate, should invest in the quality improvement project.
An entrepreneur is offered a service contract that will cost him $600,000 initially. The contract has a 5 years of life and will generate an after tax cash inflow of $160,000 per year. The cost of capital of this project is 12%. What’s the NPV of the project? Should the entrepreneur accept the contract?
The following information is given on three mutually exclusive projects. Assume a cost of capital of 15%. Which project has the highest PI?
Project 1 Project 2 Project 3
Cash flow
Year 0 -$400,000 -$500,000 -$1,000,000
Year 1 200,000 300,000 500,000
Year 2 300,000 300,000 700,000
Year 3 300,000 350,000 700,000
PI (project 1) = PV of CF(year 1-3) / initial outlay = 598,011/400,000 = 1.495
PI (project 2) = PV of CF(year 1-3) / initial outlay = 717,843/500,000 = 1.436
PI (project 3) = PV of CF(year 1-3) / initial outlay = 1,424,345/1,000,000 = 1.424
Project 1
You are provided with the following data on two mutually exclusive projects. The cost of capital is 15%.
Project 1 Project 2I
nitial cash outflow -$5,000 -$1,000
Year 1 cash inflow $5,000 $1,000
Year 2 cash inflow $2,500 $ 850
NPV $1,238 $ 512
PI 1.25 1.51
Which project should you accept? What is the problem that you should be concerned with in making this decision?
Project 1; project scale
Project 1 has higher NPV than project 2, though project 1 has a lower PI. You should be concerned with the project scale problem in making this decision.
The profitability index is most useful
in capital rationing situations
You have a $1 million capital budget and must make the decision about which investments your firm should undertake for the coming year. There are three projects available and the cash flows of each project appear below. Assume a cost of capital of 12%. Which project or projects do you select?
Project 1 Project 2 Project 3
Cash flow
Year 0 -$400,000 -$500,000 -$1,000,000
Year 1 200,000 300,000 500,000
Year 2 300,000 350,000 700,000
Year 3 300,000 350,000 700,000
PI (project 2) = PV of CF(year 1-3) / initial outlay = 795,998/500,000 = 1.59
PI (project 3) = PV of CF(year 1-3) / initial outlay = 1502,710/1,000,000 = 1.50
Begin by accepting the project with the highest PI, then continue to accept additional projects until bump into the $ 1 million capital constraint. Also, the sum of NPV of project 1 and project 2 is greater than the NPV of project 3.
You must know the discount rate of an investment project to compute its
NPV, PI , discount payback period
You must know all the cash flows of an investment project to compute its
NPV, PI, IRR
The figure below shows the NPV profile for two investment projects.
Refer to NPV Profile. What’s the IRR for project 1?
b. 14%
The figure below shows the NPV profile for two investment projects.
Refer to NPV Profile. What’s the IRR for project 2?
18%
The figure below shows the NPV profile for two investment projects.
Refer to NPV Profile. The NPV of which project is more sensitive to the discount rate?
Project 1
The figure below shows the NPV profile for two investment projects.
Refer to NPV Profile. Suppose the two projects require about the same initial investment. Which project generates more cash flows in the early years?
Project 2
The figure below shows the NPV profile for two investment projects.
Refer to NPV Profile. If Gamma Company has a hurdle rate of 11%, and the two projects are independent, which project should Gamma Company invest?
Both project 1 and project 2.
The figure below shows the NPV profile for two investment projects.
Refer to NPV Profile. If the hurdle rate is 11%, and the two projects are mutually exclusive, which project should be accepted?
Project 1
The figure below shows the NPV profile for two investment projects.
Refer to NPV Profile. If the hurdle rate is 13%, and the two projects are mutually exclusive, which project should be accepted?
Project 2
The figure below shows the NPV profile for two investment projects.
Refer to NPV Profile. If the hurdle rate is 19%, and the two projects are independent, which project should be accepted?
Neither project
Capital investment is also known as:
capital spending
The process of identifying which long-lived investment projects a firm should undertake is known as:
capital budgeting.
Capital budgeting techniques should:
D. all of the above.
The accounting rate of return is calculated as:
net income/book value of assets
The accountings rate of return:
D. all of the above.
The main virtue of the payback method is its:
simplicity.
The payback method:
fails to explicitly consider the time value of money.
A problem with the payback method is:
it assigns a 0 percent discount rate to cash flows that occur before the cutoff point.
As the discount rate increases, the NPV of a project
decreases
As the discount rate increases, the IRR of a project:
is unaffected.
The NPV method focuses on:
cash flows
The IRR method focuses on:
cash flows
Which method directly estimates the change in shareholder wealth?
NPV
When the IRR is equal to the discount rate, the NPV is:
equal to zero
The IRR is analogous to:
a bond’s yield-to-maturity.
The compound annual return on a project is known as its:
IRR
The hurdle rate used in IRR analysis should be:
the discount rate used in NPV analysis.
Which of the following is a problem with the Internal Rate of Return?
D. all of the above are problems with the Internal Rate of Return
NPV and IRR may give conflicting decisions for mutually exclusive projects because:
a. the risk of the projects may differ.
b. the scale of the projects may differ.
c. the discount rates on the projects may differ.
d. all of the above.
The NPV method is most likely to be used in:
D. all of the above.
The payback method is more likely to be used by:
D. b. and c.
The Commerce Company is evaluating a project with the following cash flows:
Year Cash Flow
0 ($10,000)
1 $ 2,000
2 $ 3,000
3 $ 4,000
4 $ 5,000
5 $ 6,000
What is the payback period of the proposed Commerce Company project?
3 + 1000/5000 = 3.2 years.
The Commerce Company is evaluating a project with the following cash flows:
Year Cash Flow
0 ($10,000)
1 $ 2,000
2 $ 3,000
3 $ 4,000
4 $ 5,000
5 $ 6,000
What is the net present value of the proposed Commerce Company project if the discount rate is 7%?
I/YR = 7%
NPV = $5,487
The Commerce Company is evaluating a project with the following cash flows:
Year Cash Flow
0 ($10,000)
1 $ 2,000
2 $ 3,000
3 $ 4,000
4 $ 5,000
5 $ 6,000
What is the profitability index of the proposed Commerce Company project if the discount rate is 7%?
NPV of CF1 - CF5 @ 7% = $15,487
PI = $15,487/$10,000 = 1.58
The Commerce Company is evaluating a project with the following cash flows:
Year Cash Flow
0 ($10,000)
1 $ 2,000
2 $ 3,000
3 $ 4,000
4 $ 5,000
5 $ 6,000
What is the IRR of the proposed Commerce Company project?
IRR = 23.29%
The Commerce Company is evaluating a project with the following cash flows:
Year Cash Flow
0 ($10,000)
1 $ 2,000
2 $ 3,000
3 $ 4,000
4 $ 5,000
5 $ 6,000
What is the discounted payback period of the proposed Commerce Company project if the discount rate is 7%?
Year Cash Flow Dis. CF Cum. CF
0 ($10,000) ($10,000.00) ($10,000.00)
1 $ 2,000 $ 1,869.16 ($ 8,130.84)
2 $ 3,000 $ 2,620.32 ($ 5,510.52)
3 $ 4,000 $ 3,265.19 ($ 2,245.33)
4 $ 5,000 $ 3,814.48 $ 1,569.14
5 $ 6,000 $ 4,277.92 $ 5,847.06
3 + 2,245.33/3814.48 = 3.59 years.
Swerling Company is considering a project with the following cash flows.
Year Cash Flow
0 ($20,000)
1 $ 3,000
2 $ 4,000
3 $ 5,000
4 $ 6,000
5 $ 7,000
What is the payback period of the proposed Swerling Company project?
4 + 2000/7000 = 4.28 years
Swerling Company is considering a project with the following cash flows.
Year Cash Flow
0 ($20,000)
1 $ 3,000
2 $ 4,000
3 $ 5,000
4 $ 6,000
5 $ 7,000
What is the net present value of the proposed Swerling Company project if the discount rate is 6%?
I/YR = 6%NPV = $572
Swerling Company is considering a project with the following cash flows.
Year Cash Flow
0 ($20,000)
1 $ 3,000
2 $ 4,000
3 $ 5,000
4 $ 6,000
5 $ 7,000
What is the profitability index of the proposed Swerling Company project if the discount rate is 6%?
NPV of CF1 - CF5 @ 6% = $20,572
PI = $20,572/$20,000 = 1.03
Swerling Company is considering a project with the following cash flows.
Year Cash Flow
0 ($20,000)
1 $ 3,000
2 $ 4,000
3 $ 5,000
4 $ 6,000
5 $ 7,000
What is the IRR of the proposed Swerling Company project?
IRR = 6.91%
Swerling Company is considering a project with the following cash flows.
Year Cash Flow
0 ($20,000)
1 $ 3,000
2 $ 4,000
3 $ 5,000
4 $ 6,000
5 $ 7,000
What is the discounted payback period of the proposed Swerling Company project if the discount rate is 6%?
