13.5 Ranking Investment Projects Flashcards
Mercken Industries is contemplating four projects, Project P, Project Q, Project R, and Project S. The capital costs and estimated after-tax net cash flows of each independent project are listed below. Mercken’s desired after-tax opportunity cost is 12%, and the company has a capital budget for the year of $450,000. Idle funds cannot be reinvested at greater than 12%.
Project P / Project Q / Project R / Project S Initial cost $200,000 / $235,000 / $190,000 / $210,000 Annual cash flows Year 1 $ 93,000 / $ 90,000 / $ 45,000 / $ 40,000 Year 2 93,000 / 85,000 / 55,000 / 50,000 Year 3 93,000 / 75,000 / 65,000 / 60,000 Year 4 0 / 55,000 / 70,000 / 65,000 Year 5 0 / 50,000 / 75,000 / 75,000 Net present value $23,370 / $29,827 / $27,333 / $(7,854) Internal rate of return 18.7% / 17.6% / 17.2% / 10.6% Excess present value index 1.12 / 1.13 / 1.14 / 0.96
During this year, Mercken will choose
A. Projects P, Q, and R.
B. Projects P, Q, R, and S.
C. Projects Q and R.
D. Projects P and Q.
C. Projects Q and R.
Only two of the projects can be selected because three would require more than $450,000 of capital. Project S can immediately be dismissed because it has a negative net present value (NPV). Using the NPV and the profitability index methods, the best investments appear to be Q and R. The internal rate of return (IRR) method indicates that P is preferable to R. However, it assumes reinvestment of funds during Years 4 and 5 at the IRR (18.7%). Given that reinvestment will be at a rate of at most 12%, the IRR decision criterion appears to be unsound in this situation.
Mercken Industries is contemplating four projects, Project P, Project Q, Project R, and Project S. The capital costs and estimated after-tax net cash flows of each independent project are listed below. Mercken’s desired after-tax opportunity cost is 12%, and the company has a capital budget for the year of $450,000. Idle funds cannot be reinvested at greater than 12%.
Project P / Project Q / Project R / Project S Initial cost $200,000 / $235,000 / $190,000 / $210,000 Annual cash flows Year 1 $ 93,000 / $ 90,000 / $ 45,000 / $ 40,000 Year 2 93,000 / 85,000 / 55,000 / 50,000 Year 3 93,000 / 75,000 / 65,000 / 60,000 Year 4 0 / 55,000 / 70,000 / 65,000 Year 5 0 / 50,000 / 75,000 / 75,000 Net present value $23,370 / $29,827 / $27,333 / $(7,854) Internal rate of return 18.7% / 17.6% / 17.2% / 10.6% Excess present value index 1.12 / 1.13 / 1.14 / 0.96
If Mercken is able to accept only one project, the company would choose
A. Project P.
B. Project Q because it has the highest net present value.
C. Project P because it has the highest internal rate of return.
D. Project P because it has the shortest payback period.
B. Project Q because it has the highest net present value.
Because unused funds cannot be invested at a rate greater than 12%, the company should select the investment with the highest net present value. Project Q is preferable to R because its return on the incremental $45,000 invested ($235,000 cost of Q – $190,000 cost of R) is greater than 12%.
The profitability index (excess present value index)
A. Represents the ratio of the discounted net cash outflows to cash inflows.
B. Is the relationship between the net discounted cash inflows less the discounted cash outflows divided by the discounted cash outflows.
C. Is calculated by dividing the discounted profits by the cash outflows.
D. Is the ratio of the discounted net cash inflows to discounted cash outflows.
D. Is the ratio of the discounted net cash inflows to discounted cash outflows.
The profitability index (excess present value index) of an investment is the ratio of discounted net cash flows to the initial investment. This tool is a variation of the NPV method that facilitates comparison of different-sized investments.
The technique that reflects the time value of money and is calculated by dividing the present value of the future net after-tax cash inflows that have been discounted at the desired cost of capital by the initial cash outlay for the investment is called the
A. Capital rationing method.
B. Average rate of return method.
C. Profitability index method.
D. Accounting rate of return method.
C. Profitability index method.
The profitability index (excess present value index) of an investment is the ratio of the present value of the future net cash flows (or only cash inflows) to the net initial investment. In organizations with unlimited capital funds, this index is unnecessary. If capital rationing is in place, the index is used to rank projects by their return per dollar invested.
A corporation’s financial analyst has identified four potential projects that are mutually exclusive. Each project will produce a constant annual cash flow for Years 1 through 4 and have an initial investment at time 0 as shown below. If the corporation has a weighted-average cost of capital of 16%, which project should be selected using net present value? The present value of an annuity for 4 years at 16% is 2.798, and the present value of $1 for Year 4 at 16% is .552.
Project 1
Time 0 Investment $2,000,000
Annual Cash Flow $772,499
Project 2
Time 0 Investment 1,000,000
Annual Cash Flow 401,020
Project 3
Time 0 Investment 5,000,000
Annual Cash Flow 1,715,854
Project 4
Time 0 Investment 3,000,000
Annual Cash Flow 987,816
A. Project 1.
B. Project 3.
C. Project 2.
D. Project 4.
A. Project 1.
The net present value (NPV) is calculated by multiplying the annual cash flow by the present value factor and then subtracting the initial investment. The NPVs of all four projects are included below. The NPV of Project 1 is the highest, and thus it should be selected.
Project 1
Time 0 Investment $2,000,000
PV of Annual Cash Flows $2,161,452
NPV $161,452
Project 2
Time 0 Investment 1,000,000
PV of Annual Cash Flows 1,122,054
NPV 122,054
Project 3
Time 0 Investment 5,000,000
PV of Annual Cash Flows 4,800,959
NPV (199,041)
Project 4
Time 0 Investment 3,000,000
PV of Annual Cash Flows 2,763,909
NPV (236,091)
Which one of the following capital budgeting techniques would results in the same project selection as the net present value method?
A. Internal rate of return.
B. Probability index.
C. Discounted payback.
D. Accounting rate of return.
B. Probability index.
The net present value of a capital project is derived by subtracting the discounted cash outflows from the discounted cash inflows. The profitability index is the ratio of the same two numbers (inflows to outflows). Thus, they will yield the same decision (if the net present value is positive, the probability index will be > 1)
A firm is evaluating three independent projects for the expansion of different product lines. The Finance Department has performed an extensive analysis of each project, and the chief financial officer has indicated that there is no capital rationing in effect. Which of the following statements are correct?
I. Reject any project with a payback period that is shorter than the company standard.
II. The project with the highest internal rate of return (IRR) exceeding the hurdle rate should be selected and the others rejected.
III. All projects with positive net present values should be selected.
IV. The company should reject any projects with negative IRRs.
A. I, II, III, and IV.
B. II and III only.
C. I, II, and IV only.
D. III and IV only.
D. III and IV only.
As long as there is no capital rationing constraint, all projects with net present values exceeding the hurdle rate should be selected. Also, rejecting projects with negative internal rates of return is a sound investment guideline. Companies prefer projects with shorter payback periods.
The statement below that best represents the definition of capital rationing is a
A. Situation where a constraint is placed on the total size of capital expenditures during a particular period.
B. Budget constraint limiting total depreciation expense related to new capital expenditures for a given period.
C. Limitation where a company selects projects that will meet the minimum number of cash inflow requirements in a given year.
D. Policy that helps optimize investment policy by ensuring that the best mix of products is selected.
A. Situation where a constraint is placed on the total size of capital expenditures during a particular period.
Capital Invest, Inc., uses a 12% hurdle rate for all capital expenditures and has done the following analysis for four projects for the upcoming year:
Project 1:
Initial capital outlay $200,000
Annual net cash inflows
Year 1: 65,000
Year 2: 70,000
Year 3: 80,000
Year 4: 40,000
Net Present Value (3,798)
Profitability Index 98%
Internal rate of return 11%
Project 2:
Initial capital outlay $298,000
Annual net cash inflows
Year 1: 100,000
Year 2: 135,000
Year 3: 90,000
Year 4: 65,000
Net Present Value 4,276
Profitability Index 101%
Internal rate of return 13%
Project 3:
Initial capital outlay $248,000
Annual net cash inflows
Year 1: 80,000
Year 2: 95,000
Year 3: 90,000
Year 4: 80,000
Net Present Value 14,064
Profitability Index 106%
Internal rate of return 14%
Project 4:
Initial capital outlay $272,000
Annual net cash inflows
Year 1: 95,000
Year 2: 125,000
Year 3: 90,000
Year 4: 60,000
Net Present Value 14,662
Profitability Index 105%
Internal rate of return 15%
Which project(s) should Capital Invest undertake during the upcoming year, assuming it has no budget restrictions?
A. Projects 1, 2, and 3.
B. All of the projects.
C. Projects 2, 3, and 4.
D. Projects 1, 3, and 4.
C. Projects 2, 3, and 4.
A company using the NPV method should undertake all projects with a positive NPV, unless some of those projects are mutually exclusive. Given that Projects 2,3, and 4 have positive NPVs, they should be undertaken. Project 1 has a negative NPV.
A company has a maximum of $5,000,000 available for investments. The company has identified the following investment options:
Project / Investment / Discounted Cash Flow
Project I / $2,800,000 / $3,360,000
Project II / 1,500,000 / 1,720,000
Project III / 2,300,000 / 2,617,000
Project IV / 1,200,000 / 1,368,000
Project V / 800,000 / 1,000,000
Which of the following project alternatives should be recommended to management?
A. II, III, and IV.
B. I, IV, and V.
C. II, III, and V.
D. I and II.
B. I, IV, and V.
The profitability index is an efficient means for ranking capital projects. It is the ratio of the net present value of a project’s cash flows to the net investment but it does not necessarily yield the optimal decisions given no capital rationing and projects of different sizes. The indexes for these projects can be calculated as follows:
Discounted Cash Flow / Initial Investment / Profitability Index
Project I: $3,360,000 / $2,800,000 / 1.20
Project II: 1,720,000 / 1,500,000 / 1.15
Project III: 2,617,000 / 2,300,000 / 1.14
Project IV: 1,368,000 / 1,200,000 / 1.14
Project V: 1,000,000 / 800,000 / 1.25
They can now be ranked in order of desirability, and those projects fitting within the $5,000,000 capital constraint can be selected. The projects with the two highest profitability indexes, V and I, can both be undertaken ($800,000 + $2,800,000 = $3,600,000). One more project from among the others can be undertaken if its initial investment is less than $1,400,000 ($5,000,000 – $3,600,000). Project IV fits this criterion. Thus, the combination of I, IV, and V has the highest total NPV ($5,728,000).
A firm has no capital rationing constraint and is analyzing many independent investment alternatives. The firm should accept all investment proposals
A. That provide returns greater than the before-tax cost of debt.
B. If debt financing is available for them.
C. That have positive cash flows.
D. That have a positive net present value.
D. That have a positive net present value.
A company should accept any investment proposal, unless some are mutually exclusive, that has a positive net present value or an internal rate of return greater than the company’s desired rate of return.
Maloney Company uses a 12% hurdle rate for all capital expenditures and has done the following analysis for four projects for the upcoming year:
Project 1
Initial outlay $4,960,000
Annual net cash inflows:
Year 1: 1,600,000
Year 2: 1,900,000
Year 3: 1,800,000
Year 4: 1,600,000
Net present value 281,280
Profitability index 106%
Internal rate of return 14%
Project 2
Initial outlay $5,440,000
Annual net cash inflows:
Year 1: 1,900,000
Year 2: 2,500,000
Year 3: 1,800,000
Year 4: 1,200,000
Net present value 293,240
Profitability index 105%
Internal rate of return 15%
Project 3
Initial outlay $4,000,000
Annual net cash inflows:
Year 1: 1,300,000
Year 2: 1,400,000
Year 3: 1,600,000
Year 4: 800,000
Net present value (75,960)
Profitability index 98%
Internal rate of return 11%
Project 4
Initial outlay $5,960,000
Annual net cash inflows:
Year 1: 2,000,000
Year 2: 2,700,000
Year 3: 1,800,000
Year 4: 1,300,000
Net present value 85,520
Profitability index 101%
Internal rate of return 13%
Which project(s) should Maloney undertake during the upcoming year assuming it has no budget restrictions?
A. All of the projects.
B. Projects 1, 2, and 4.
C. Projects 1 and 2.
D. Projects 1, 2, and 3.
B. Projects 1, 2, and 4.
A company using the net present value (NPV) method should undertake all projects with positive NPVs that are not mutually exclusive. Given that Projects 1, 2, and 4 have positive NPVs, those projects should be undertaken. Furthermore, a company using the internal rate of return (IRR) as a decision rule ordinarily chooses projects with a return greater than the cost of capital. Given a 12% cost of capital, Projects 1, 2, and 4 should be chosen using an IRR criterion if they are not mutually exclusive. Use of the profitability index yields a similar decision because a project with an index greater than 100% should be undertaken.
A company should use the profitability index instead of the net present value method to rank investment projects when the investments have
A. Different initial costs.
B. Uneven cash flows.
C. Different time lengths.
D. More than one cash flow.
A. Different initial costs.
The profitability index (excess present value index) facilitates the comparison of investments that have different initial costs. The profitability index is the ratio of the present value of the future net cash flows (or only cash inflows) to the net initial investment. The investment with the greater profitability index will be the preferred investment.
The technique used to evaluate all possible capital projects of different dollar amounts and then rank them according to their desirability is the
A. Payback method.
B. Profitability index method.
C. Discounted cash flow method.
D. Net present value method.
B. Profitability index method.
The profitability index (excess present value index) is the ratio of the present value of future net cash inflows to the initial cash investment; that is, the figures are those used to calculate the net present value (NPV), but the numbers are divided rather than subtracted. This variation of the NPV method facilitates comparison of different-sized investments. It provides an optimal ranking in the absence of capital rationing.
When ranking two mutually exclusive investments with different initial amounts, management should give first priority to the project
A. That has the greater accounting rate of return.
B. That generates cash flows for the longer period of time.
C. That has the greater profitability index.
D. Whose net after-tax flows equal the initial investment.
C. That has the greater profitability index.
The profitability index (excess present value index) facilitates the comparison of investments that have different initial costs. The profitability index is the ratio of the present value of the future net cash flows (or only cash inflows) to the net initial investment. The investment with the greater profitability index will be the preferred investment.
MS Trucking is considering the purchase of a new piece of equipment that has a net initial investment with a present value of $300,000. The equipment has an estimated useful life of 3 years. For tax purposes, the equipment will be fully depreciated at rates of 30%, 40%, and 30% in Years 1, 2, and 3, respectively. The new machine is expected to have a $20,000 salvage value. The machine is expected to save the company $170,000 per year in operating expenses. MS Trucking has a 40% marginal income tax rate and a 16% cost of capital. Discount rates for a 16% rate are as follows:
PV of an Ordinary Annuity of $1 / Present Value of $1
Year 1: .862 / .862
Year 2: 1.605 / .743
Year 3: 2.246 / .641
What is the profitability index for the project?
A. 0.789
B. 1.315
C. 1.059
D. 1.089
D. 1.089
The profitability index is the present value of the future net cash inflows divided by the present value of the net initial investment. The present value of the future net cash inflows is $326,556. The future cash inflows consist of $170,000 of saved expenses per year minus income taxes after deducting depreciation. In the first year, the after-tax cash inflow is $170,000 minus taxes of $32,000 {[$170,000 – ($300,000 × 30%) depreciation] × 40%}, or $138,000. In the second year, the after-tax cash inflow is $170,000 minus taxes of $20,000 {[$170,000 – ($300,000 × 40%) depreciation] × 40%}, or $150,000. In the third year, the after-tax cash inflow is again $138,000. Also in the third year, the after-tax cash inflow from the salvage value is $12,000 [$20,000 × (1 – 40%)]. Accordingly, the sum of these cash flows discounted using the factors for the present value of $1 at a rate of 16% is $326,556. Year 1: $138,000 × .862 = $118,956. Year 2: $150,000 × .743 = $111,450. Year 3: $150,000 × .641 = $96,150. Discounted cash inflows = $118,956 + $111,450 + $96,150 = $326,556. Hence, the profitability index is 1.089 ($326,556 ÷ $300,000).
NOTE: On the CMA exam, the numerator of the profitability index may be based on (1) all cash flows or (2) only the future net cash inflows (excluding the initial investment). The second option is used in this question.
Using the profitability index, which one of the following projects is the best investment?
Project A
Initial investment: $10,000,000
Net present value: 1,100,000
Internal rate of return: 11%
Project B
Initial investment: $7,000,000
Net present value: 700,000
Internal rate of return: 12%
Project C
Initial investment: $5,000,000
Net present value: 300,000
Internal rate of return: 8%
Project D
Initial investment: $2,000,000
Net present value: 250,000
Internal rate of return: 10%
A. Project C.
B. Project D.
C. Project A.
D. Project B.
B. Project D.
The profitability index can be calculated by dividing the discounted net cash flows of the project by the net initial investment. The profitability index for each project can be calculated as follows: Project A = 1.11 [($10,000,000 + $1,100,000) ÷ $10,000,000], Project B = 1.10 [($7,000,000 + $700,000) ÷ $7,000,000], Project C = 1.06 [($5,000,000 + $300,000) ÷ $5,000,000], and Project D = 1.125 [($2,000,000 + $250,000) ÷ $2,000,000]. The highest profitability index is 1.125, which belongs to Project D, making it the best investment.
Capital Invest, Inc., uses a 12% hurdle rate for all capital expenditures and has done the following analysis for four projects for the upcoming year:
Project 1:
Initial capital outlay $200,000
Annual net cash inflows
Year 1: 65,000
Year 2: 70,000
Year 3: 80,000
Year 4: 40,000
Net Present Value (3,798)
Profitability Index 98%
Internal rate of return 11%
Project 2:
Initial capital outlay $298,000
Annual net cash inflows
Year 1: 100,000
Year 2: 135,000
Year 3: 90,000
Year 4: 65,000
Net Present Value 4,276
Profitability Index 101%
Internal rate of return 13%
Project 3:
Initial capital outlay $248,000
Annual net cash inflows
Year 1: 80,000
Year 2: 95,000
Year 3: 90,000
Year 4: 80,000
Net Present Value 14,064
Profitability Index 106%
Internal rate of return 14%
Project 4:
Initial capital outlay $272,000
Annual net cash inflows
Year 1: 95,000
Year 2: 125,000
Year 3: 90,000
Year 4: 60,000
Net Present Value 14,662
Profitability Index 105%
Internal rate of return 15%
Which project(s) should Capital Invest undertake during the upcoming year if it has only $600,000 of funds available?
A. Projects 3 and 4.
B. Projects 1 and 3.
C. Projects 2 and 3.
D. Projects 2, 3, and 4.
A. Projects 3 and 4.
Given that only $600,000 is available and that each project costs $200,000 or more, no more than two projects can be undertaken. Because Projects 3 and 4 have the greatest NPVs, profitability indexes, and IRRs, they are the projects in which the company should invest.
A manufacturer is considering two independent projects, each requiring a cash outlay of $500,000 and having an expected life of 10 years. The forecasted annual net cash inflows for each project and the probability distributions for these cash inflows are as follows:
Project R
Probabilities / Cash Inflows
0.10 / $ 75,000
0.80 / 95,000
0.10 / 115,000
Project S
Probabilities / Cash Inflows
0.25 / $ 70,000
0.50 / 110,000
0.25 / 150,000
The manufacturer has decided that the project with the greatest relative risk should meet a hurdle rate of 16% and the project with less risk should meet a hurdle rate of 12%. Given these parameters, which of the following actions should be recommended for the manufacturer to undertake?
A. Accept Project R and reject Project S.
B. Reject both projects.
C. Accept both projects.
D. Reject Project R and accept Project S.
C. Accept both projects.
The probable annual cash inflows for the two projects can be calculated as follows:
Project R
Cash Inflow x Probability = Probable Outcome
$ 75,000 x 10% = $7,500
95,000 x 80% = 76,000
115,000 x 10% = 11,500
100% = $95,000
Project S
Cash Inflow x Probability = Probable Outcome
$ 70,000 x 25% =$17,500
110,000 x 50% = 55,000
150,000 x 25% = 37,500
100% = $110,000
Project R is less risky as the anticipated cash flows are more certain, both in probability and in spread; whereas Project S has a wide range of possible cash flows, and it is less certain that a profitable level of cash flow will be achieved. Therefore, Project R should be discounted at 12% and Project S at 16%. Discounting the cash flows from Project R (ordinary annuity of $95,000 for 10 years) at 12% and discounting the cash flows from Project S (ordinary annuity of $110,000 for 10 years) at 16% yields results of $536,771 and $531,655, respectively. Since both projects exceed the present value of the total cash outflows ($500,000), they should both be accepted.
A firm has the following investment opportunities. Required investment outlays and the profitability index for each of these investments are as follows:
Project: Investment Cost / Profitability Index
I: $300,000 / 0.5
II: 450,000 / 1.4
III: 650,000 / 1.8
IV: 750,000 / 1.6
The firm’s budget ceiling for initial outlays during the present period is $1,500,000. The proposed projects are independent of each other. Which project or projects would you recommend that the firm accept?
A. III and IV.
B. I, III, and IV.
C. I, II, and IV.
D. III.
A. III and IV.
The profitability index is an efficient means for ranking capital projects, but it has limitations when capital is rationed and projects are of different sizes. It is the ratio of the net present value of a project’s cash flows to the net investment. Any project with a profitability index > 1 is expected to be profitable. Projects III and IV, the projects with the two highest indexes, fit within the $1,500,000 capital constraint.
If a project has a profitability index that is greater than 1.0, it means that the
A. Required return is less than the internal rate of return.
B. Future unadjusted cash flows exceed the initial investment.
C. Initial investment exceeds the cash flows.
D. Internal rate of return is equal to the required return.
A. Required return is less than the internal rate of return.
The profitability index can be calculated by dividing the PV of future cash flows by the net investment. In order for this to be greater than 1, the required return must be less than the internal rate of return. If the required rate of return is less than the internal rate of return, this means that the project will be profitable for the company because the return on the project is higher than the company’s required rate.
Capital budgeting methods are often divided into two classifications: project screening and project ranking. Which one of the following is considered a ranking method rather than a screening method?
A. Profitability index.
B. Accounting rate of return.
C. Net present value.
D. Time-adjusted rate of return.
A. Profitability index.
The profitability index is the ratio of the present value of future net cash inflows to the initial cash investment. This variation of the net present value method facilitates comparison of different-sized investments. Were it not for this comparison feature, the profitability index would be no better than the net present value method. Thus, it is the comparison, or ranking, advantage that makes the profitability index different from the other capital budgeting tools.
A company is considering an investment to open a new banana processing division. The project involves an initial investment of $45,000, and cash inflows of $20,000 can be expected in each of the next 3 years. The hurdle rate is 10%. What is the profitability index for the project?
A. 1.1771
B. 1.1379
C. 1.0784
D. 1.1053
D. 1.1053
At a 10% hurdle rate, the present value of the future cash inflows is $49,740 ($20,000 × 2.487). The NPV for the project is $4,740 ($49,740 – $45,000). The profitability index is therefore 1.1053 ($49,740 ÷ $45,000).
