Capital Budgeting Process and Techniques 105
Chapter 7: Capital Budgeting Process and Techniques
Answers to questions
7-1. a. Type I error means rejecting a good project. Payback could lead to Type 1 errors when it rejects a good project that has large cash flows after the payback period cutoff. Payback ignores cash flows after the cutoff.
b. Type II error means accepting a project that should have been rejected. Type II errors occur when payback says to accept a project that doesn't return enough to compensate for the risk taken. This occurs because payback makes no adjustments for risk or time value of money.
c. If firms apply the payback rule with a fairly short cutoff period, then a type I error is more likely¾good projects with higher cash flows in later years may be rejected. On the other hand, if firms apply the payback rule but use a long cutoff period, then a Type II error becomes more likely because the payback method makes no adjustment for the time value of money.
7-2. Discounted payback has a more severe bias¾discounted cash flows will be smaller, making it even harder for a project to pass the payback hurdle. For example, if the cutoff period is four years, then every project that satisfies the discounting payback rule will also satisfy payback, but the reverse is not true.
7-3. The NPV approach is consistent with shareholder maximization because it suggests that firms should only accept projects that earn returns above the opportunity costs of the firm’s investors. The NPV in effect measures the dollar contribution that the given project is expected to make to the firm’s overall value. If a firm invests in a project with NPV > $0, then the share price will rise. Conversely, a firm’s share price will fall if it invests in projects with NPV < $0.
7-4. It is true that long-term projections are more prone to error than are short-term projections. However, there are two reasons why this simple truth does not lead to the conclusion that the payback approach is superior to NPV. First, the payback approach itself implicitly makes long-term cash flow projections. Specifically, the payback approach forecasts zero cash flows beyond the payback horizon. The real question is not whether long-term forecasts are more or less accurate than short-term forecasts are, but whether a long-term forecast can be more accurate than a naïve guess of zero. Second, via discounting, the NPV approach makes an adjustment for the high degree of risk in long-term projections. The farther into the future that a given project’s cash flows arrive, the less valuable those cash flows are in an NPV calculation. NPV automatically adjusts for project time by using an exponentially smaller discount rate applied to later cash flows.
7-5. Any method can be manipulated. Smart managers must be aware of this and must be prepared to press analysts to justify their numbers. Opportunities to manipulate the numbers are not unique to the NPV approach and can therefore not be used to justify payback, accounting rate of return, or any other approach over NPV. It would be hard to argue that accounting numbers can’t be manipulated after all the accounting scandals, starting with Enron in late 2001. Managers should have incentives to provide the most accurate information possible.
7-6. a. A firm that consistently earns returns higher than its opportunity cost of capital is adding value to the firm, and its stock returns should increase. Stock returns should be well above average for companies of this risk level.
b. For the project returning 18%, as long as it returns enough to compensate for the risk of the project, it is adding value and shareholders will be happy about the decision to accept the project.
7-7. The IRR suffers from several problems. The IRR is not well suited to ranking projects with very different scales or projects with very different cash flow timing patterns due to the reinvestment assumption. The IRR method can also yield no solution or multiple solutions that are hard to interpret. Despite the flaws, the IRR method enjoys widespread use because in most investment situations it generates reliable accept/reject recommendations and it is easy to interpret intuitively. The MIRR method uses a more realistic reinvestment rate. Also, there can be only one MIRR for a project.
7-8. Because the discounted payback period equals the life of the projected, the sum of all of the discounted cash flows must equal the cost of the project. This indicates that the NPV must also be zero and that the IRR equals 10% because the NPV is zero.
7-9. The NPV is the most appropriate capital budgeting method because it yields correct accept/reject situations and correct project rankings. Nevertheless, it is somewhat less intuitive than the IRR. In projects with cash flow streams that switch signs, the IRR method can yield multiple solutions. In those cases, it is difficult for a firm to know whether to accept or reject a project based upon its IRR.
7-10. The NPV is calculated by discounting all of a project’s cash flows to the present. The IRR is calculated by finding the discount rate, which equates the NPV to zero. The profitability index is the ratio of the present value of a project’s cash flows (excluding the initial cash outflow) divided by the initial cash outflow. All three methods lead to the same accept/reject decision when evaluating a single project, but IRR and PI have problems when ranking projects. NPV generally overcomes these problems.
7-11. IRR, NPV, and PI can lead to different decisions when they are used to rank projects or to select between mutually exclusive projects. IRR and PI methods are not well suited to evaluating projects that vary in scale. The NPV method yields correct project rankings no matter what the scale of the project.
7-12. If an unlimited capital budget exists, firms should always accept every independent project with NPV > $0. When funds are limited, firms should select the group of projects which has the highest aggregate NPV yet stays within the budget constraint.
7-13. Project A recovers its cost in 2 years and Project B recovers its cost in 3 years. Consequently, the payback period for Project A is two years and the payback period for Project B is three years making Project A preferred based on the shortest payback period criteria. However, Project B is the better project because of the $10,000.00 cash flow in the fourth year. The problem with the payback criteria is that it does not encompass all of the cash flows of the project.
Answers to problems
7-1. a. If the computers are depreciated on a straight-line basis, depreciation will be $5,000 per year for 4 years. Contribution to net income will be:
Year 1 / Year 2 / Year 3 / Year 4$7,500 / $9,100 / $9,100 / $9,100
–5,000 / –5,000 / –5,000 / –5,000
$2,500 / $4,100 / $4,100 / $4,100
The average net income is ($2,500 + $4,100 + $4,100 + $4,100)/4 = $3,700
b. The average book value of the investment is ($20,000 + 0)/2 = $10,000.
c. The average accounting rate of return = Average net income/Average book value of the investment = $3,700/$10,000 = .37 or 37%.
d. The payback period is 2.37 years, based on cash flow numbers, not net income.
e. This is not an appropriate method for evaluating capital budgeting projects. It does not take time value of money into account, nor does it look at cash flows. It also does not consider the risk of the project and what would be an appropriate discount rate in light of the project's cash flows.
7-2. a. Payback on this bond is 25 years. You pay $1,000; you receive $40 a year for 25 years, a total of $1,000.
b. The bond is not necessarily a bad investment. Payback does not take time value of money into account, nor does it account for cash flows received after the payback period. It is more appropriate to calculate the NPV of an investment. Given the risk level of the bond, is 4% a fair return? If the answer is yes, then the bond may be a good investment.
c. The discounted payback, using a 4% discount rate, is 30 years. This shows that unless the acceptable payback period is decreased when discounted payback is used, vs. regular payback, then projects that return money late in the life of the investment are even more disadvantaged under discounted payback than under regular payback. NPV is a more appropriate method to use to determine the value of an investment project. The general rule is that when a project’s discounted payback period is the same as its life, then the NPV must be zero.
7-3. a. Payback of Alpha = 3.5 years, payback of Beta = 2.5 years, payback of Gamma = 3.33 years
b. If the cutoff is 3 years, then only Beta is acceptable. If the cutoff is 4 years, then all of the projects are acceptable.
c. Beta has the fastest payback.
d. If the firm uses discounted payback with a cutoff of 4 years, then Alpha will payback in more than 5 years, Beta in just under 3 years and Gamma in between 4 and 5 years. This means only Beta is acceptable. Calculations are shown in the table that follows.
Alpha ($1,500,000) / Beta ($400,000) / Gamma ($7,500,000)End of Year / CF / PV of CF @ 15% / Cum PV / CF / PV of CF @ 15% / Cum PV / CF / PV of CF @ 15% / Cum PV
1 / 300K / $260,870 / $260,870 / 100K / $86,957 / $86,957 / 2,000K / $1,739,130 / $1,739,130
2 / 500K / 378,072 / 638,942 / 200K / 165,997 / 252,954 / 3,000K / 226,8431 / 4,007,561
3 / 500K / 328,758 / 967,700 / 200K / 151,229 / 404,183 / 2,000K / 1,315,032 / 5,322,593
4 / 400K / 228,701 / 1,196,401 / 100K / 68,887 / 473,070 / 1,500K / 857,630 / 6,180,223
5 / 300K / 149,153 / 1,354,554 / -200K / -125,517 / 347,553 / 5,500K / 2,734,472 / 8,914,695
Disc Pay-back / >5 years
Reject / >3 & 4 years <
Accept / >4 & 5 years<
Reject
e. Project Beta should be rejected. You must pay out a total of .6 million and take in .6 million. When there is a time value to money, in other words, a positive interest rate, this is unacceptable. If cash inflows and outflows are the same, this is a negative net present value project.
f. Project Gamma is rejected using discounted payback (as noted in d.), but even without discounting, seems to have a high dollar return for the investment. You pay $7.5 million and receive a total of $14 million in cash inflows. Unless the firm has a very high discount rate, greatly lowering the value of the last $5.5 million cash flow, this is likely to be an attractive investment.
7-4. a. To determine the accounting rate of return (AAR) we need to first determine the annual net income by subtracting the depreciation from the Cash Flow, as shown in the table below.
Asset A / Asset B$200,000 ÷ 2 = $100,000 / $180,000 ÷ 2 = $90,000
Year / CF / Depr. / Net Income / CF / Depr. / Net Income
1 / $70,000 / $40,000 / $30,000 / $80,000 / $36,000 / $44,000
2 / $80,000 / $40,000 / $40,000 / $90,000 / $36,000 / $54,000
3 / $90,000 / $40,000 / $50,000 / $30,000 / $36,000 / $(6,000)
4 / $90,000 / $40,000 / $50,000 / $40,000 / $36,000 / $4,000
5 / $100,000 / $40,000 / $60,000 / $40,000 / $36,000 / $4,000
Average = / $46,000 / Average = / $20,000
ARRA = $46,000 ÷ $100,000 = 46%
ARRB = $20,000 ÷ $90,000 = 22.22%
Given that the minimum acceptable ARR is 30%, only Asset A is acceptable.
b.
Asset A / Asset BYear / Cash Flows / Amount still to be recovered / Cash Flows / Amount still to be recovered
0 / -$200,000 / -$180,000
1 / $70,000 / ($130,000) / $80,000 / ($100,000)
2 / $80,000 / ($50,000) / $90,000 / ($10,000)
3 / $90,000 / $30,000
4 / $90,000 / $40,000
5 / $100,000 / $40,000
Asset A has $50,000 left to be recovered after year 2, or 0.56 of year 3. Thus, Asset A’s payback is 2.56 years. Asset B has $10,000 to be recovered after year 2, or 0.33 of year 3. Asset B’s payback period is 2.33 years. According to the maximum payback period requirement of 2.5 years, only Asset B is acceptable.
c.
Year / Asset A / Asset BDiscounted Cash Flows / Amount still to be recovered / Discounted Cash Flows / Amount still to be recovered
0 / ($200,000) / ($180,000)
1 / $62,500 / ($137,500) / $71,429 / ($108,571)
2 / $63,776 / ($73,724) / $71,747 / ($36,824)
3 / $64,060 / ($9,664) / $21,353 / ($15,471)
4 / $57,197 / $25,421
5 / $56,743 / $22,697
After the third year, Asset A still has $9,664 left to be recovered. This represents 0.17 of the year; thus, Asset A’s discounted payback period is 3.17 years. Asset B still needs to recover $15,471 after the third year. This is 0.61 of the fourth year. Thus, Asset B’s discounted payback period is 3.61 years. Asset A is acceptable according to the firm’s maximum discounted payback period.
d. All the evaluation methods suffer from serious flaws. The firm should re-evaluate the projects using the NPV method or the MIRR method.
7-5. a. This project has CF0 = –$15,000, and 20 inflows of $13,000. At a 14% discount rate, its NPV is $71,100.70. This is a positive NPV and an acceptable project.
b. This project has CF0 = –$32,000 and 20 inflows of $4,000. At 14%, its NPV is –$5,507.48. This is a negative NPV and is not acceptable.
c. This project has CF0 = –$50,000, and 20 inflows of $8,500. At a 14% discount rate, its NPV is $6,296.61. This is a positive NPV and an acceptable project.
7-6. CF0 = –$19,000
Cash flows of $4,000/year for 8 years.
a. NPV at 10% = $2,339.70, accept
b. NPV at 12% = $870.56, accept
c. NPV at 14% = –$444.54, reject
Only positive NPV projects are acceptable. As the discount rate increases, NPV decreases. At some point, if the discount rate is high enough, a previously acceptable project at lower discount rates may become unacceptable.
7-7. Discount rate = 14%
Project
/NPV
/Decision
A / –$4,351.65 / RejectB / $67,678.24 / Accept
C / –$71,798.07 / Reject
D / $98,189.82 / Accept
E / $8,548.44 / Accept
7-8. Discount rate = 15%