2. Risk and Refinements in Capital Budgeting
9&10
Lecture
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

3. Learning Goals
LG1 Understand the importance of recognizing risk in the analysis of capital budgeting projects.
LG2 Discuss risk and cash inflows, scenario analysis, and simulation as behavioral approaches for dealing with risk.
LG3 Review the unique risks that multinational companies face.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

4. Learning Goals (cont.)
LG4 Describe the determination and use of risk-adjusted discount rates (RADRs), portfolio effects, and the practical aspects of RADRs.
LG5 Select the best of a group of unequal-lived, mutually exclusive projects using annualized net present values (ANPVs).
LG6 Explain the role of real options and the objective and procedures for selecting projects under capital rationing.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

5. Introduction to Risk in Capital Budgeting
Thus far, we have assumed that all investment projects have the same level of risk as the firm.
In other words, we assumed that all projects are equally risky, and the acceptance of any project would not change the firm’s overall risk.
In actuality, these situations are rare—projects are not equally risky, and the acceptance of a project can affect the firm’s overall risk.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

6. Table 12.1 Cash Flows and NPVs for Bennett Company’s Projects
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

7. Behavioral Approaches for Dealing with Risk: Risk and Cash Inflows
Behavioral approaches can be used to get a “feel” for the level of project risk, whereas other approaches try to quantify and measure project risk.
Risk (in capital budgeting) refers to the uncertainty surrounding the cash flows that a project will generate or, more formally, the degree of variability of cash flows.
In many projects, risk stems almost entirely from the cash flows that a project will generate several years in the future, because the initial investment is generally known with relative certainty.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

8. Behavioral Approaches for Dealing with Risk: Risk and Cash Inflows (cont.)
Treadwell Tire Company, a tire retailer with a 10% cost of capital, is considering investing in either of two mutually exclusive projects, A and B. Each requires a $10,000 initial investment, and both are expected to provide constant annual cash inflows over their 15-year lives. For either project to be acceptable its NPV must be greater than zero.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

9. Behavioral Approaches for Dealing with Risk: Risk and Cash Inflows (cont.)
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

10. Behavioral Approaches for Dealing with Risk: Scenario Analysis
Scenario analysis is a behavioral approach that uses several possible alternative outcomes (scenarios), to obtain a sense of the variability of returns, measured here by NPV.
Scenario analysis is a risk analysis technique that consider both-
1. the sensitivity of NPV to changes in key variables
2. the likely range of variable values
On which a project’s stand – alone risk depends.
In capital budgeting, one of the most common scenario approaches is to estimate the NPVs associated with pessimistic (worst), most likely (expected), and optimistic (best) estimates of cash inflow.
The range can be determined by subtracting the pessimistic-outcome NPV from the optimistic-outcome NPV.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

11. Table 12.2 Scenario Analysis of Treadwell’s Projects A and B
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

12. Scenario Analysis of Treadwell’s Projects A and B
Continuing with Treadwell Tire Company, assume that the financial manager created three scenarios for each project: pessimistic, most likely, and optimistic. The cash inflows and resulting NPVs in each case are summarized in Table Comparing the ranges of cash inflows ($1,000 for project A and $4,000 for B) and, more important, the ranges of NPVs ($7,606 for project A and $30,424 for B) makes it clear that project A is less risky than project B. Given that both projects have the same most likely NPV of $5,212, the assumed risk-averse decision maker will take project A because it has less risk (smaller NPV range) and no possibility of loss (all NPVs $0).
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

13. Classroom Practice
Murdock Paints is in the process of evaluating two mutually exclusive additions to its processing capacity. The firm’s financial analysts have developed pessimistic, most likely, and optimistic estimates of the annual cash inflows associated with each project. These estimates are shown in the following table.
a. Determine the range of annual cash inflows for each of the two projects.
b. Assume that the firm’s cost of capital is 10% and that both projects have 20-year lives. Construct a table similar to this for the NPVs for each project. Include the range of NPVs for each project.
c. Do parts a and b provide consistent views of the two projects? Explain.
d. Which project do you recommend? Why?
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

14. Solution:1/3 Range of NPV = 7,324.41-(-6,297.29)= $ 13621.70
Range A = $1,800 - $200 = $1,600, Range B = $1,100 - $900 = $200
Calculation of NPV and Range of NPV for project A :
Range of NPV = 7, (-6,297.29)= $
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

15. Solution:2/3 Range of NPV = 1,364.92-(-337.79)= $ 1,702.71
Calculation of NPV and Range of NPV for project B :
Range of NPV = 1, ( )= $ 1,702.71
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

16. Solution:2/3 Summary of part b:
c. Although the “most likely” outcome is identical for Project A and B, the NPV range varies considerably.
d. From the summary of part b, We have seen that Project A has more risk and greater return than project B. Thus selection of project would depend upon the risk attitude of the management.
NPVs
Outcome
Project A
Project B
Pessimistic
-$ 6,297.29 -$
Most likely
513.56
Optimistic
7,324.41
1,364.92
Range
$13,621.70
$1,702.71
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

17. Behavioral Approaches for Dealing with Risk: Simulation
Simulation is a statistics-based behavioral approach that applies predetermined probability distributions and random numbers to estimate risky outcomes.
Again it is a risk analysis technique in which probable future events are simulated on a computer, generating a probability distribution that indicates the most likely outcomes.
Using a computer because the process just described is repeated again and again, say, for 500 times, which results in 500 NPVs and a probability distribution for the project’s NPV values.
By tying the various cash flow components together in a mathematical model and repeating the process numerous times, the financial manager can develop a probability distribution of project returns.
This probability distribution of project returns can be used to determine the most likely range of outcomes to be expected from a project.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

18. Why Monte Carlo simulation rarely used in industry?
One of the problems with using a Monte Carlo program is the difficulty of establishing the correct input ranges for the variables and determining the correlation coefficients for those variables.
Monte Carlo simulation is not easy to apply because it is often difficulty to specify the relationship, or correlations, among the uncertain cash flow variables.
The problem is not insoluble, but it is important not to underestimate the difficulty of obtaining valid estimates.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

19. Figure 12.1 NPV Simulation
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

20. Behavioral Approaches for Dealing with Risk: Simulation
Figure 12.1 presents a flowchart of the simulation of the net present value of a project. The process of generating random numbers and using the probability distributions for cash inflows and cash outflows enables the financial manager to determine values for each of these variables.
Substituting these values into the mathematical model results in an NPV. By repeating this process perhaps a thousand times, managers can create a probability distribution of net present values.
Although Figure 12.1 simulates only gross cash inflows and cash outflows, more sophisticated simulations using individual inflow and outflow components, such as sales volume, sale price, raw material cost, labor cost, or maintenance expense, are quite common. From the distribution of returns, the decision maker can determine not only the expected value of the return but also the probability of achieving or surpassing a given return.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

21. Behavioral Approaches for Dealing with Risk: Simulation
A Monte Carlo simulation program requires the user to first build an Excel spreadsheet model that captures the input variables for the proposed project. What issues and what benefits can the user derive from this process?
The use of computers has made the simulation approach feasible.
Monte Carlo simulation programs, made popular by widespread use of personal computers, are described in the nearby Focus on Practice box.
The output of simulation provides an excellent basis for decision making, because it enables the decision maker to view a continuum of risk–return tradeoffs rather than a single-point estimate.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

22. International Risk Considerations
Exchange rate risk is the danger that an unexpected change in the exchange rate between the dollar and the currency in which a project’s cash flows are denominated will reduce the market value of that project’s cash flow.
In the short term, much of this risk can be hedged by using financial instruments such as foreign currency futures and options.
Long-term exchange rate risk can best be minimized by financing the project in whole or in part in the local currency.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

23. Matter of Fact
A 2001 survey of Chief Financial Officers (CFOs) found that more than 40% of the CFOs felt that it was important to adjust an investment project’s cash flows or discount rates to account for foreign exchange risk.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

24. International Risk Considerations (cont.)
Political risk is much harder to protect against. Firms that make investments abroad may find that the host-country government can limit the firm’s ability to return profits back home. Governments can seize the firm’s assets, or otherwise interfere with a project’s operation.
The difficulties of managing political risk after the fact make it even more important that managers account for political risks before making an investment.
They can do so either by adjusting a project’s expected cash inflows to account for the probability of political interference or by using risk-adjusted discount rates in capital budgeting formulas.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

25. International Risk Considerations (cont.)
Other special issues relevant for international capital budgeting include:
Taxes: financial managers must carefully account for taxes paid to foreign governments on profits earned within their borders. They must also assess the impact of these tax payments on the parent company’s U.S. tax liability.
Transfer pricing: MNCs is involving, in reality, simply the shipment of goods and services from one of a parent company’s subsidiaries to another subsidiary located abroad. The parent company therefore has great discretion in setting transfer prices, the prices that subsidiaries charge each other for the goods and services traded between them. The widespread use of transfer pricing in international trade makes capital budgeting in MNCs very difficult unless the transfer prices that are used accurately reflect actual costs and incremental cash flows.
Strategic, rather than financial considerations: For example, an MNC may feel compelled to invest in a country to ensure continued access, even if the project itself may not have a positive net present value.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

26. Risk-Adjusted Discount Rates
Risk-adjusted discount rates (RADR) are rates of return that must be earned on a given project to compensate the firm’s owners adequately—that is, to maintain or improve the firm’s share price.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

27. Personal Finance Example
Talor Namtig is considering investing $1,000 in either of two stocks—A or B. She plans to hold the stock for exactly 5 years and expects both stocks to pay $80 in annual end- of-year cash dividends. At the end of the year 5 she estimates that stock A can be sold to net $1,200 and stock B can be sold to net $1,500. Her research indicates that she should earn an annual return on an average risk stock of 11%. Because stock B is considerably riskier, she will require a 14% return from it. Talor makes the following calculations to find the risk-adjusted net present values (NPVs) for the two stocks:
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

28. Personal Finance Example (cont.)
Although Talor’s calculations indicate that both stock investments are acceptable (NPVs > $0), on a risk-adjusted basis, she should invest in Stock B because it has a higher NPV.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

29. Risk-Adjusted Discount Rates: Review of CAPM
Using beta, bj, to measure the relevant risk of any asset j, the CAPM is
rj = RF + [bj  (rm – RF)]
where rj =
required return on asset j RF
risk-free rate of return bj
beta coefficient for asset j rm
return on the market portfolio of assets
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

30. Figure CAPM and SML
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

31. Risk-Adjusted Discount Rates: Using CAPM to Find RADRs (cont.)
Figure 12.2 shows two projects, L and R.
Project L has a beta, bL, and generates an internal rate of return, IRRL. The required return for a project with risk bL is rL.
Because project L generates a return greater than that required (IRRL > rL), project L is acceptable.
Project L will have a positive NPV when its cash inflows are discounted at its required return, rL.
Project R, on the other hand, generates an IRR below that required for its risk, bR (IRRR < rR).
This project will have a negative NPV when its cash inflows are discounted at its required return, rR.
Project R should be rejected.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

32. Risk-Adjusted Discount Rates: Applying RADRs in Bennett Company
Bennett Company wishes to apply the Risk-Adjusted Discount Rate (RADR) approach to determine whether to implement Project A or B. In addition to the data presented earlier, Bennett’s management assigned a “risk index” of to project A and 1.0 to project B as indicated in the following table. The required rates of return associated with these indexes are then applied as the discount rates to the two projects to determine NPV.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

33. Risk-Adjusted Discount Rates: Applying RADRs (cont.)
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

34. Figure 12.3a Calculation of NPVs for Bennett Company’s Capital Expenditure Alternatives Using RADRs
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

35. Figure 12.3b Calculation of NPVs for Bennett Company’s Capital Expenditure Alternatives Using RADRs
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

36. Risk-Adjusted Discount Rates: Applying RADRs (cont.)
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

37. Risk-Adjusted Discount Rates: Portfolio Effects
As noted earlier, individual investors must hold diversified portfolios because they are not rewarded for assuming diversifiable risk.
Because business firms can be viewed as portfolios of assets, it would seem that it is also important that they too hold diversified portfolios.
Surprisingly, however, empirical evidence suggests that firm value is not affected by diversification.
In other words, diversification is not normally rewarded and therefore is generally not necessary.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

38. Risk-Adjusted Discount Rates: Portfolio Effects (cont.)
It turns out that firms are not rewarded for diversification because investors can do so themselves.
An investor can diversify more readily, easily, and costlessly simply by holding portfolios of stocks.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

39. Table 12.3 Bennett Company’s Risk Classes and RADRs
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

40. Risk-Adjusted Discount Rates: RADRs in Practice (cont.)
Assume that the management of Bennett Company decided to use risk classes to analyze projects and so placed each project in one of four risk classes according to its perceived risk. The classes ranged from I for the lowest-risk projects to IV for the highest-risk projects.
The financial manager of Bennett has assigned project A to class III and project B to class II. The cash flows for project A would be evaluated using a 14% RADR, and project B’s would be evaluated using a 10% RADR. The NPV of project A at 14% was calculated in Figure 12.3 to be $6,063, and the NPV for project B at a 10% RADR was shown in Table 12.1 to be $10,924.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

41. Classroom Practice:
Centennial Catering, Inc., is considering two mutually exclusive investments. The company wishes to use a CAPM-type risk adjusted discount rate (RADR) in its analysis. Centennial’s managers believe that the appropriate market rate of return is 12%, and they observe that the current risk-free rate of return is 7%. Cash flows associated with the two projects are shown in the following table.
a. Use a risk-adjusted discount rate approach to calculate the net present value of each project, given that project X has an RADR factor of and project Y has an RADR factor of The RADR factors are similar to project betas.
b. Discuss your findings in part a, and recommend the preferred project.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

42. Solution: a. rX = 7% + 1.2(12% - 7%) = 7% + 6% = 13%
rY = 7% + 1.4(12% - 7%) = 7% + 7% = 14%
NPV calculation for X:
NPV = $19,234.14
NPV calculation for Y:
NPV = $18,805.82
b. The RADR approach prefers Project Y over Project X. The RADR approach combines the risk adjustment and the time adjustment in a single value. The RADR approach is most often used in business.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

43. Capital Budgeting Refinements: Comparing Projects With Unequal Lives
The financial manager must often select the best of a group of unequal-lived projects.
If the projects are independent, the length of the project lives is not critical.
But when unequal-lived projects are mutually exclusive, the impact of differing lives must be considered because the projects do not provide service over comparable time periods.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

44. Capital Budgeting Refinements: Comparing Projects With Unequal Lives (cont.)
The AT Company, a regional cable-TV firm, is evaluating two projects, X and Y. The projects’ cash flows and resulting NPVs at a cost of capital of 10% is given below.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

45. NPV for Project X NPV for Project Y
Capital Budgeting Refinements: Comparing Projects With Unequal Lives (cont.)
NPV for Project X NPV for Project Y
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

46. Capital Budgeting Refinements: Comparing Projects With Unequal Lives (cont.)
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

47. Capital Budgeting Refinements: Comparing Projects With Unequal Lives (cont.)
Ignoring the difference in their useful lives, both projects are acceptable (have positive NPVs). Furthermore, if the projects were mutually exclusive, project Y would be preferred over project X. However, it is important to recognize that at the end of its 3 year life, project Y must be replaced, or renewed.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

48. Step 3 Select the project that has the highest ANPV.
Capital Budgeting Refinements: Comparing Projects With Unequal Lives (cont.)
The annualized net present value (ANPV) approach is an approach to evaluating unequal-lived projects that converts the net present value of unequal-lived, mutually exclusive projects into an equivalent annual amount (in NPV terms).
Step 1 Calculate the net present value of each project j, NPVj, over its life, nj, using the appropriate cost of capital, r.
Step 2 Convert the NPVj into an annuity having life nj. That is, find an annuity that has the same life and the same NPV as the project.
Step 3 Select the project that has the highest ANPV.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

49. NPVX = $11,277.24 (table value = $11,248)
Capital Budgeting Refinements: Comparing Projects With Unequal Lives (cont.)
By using the AT Company data presented earlier for projects X and Y, we can apply the three-step ANPV approach as follows:
Step 1 The net present values of projects X and Y discounted at 10%—as calculated in the preceding example for a single purchase of each asset—are
NPVX = $11, (table value = $11,248)
NPVY = $19, (table value = $18,985)
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

50. Capital Budgeting Refinements: Comparing Projects With Unequal Lives (cont.)
Step 2 In this step, we want to convert the NPVs from Step 1 into annuities. For project X, we are trying to find the answer to the question, what 3- year annuity (equal to the life of project X) has a present value of $11,248 (the NPV of project X)? Likewise, for project Y we want to know what 6-year annuity has a present value of $18,985. Once we have these values, we can determine which project, X or Y, delivers a higher annual cash flow on a present value basis.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

51. Capital Budgeting Refinements: Comparing Projects With Unequal Lives (cont.)
Project X Project Y
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

52. Capital Budgeting Refinements: Comparing Projects With Unequal Lives (cont.)
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

53. Capital Budgeting Refinements: Comparing Projects With Unequal Lives (cont.)
Step 3 Reviewing the ANPVs calculated in Step 2, we can see that project X would be preferred over project Y. Given that projects X and Y are mutually exclusive, project X would be the recommended project because it provides the higher annualized net present value.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

54. Class Work
Evans Industries wishes to select the best of three possible machines, each of which is expected to satisfy the firm’s ongoing need for additional aluminum-extrusion capacity. The three machines—A, B, and C—are equally risky. The firm plans to use a 12% cost of capital to evaluate each of them. The initial investment and annual cash inflows over the life of each machine are shown in the following table.
a. Calculate the NPV for each machine over its life. Rank the machines in descending order on the basis of NPV.
b. Use the annualized net present value (ANPV) approach to evaluate and rank the machines in descending order on the basis of ANPV.
c. Compare and contrast your findings in parts a and b. Which machine would you recommend that the firm acquire? Why?
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

55. Solution: b. a. NPV for Machine A = -$42,663.11
NPV for Machine B = $6,646.58
NPV for Machine C = $7,643.29 b.
Rank
Machine 1 C 2 B 3 A
Rank
Machine 1 B 2 C 3 A
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

56. Recognizing Real Options
Real options are opportunities that are embedded in capital projects that enable managers to alter their cash flows and risk in a way that affects project acceptability (NPV).
Also called strategic options.
By explicitly recognizing these options when making capital budgeting decisions, managers can make improved, more strategic decisions that consider in advance the economic impact of certain contingent actions on project cash flow and risk.
NPVstrategic = NPVtraditional + Value of real options
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

57. Table 12.4 Major Types of Real Options
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

58. Recognizing Real Options (cont.)
Assume that a strategic analysis of Bennett Company’s projects A and B finds no real options embedded in Project A but two real options embedded in B:
During it’s first two years, B would have downtime that results in unused production capacity that could be used to perform contract manufacturing;
Project B’s computerized control system could control two other machines, thereby reducing labor costs.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

59. Recognizing Real Options (cont.)
Bennett’s management estimated the NPV of the contract manufacturing over the two years following implementation of project B to be $1,500 and the NPV of the computer control sharing to be $2,000. Management felt there was a 60% chance that the contract manufacturing option would be exercised and only a 30% chance that the computer control sharing option would be exercised. The combined value of these two real options would be the sum of their expected values.
Value of real options for project B
= (0.60  $1,500) + (0.30  $2,000)
= $900 + $600 = $1,500
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

60. Recognizing Real Options (cont.)
Adding the $1,500 real options value to the traditional NPV of $10,924 for project B, we get the strategic NPV for project B.
NPVstrategic = $10,924 + $1,500 = $12,424
Bennett Company’s project B therefore has a strategic NPV of $12,424, which is above its traditional NPV and now exceeds project A’s NPV of $11,071. Clearly, recognition of project B’s real options improved its NPV (from $10,924 to $12,424) and causes it to be preferred over project A (NPV of $12,424 for B > NPV of $11,071 for A), which has no real options embedded in it.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

61. Capital Rationing
Firm’s often operate under conditions of capital rationing—they have more acceptable independent projects than they can fund.
In theory, capital rationing should not exist—firms should accept all projects that have positive NPVs.
However, in practice, most firms operate under capital rationing.
Generally, firms attempt to isolate and select the best acceptable projects subject to a capital expenditure budget set by management.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

62. Capital Rationing (cont.)
The internal rate of return approach is an approach to capital rationing that involves graphing project IRRs in descending order against the total dollar investment to determine the group of acceptable projects.
The graph that plots project IRRs in descending order against the total dollar investment is called the investment opportunities schedule (IOS).
The problem with this technique is that it does not guarantee the maximum dollar return to the firm.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

63. Capital Rationing (cont.)
Tate Company, a fast growing plastics company with a cost of capital of 10%, is confronted with six projects competing for its fixed budget of $250,000.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

64. Figure 12.4 Investment Opportunities Schedule
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

65. Capital Rationing (cont.)
The net present value approach is an approach to capital rationing that is based on the use of present values to determine the group of projects that will maximize owners’ wealth.
It is implemented by ranking projects on the basis of IRRs and then evaluating the present value of the benefits from each potential project to determine the combination of projects with the highest overall present value.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

66. Table 12.5 Rankings for Tate Company Projects
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

67. Class Work & Home Work
Valley Corporation is attempting to select the best of a group of independent projects competing for the firm’s fixed capital budget of $4.5 million. The firm recognizes that any unused portion of this budget will earn less than its 15% cost of capital, thereby resulting in a present value of inflows that is less than the initial investment. The firm has summarized, in the following table, the key data to be used in selecting the best group of projects.
a. Use the internal rate of return (IRR) approach to select the best group of projects.
b. Use the net present value (NPV) approach to select the best group of projects.
c. Compare, contrast, and discuss your findings in parts a and b.
d. Which projects should the firm implement? Why?
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

68. Solution:
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

69. Homework-1
Birkenstock is considering an investment in a nylon-knitting machine. The machine requires an initial investment of $25,000, has a 5-year life, and has no residual value at the end of the 5 years. The company’s cost of capital is 12%. Known with less certainty are the actual after-tax cash inflows for each of the 5 years. The company has estimated expected cash inflows for three scenarios: pessimistic, most likely, and optimistic. These expected cash inflows are listed in the following table. Calculate the range for the NPV given each scenario.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

70. Homework-2
James Secretarial Services is considering the purchase of one of two new personal computers, P and Q. The company expects both to provide benefits over a 10-year period, and each has a required investment of $3,000. The firm uses a 10% cost of capital. Management has constructed the following table of estimates of annual cash inflows for pessimistic, most likely, and optimistic results.
a. Determine the range of annual cash inflows for each of the two computers.
b. Construct a table similar to this for the NPVs associated with each outcome for both computers.
c. Find the range of NPVs, and subjectively compare the risks associated with purchasing these computers.
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU

71. Homework-3
Richard and Linda Butler decide that it is time to purchase a high-definition (HD) television because the technology has improved and prices have fallen over the past 3 years. From their research, they narrow their choices to two sets, the Samsung 42-inch LCD with 1080p capability and the Sony 42-inch LCD with 1080p features. The price of the Samsung is $2,350 and the Sony will cost $2,700. They expect to keep the Samsung for 3 years; if they buy the more expensive Sony unit, they will keep the Sony for 4 years. They expect to be able to sell the Samsung for $400 by the end of 3 years; they expect they could sell the Sony for $350 at the end of year 4. Richard and Linda estimate the end-of-year entertainment benefits (that is, not going to movies or events and watching at home) from the Samsung to be $900 and for the Sony to be $1,000. Both sets can be viewed as quality units and are equally risky purchases. They estimate their opportunity cost to be 9%. The Butlers wish to choose the better alternative from a purely financial perspective. To perform this analysis they wish to do the following: a. Determine the NPV of the Samsung HD LCD. b. Determine the ANPV of the Samsung HD LCD. c. Determine the NPV of the Sony HD LCD. d. Determine the ANPV of the Sony HD LCD. e. Which set should the Butlers purchase and why?
Md. Kayes Bin Rahaman, Assistant professor, SOB, BOU