2. A project under consideration at Stanley's Chemical Company would cost $30 million and return

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1 Basic Capital Budgeting Problems 1. A project under consideration at Robert's Chemical Company would cost $10 million and return benefits of $6 million, $5 million, and $4 million at the end of years 1 through 3, respectively. Calculate the NPV at 10%, and then calculate the internal rate of return. 2. A project under consideration at Stanley's Chemical Company would cost $30 million and return benefits of $25 million at the end of year 1 followed by $ million at the end of year 2. Calculate the NPV at 15%, and then calculate the internal rate of return. 3. A project under consideration at Sarah's Chemical Company would cost $50 million and return benefits of $26 million at the end of year 1 followed by $50.7 million at the end of year 2. Calculate the NPV at 15%, and then calculate the internal rate of return. 4. North States Power Company is considering a hydropower project. It would cost $100 million to build a facility that would take advantage of a serendipitous gift of nature. A certain swift river running through a mountainous region passes through a narrow valley adjacent to a mountain called White's Peak. On the other side of White's Peak is a much deeper valley, but the mountain prevents the river from reaching it. An abandoned mine, however, bores through the mountain and comes within a short distance of the river. By running a pipeline through the mine and boring on to the river, a substantial flow of water could be diverted into penstocks flowing to the lower valley. A hydroelectric power plant would be built to take advantage of the steady flow of water to drive its turbines. Once built, the plant would operate automatically and require minimal maintenance. North States Power expects to get electricity worth $12 million per year over the thirty-year life of the plant, net of operating and maintenance costs as well as tax considerations. It is reasonable to consider this cash flow to be spread continuously over the life of the plant, rather than arriving in lump sums at discrete intervals. Discounting at 10% compounded continuously, calculate the project's NPV. 5. Morgana Industries has been working for several years to develop a new bio-engineered membrane for use in oil refining. Over the years, there have been several setbacks, and the total investment to date is $30 million. To complicate matters, an additional investment of $10 million is needed to finish the work. At this point it is virtually certain that a successful product would result from the additional investment, and it would be expected to produce after-tax revenues of $5 million per year for the next five years. Myron Blomquist, the CFO, is opposed to the additional investment. He recently stated, After this new investment, we would have a total of $40 million sunk into this activity. The projections indicate only $25 million in total return, spread over a five year period. I just don't know any way to explain to the stockholders why we would spend $40 million in order to get back $25 million. The opportunity cost of capital for the project is 15%. What is the project's expected NPV at this time? What should the company do? 6. Abernathy Products Company management is considering buying a new machine for the production line. They are considering two choices, one of which might go on the line if justified by anticipated benefits. The Linear Processor would cost $100,000 and produce expected benefits of $22,000 annually after tax for the next 5 years. The Non-Linear Processor would cost an extra $50,000 and produce an additional $14,000 in annual after-tax benefits. Both machines have the same expected life, and an expected salvage value of zero. Abernathy traditionally uses an incremental approach to project analysis, so management is focusing on the extra costs and benefits associated with the Non- Linear Processor. The opportunity cost of capital is 8%. Compute the incremental NPV for the Nonlinear processor. Then compute the NPV on a full cost basis. What should management decide? What does this problem reveal about incremental analysis? 7. A project under consideration at Oxxon Petroleum Company is considered to be about half as risky as the average-risk investment, from the viewpoint of relevant risk. The T-Bill rate is 10%, and the expected return for average-risk investments is 15%. What should be the required rate of return for the project. 8. A project under consideration at Brandywine Industries has an estimated beta of 1.1 (it is 1.1 times as risky as average), and has an expected return of 22%. The expected return on the average-risk investment is 15%, and the return on T-Bills is 10%. Is the project's NPV positive, negative, or zero? Prof. Kensinger page 1

2 9. A project under consideration at Acme Manufacturing Company has expected return of 16% with beta of.75. The T-Bill rate is 12% and the expected return on the average-risk investment is 17%. Is the project's NPV positive, negative, or zero? 10. The managers of Flying Aces Courier Service are analyzing a proposed aircraft modification that would save the company an estimated 100,000 gallons of fuel per year. Flying Aces has a large enough fuel storage facility to enable them to buy all their fuel for a year's operations at one time, and they currently have enough fuel on hand for the next year. Thus they won't need to buy more fuel until the end of the first year of the proposed project's life. It would cost $800,000 to have the fleet modified, and the resulting savings would go on for five years. At the current price of $2 per gallon for fuel, the savings would be $200,000 per year. The nominal opportunity cost of capital for the project is 15% compounded annually, and the expected rate of inflation in fuel prices is 10% compounded annually. Calculate the project's net present value. 11. Art Grunnion wants to start a company which would build open-ocean speedboats of the highest possible quality. He would put $1 million into the company on October 10, Even with all its earnings plowed back into the company, he expects that he will have to follow up his initial investment with additional $1 million investments on the company's anniversary date in each of the next four years (2007, 2008, 2009, and 2010). In 2011 (assume that it will be on the 10 th of October), he expects to be able to sell the company for $10 million. Calculate the expected IRR for this bit of venture capital financing. Is it a good investment, if the opportunity cost of capital is 15%. 12. Abercrombie Products is considering a project that has the following series of expected cash flows: Initial cash flow is positive $125,000, followed by outflows of $42,000 per year at the end of years 1 through 5. The opportunity cost of capital is 12%. Calculate the project's IRR and decide whether to recommend acceptance or rejection. 13. Amalgamated Ajax management must choose between two mutually-exclusive projects. Project A requires an investment of $30 million, has a life of 10 years, a net present value of $3 million, and an internal rate of return of 20%. Project B has the same level of risk as A, but costs only $12 million. It has a net present value of $2.25 million, an economic life of 5 years, and an internal rate of return of 25%. Capital rationing is not in effect in the firm. Which project should be selected and why? Why is there a conflict between IRR and NPV? 14. Mort Enterprises is looking at a project that would cost $10,000 to get started. It would return $62,500 at the end of year 1, and would cost $62,500 at the end of year 2 to shut down. Calculate its NPV at 25%. Then calculate its NPV at 400%. What is its IRR? 15. The last problem is a mini-case for discussion in class. The Case of the Oxxon PC Oxxon Oil Company is one of the world's largest integrated oil companies. It explores for new reserves, produces from proven reserves, refines, and markets petroleum products around the world. In a recent meeting of the executive council, the company's strategy for the 21st Century was discussed at length. Several members expressed concern that the days of the large integrated oil firm were numbered, and proposed that the company look for new fields of endeavor. One of the suggestions that emerged from the meeting was the proposal to invest $100 million in order to get into the computer business. Mort Gronsky was the chief architect of the idea. Mort was widely respected in the oil industry for his seemingly instinctive ability to find oil in unlikely places. A very well-trained geologist, he credited his success more to good science than to good luck. Because Mort had a solid track record at finding money in the ground, many of the executives at Oxxon were predisposed to side with him on the computer proposal. The proposal was to throw the muscle of Oxxon behind a new entry into the personal computer market. As Mort pointed out, IBM designed their own PC around stock components that can be readily bought in the open markets. All IBM does is assemble the computers, brand them with the corporate logo, and market them, he remarked on one occasion. Mort went on to propose that Oxxon build an assembly facility in one of its overseas locations and produce a clone of the IBM PC. He suggested that a company the size of Oxxon ought to be able to market such machines as well as IBM. Mort had his staff do an analysis of the project. They projected sales, revenues, and costs for the operation fifteen years into the future. From the resulting cash flow estimates, they calculated a net present Prof. Kensinger page 2

3 value of $10 million for the project (its internal rate of return was 32%). Mort was very pleased with the numbers, and recommended bonuses for all of the people who had worked on the analysis. Not everyone on the executive committee was thrilled with the idea. A sample of dissenting comments includes the following: Does the world need another IBM clone? --Mary Sprotnik The big computer people will eat our lunch. --Myron Grabnash We know oil; we don't know beans about electronics. --Shirley Smithers What about software. IBM is successful because they are in a position to set the standard. Can we do that? --Ivan Eisenkopf Mort's response to this criticism was to assert that Oxxon was strong enough to overcome the difficulties. He also pointed out that if the great Oxxon company was to survive into the next century, it had to get with the important new technologies. Computers are only the start. Once we establish our high-tech credentials, we can move into bioengineering as well. Besides, the numbers are exceptional, he said in parting. Put yourself into this situation, and make your own contribution to the discussion. Try to work the spirit of the NPV Rule into your analysis. Prof. Kensinger page 3

4 FINA 5170 Solutions: Problem Set 4 Fall Use cash flow mode. Initial flow is $10MM, cash flows 1 through 3, respectively, are $6MM, $5MM, and $4MM. %I is 10, calculate NPV.. Result is $2,592,036 Next, calculate IRR. Result is 25.35% 2. Use cash flow mode. Initial flow is $30MM, cash flows 1 and 2, respectively, are $25MM and $15.625MM. %I is 15, calculate NPV.. Result is $3,553,875 Next, calculate IRR. Result is 25.00% 3. Use cash flow mode. Initial flow is $50MM, cash flows 1 and 2, respectively, are $26MM and $50.7MM. %I is 15, calculate NPV.. Result is $10,945,180 Next, calculate IRR. Result is 30.00% 4. #.1! " e" NPV = ( 30! $12, 000, 000) ( ) & % ( " $100,000,000 = $14, 025, $.1! 30 ' 5. Easiest method is cash flow mode. Then initial flow is $10MM, cash flow 1 is $5MM, and frequency is 5. %I is 15, calculate NPV.. Result is $6,760,775 The $30M invested earlier is sunk. It cannot be recovered, and is irrelevant to the decision at hand. What matters is the discretionary investment of $10M and the benefits expected from it. 6. To calculate incremental NPV, use cash flow mode. Initial flow is $50MM, cash flow 1 is $14MM, and frequency is 5. %I is 8, calculate NPV.. Result is positve, $5, Next, let s check the full-cost NPV. Initial flow is $150MM, cash flow 1 is $36MM, and frequency is 5. %I is 8, calculate NPV.. Result is negative, $6, So, why the conflict? Let s look at the base case, the linear processor. Initial flow is $100MM, cash flow 1 is $22MM, and frequency is 5. %I is 8, calculate NPV.. Result is negative, $12, So, although the incremental NPV is positive, it is not large enough to overcome the negative value of the base case. (If you add the incremental NPV to the base case NPV, you get the full-cost NPV. Recommendation: Don t buy either machine. 7. Opportunity cost of capital = 10% +.5(15% 10%) = 12.50%. 8. Opportunity cost of capital = 10% + 1.1(15% 10%) = 15.50%. Since expected return is 22%, which is above the opportunity cost, the expected NPV is positive (assuming this is a lending project). 9. Opportunity cost of capital = 12% +.75(17% 12%) = 15.75%. Since expected return is 16%, which is above the opportunity cost, the expected NPV is positive (assuming this is a lending project). 10. The easiest approach is to discount the real cash flows at the real rate. Then the data inputs for cash flow mode are as follows: initial flow is $800,000, cash flow 1 is $200,000, and frequency is 5. %I is the real rate, r. r = (15% 10%) / %. Compute the real rate, enter it directly as %I, page 1

5 FINA 5170 Solutions: Problem Set 4 Fall 2006 and calculate NPV.. Result is $76, Another approach is to discount the nominal cash flows at the nominal rate. Then the data inputs for cash flow mode are as follows: initial flow is $800,000, cash flows 1 through 5, respectively, are $220,000, $242,000, $266,200, $292,820, and $322,102. %I is 15, calculate NPV.. Here again, the result is $76, Answer is 24.07%. This can be solved as an annuity. N is 5, PMT is 1,000,000 and FV is +10,000,000. Periods-peryear setting is 1 and mode is BEGIN. Compute interest. (Note: This is an annuity due because the last payment is one period before the future value). Cash flow mode is an alternative method for calculation. Then initial flow is 1,000,000. Next flow is also 1,000,000 with frequency of 4. Final flow is +10,000,000. Then calculate IRR. 12. Easiest method is cash flow mode. Then initial flow is , cash flow 1 is 42000, and frequency is 5. When you calculate IRR, you get 20.2%, so the project might seem attractive. Yet, if you calculate NPV at 12% (that is, after setting %I at 12) you find that the NPV is negative ( $26,401); so the project should be rejected. Why the conflict? If you decided to do this project, you would be borrowing money from it at an interest rate of 20.2%, when your cost of capital is significantly less. 13. Project A has higher net present value and should be selected. The internal rate of return is biased toward shorter-lived, quicker payout projects. 14. Use cash flow mode. Initial flow is 10000, cash flow 1 is 62500, and cash flow 3 is %I is 25, calculate NPV.. Result is zero. Then change %I to 400 and calculate NPV> The result is again zero. Thus there are two correct answers for the IRR, which can happen whenever there are two sign changes in the cash flow stream. 15. The case is for class discussion. page 2