15.E: Making Good Decisions (Exercises)
- Page ID
- 22162
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15.1: Net Present Value
Mechanics
For questions 1–4, calculate the net present value and the net present value ratio.
| Problem Number | Investment (today) | Cost of Capital (annually) | Cash Outflows (at beginning) | Cash Inflows (at end) |
|---|---|---|---|---|
| 1. | $500,000 | 13% | Year 2: $100,000 | Years 2-3: $500,000 |
| 2. | $1,000,000 | 16% | Year 3: $250,000 | Years 1-4: $400,000 |
| 3. | $750,000 | 15% | Years 3 & 5: $100,000 | Years 1-6: $200,000 |
| 4. | $300,000 | 11% |
Year 2: $25,000 Year 6: $40,000 |
Years 1-3: $150,000 Year 4: $125,000 Years 5-6: $75,000 |
For questions 5 and 6, given the capital budget indicated determine the combination of projects that should be chosen, the total net present value, and total budget spent.
| 5. | 6. | ||
|---|---|---|---|
| Project #1 | Initial Cash Flow | $300,000 | $325,000 |
| \(NPV\) | $360,000 | $357,500 | |
| \(NPV_{RATIO}\) | 1.20 | 1.10 | |
| Project #2 | Initial Cash Flow | $150,000 | $400,000 |
| \(NPV\) | $165,000 | $500,000 | |
| \(NPV_{RATIO}\) | 1.10 | 1.25 | |
| Project #3 | Initial Cash Flow | $185,000 | $315,000 |
| \(NPV\) | $240,500 | $378,000 | |
| \(NPV_{RATIO}\) | 1.30 | 1.20 | |
| Capital Budget Available | $500,000 | $650,000 | |
Applications
- Citywide Courier Services projects that demand for its services will rise for a period of three years before subsiding. It can lease additional communication equipment for $1,000 at the beginning of every quarter for three years. Alternatively, it can purchase the equipment for $13,995 at 7.5% compounded quarterly. The salvage value of the equipment after three years is expected to be $4,000. Which option would you recommend? How much better is that option in today's dollars?
- A new diamond deposit has been found in northern Alberta. Your researchers have determined that it will cost $2.5 million to purchase the land and prepare it for mining. At the beginning of both the second and third years, another $1 million investment will be required to establish the mining operations. Starting at the end of the second year, the deposit is expected to earn net profits of $3 million, which will be sustained for three years before the deposit is depleted. If the cost of capital is 16%, should your company pursue this venture? Provide calculations to support your decision.
- Toys “R” Us has identified several projects that it can pursue, as listed in the table below. A capital budget of $500,000 has been set. Which projects should be undertaken? What total budget will be spent? What total net present value will be realized?
| Project | Initial Cash Flow | Net Present Value |
|---|---|---|
| #1: Renovate Manitoba outlets | $180,000 | $125,000 |
| #2: Renovate Alberta outlets | $230,000 | $210,000 |
| #3: Renovate Maritime outlets | $75,000 | $60,000 |
| #4: Renovate BC outlets | $245,000 | $250,000 |
- A company can pursue only one of two available projects, both of which require a $3 million investment today. In project A, another investment of $2 million is required at the beginning of the second year, and three years of $2.5 million in year-end profits will start in the second year. In project B, another investment of $2 million is required at the beginning of the fourth year, and four years of $1.7 million in year-end profits will start in the first year. If the cost of capital is 12%, which project should be chosen? How much better is your chosen alternative?
- A new marketing project requires initial research and development costs of $550,000 today with further investments of $100,000 and $75,000 in the fourth and sixth year, respectively. Initially the project will lose $50,000 in its first year and then earn profits of $250,000 for the next four years followed by profits of $140,000 in the last two years. At the end of the project, its capital goods can be sold for an estimated $50,000. If the cost of capital is 9%, should the marketing project be pursued? Show calculations to support your recommendation.
- Olfert has received three offers to purchase his used combine. Farmer A has offered him $95,000 today and $105,000 two years from now. Farmer B has offered him $50,000 today and $37,500 every six months for two years. Farmer C has offered him three annual payments of $67,500 starting today. If prevailing interest rates are 7.5% compounded annually, which offer should Olfert accept? Provide calculations to support your decision.
- One of your company's clients has proposed a contract offering an estimated $150,000 in net profits for the next six years; however, your company would be required to invest $585,000 today to acquire the needed resources for the project. Determine whether the project should be accepted if the cost of capital is a. 10% b. 13% c. 16% Provide calculations to support your decisions.
- A rural municipality has received various proposals from local business developers. The capital budget for the year is $4.5 million. In all projects, the city will initially develop lands that will then result in future returns. Which projects should be undertaken? What total budget will be spent? What total net present value will be realized?
| Project | Initial Cash Flow | Net Present Value |
|---|---|---|
| Project A | $1,250,000 | $1,100,000 |
| Project B | $775,000 | $900,000 |
| Project C | $2,335,000 | $1,750,000 |
| Project D | $1,850,000 | $2,010,000 |
| Project E | $495,000 | $335,000 |
| Project F | $940,000 | $1,000,000 |
- Recalculate question 11 using a cost of capital of 20%. Why does the result differ from the answer to question 11?
Challenge, Critical Thinking, & Other Applications
- A company has a $100,000 capital budget. After analyzing opportunities, management has narrowed down the choices to four projects. If the cost of capital is 14%, make your recommendation about which project(s) to pursue and provide calculations to support your choice(s).
| Project | Investment (today) | Cash Outflows (at beginning) | Cash Inflows (at end) |
|---|---|---|---|
| A | $40,000 | Year 2: $20,000 | Years 1–4: $25,000 |
| B | $26,000 | Year 3: $35,000 | Years 1–4: $25,000 |
| C | $40,000 | Year 4: $15,000 | Years 1–2: $30,000; Years 3–4: $20,000 |
| D | $34,000 | Years 2 & 4: $25,000 | Years 1–3: $35,000; Year 4: $15,000 |
- To replace an aging production machine, Johnston Distributors is considering the purchase of a new robotic machine for $950,000. The machine is expected to have a service life of eight years and an estimated residual value of $75,000. In each of the first four years, the machine is expected to produce production efficiencies and labour savings of $250,000. In the last four years, the annual savings are expected to rise to $300,000. Hydro costs for the machine are estimated at $25,000 starting at the beginning of the second year and increasing by 5% each year thereafter. Maintenance costs are estimated at the beginning of the third, fifth, and seventh years in the amounts of $40,000, $60,000, and $80,000, respectively. If the cost of capital is 16%, determine if the new robotic machine should be purchased. Provide calculations to support your answer.
- If the cost of capital changes, then the net present value changes as well. For illustration purposes, recalculate question 11 using costs of capital of 7.5%, 13.5%, and 17.5%.
- Rank the three offers.
- Determine how much better the chosen alternative is than the worst alternative.
- Summarize your findings about the cost of capital.
- A company can choose only one of two comparably performing machines to purchase. Expected costs and savings are identified in the table below. If the cost of capital is 14% compounded quarterly, determine which machine should be purchased and show calculations to support your decision.
| Machine | Investment (today) | Cash Outflows (at beginning) | Cash Inflows (at end) |
|---|---|---|---|
| A | $104,000 | 12 months: $10,000; 24 months: $15,000; 36 months: $20,000 | Every 6 months for 4 years: $30,000 |
| B | $92,000 | 18 months: $17,500; 42 months: $22,500 | Every 6 months for 4 years: $28,000 |
- Through market research, a company has identified eight different market opportunities. The capital available to pursue these opportunities is $10 million. Which projects should be undertaken? What total budget will be spent? What total net present value will be realized?
| Project | Initial Cash Flow | Net Present Value |
|---|---|---|
| Project #1 | $3,000,000 | $3,500,000 |
| Project #2 | $2,500,000 | $2,850,000 |
| Project #3 | $4,000,000 | $3,750,000 |
| Project #4 | $1,500,000 | $1,437,500 |
| Project #5 | $1,900,000 | $2,050,000 |
| Project #6 | $2,700,000 | $2,450,000 |
| Project #7 | $3,500,000 | $3,550,000 |
| Project #8 | $1,200,000 | $1,325,000 |
15.2: Other Measures For Making Decisions
Mechanics
For questions 1–4, calculate the equivalent annual cash flow for each project.
| Problem Number | NPV | Annual Cost of Capital | Years |
|---|---|---|---|
| 1. | $8,439 | 15% | 4 |
| 2. | $15,783 | 12% | 6 |
| 3. | $43,985 | 14% | 8 |
| 4. | −$31,255 | 16% | 5 |
For questions 5–8, calculate the internal rate of return.
| Problem Number | Cash Outflow Today | Future Cash Outflows (at beginning) | Future Cash Inflows (at end) |
|---|---|---|---|
| 5. | $50,000 | Year 2: $25,000 | Years 2–4: $40,000 |
| 6. | $350,000 | Year 4: $100,000 | Years 1–6: $150,000 |
| 7. | $100,000 |
Year 3: $40,000 Year 6: $25,000 |
Years 1–3: $45,000 Years 4–6: $35,000 |
| 8. | $800,000 |
Year 4: $150,000 Year 8: $125,000 |
Years 1–4: $200,000 Years 5–8: $175,000 |
Applications
- Sanchez is looking at purchasing a new snow blower and has found three models he thinks are equivalent. A Brute model at Walmart retails for $458 with an expected life of five years. A Sno-Tek model at Home Depot retails for $749 with an expected life of 10 years. A YardWorks model at Canadian Tire retails for $649 with an expected life of eight years. If the money to acquire the snow blower is obtained at a rate of 8% compounded annually, which snow blower should be selected? (Hint: Since these are costs, look for the lowest value.)
- A municipality is considering purchasing a police helicopter to assist its ground patrols. A Eurocopter EC120 model is being considered for a purchase price of $1.7 million with annual operating costs expected to be $150,000 at every yearend and a salvage value of $500,000 after six years, which is its predicted life expectancy. A Eurocopter AS350 model could also be purchased for $2 million with annual operating costs expected to be $120,000 at every year-end and with a salvage value of $550,000 after seven years, which is its predicted life expectancy. If both helicopters are deemed suitable, which model should be selected at a cost of capital of 10%? Provide calculations to support your answer.
- A project requires an investment of $225,000 today and is projected to have annual profits of $34,000 for nine years. The capital assets can be sold at the end of the ninth year for $23,500. Calculate the IRR for this project. If capital could be acquired at a cost of 12%, should the project be pursued?
- A new diamond deposit has been found in northern Alberta. Your researchers have determined that it will cost $4.5 million to purchase the land and prepare it for mining. Starting at the end of the second year, the lode is expected to earn net profits of $3 million, which will be sustained for three years before the deposit is depleted. Calculate the IRR on the diamond mine. If the cost of capital is 21%, should the deposit be acquired?
- Schick is considering launching only one of two new products to compete with the Gillette Fusion ProGlide Power razor. For Product A, research and development costs are estimated at $10 million. Forecasted profits are expected to be $3 million in years two to four, $1.5 million in years five to seven, and $0.5 million in years eight to ten. Alternatively, Schick can launch Product B, requiring only a $6.5 million investment and producing forecasted profits of $2.75 million in years one to two, $1 million in years three to four, and $0.35 million in years five to six. The cost of capital is estimated at 8.5% compounded semi-annually. Determine which product should be selected based on the equivalent annual cash flow.
- The Toronto Transit Commission (TTC) is looking to purchase 75 new buses to replace some of its aging fleet. The selection has been narrowed down to two equivalent products from two different suppliers. New Flyer Industries offers a bus for $275,000 with an expected life of 15 years and an estimated residual value of $10,000. The bus requires $5,000 in maintenance at the end of every year, plus a $20,000 overhaul at the beginning of the fourth year and every three years thereafter except for the final year. Motorcoach Industries offers a bus for $250,000 with an expected life of 12 years and an estimated residual value of $13,500. The bus requires $6,000 in maintenance at the end of every year and requires a $30,000 overhaul at the beginning of the fifth, eighth, and eleventh years. The cost of capital is estimated at 11%. Which supplier should the TTC select? What total annual savings will it realize by choosing the supplier?
- The Dragons (from CBC's Dragon's Den) are considering a venture from an Albertan entrepreneur. His proposal requires the Dragons to invest $500,000 immediately. Based on market conditions, the product is estimated to have year-end profits of $100,000, $200,000, $300,000, $200,000, and finally $100,000. The Dragons will invest only if the internal rate of return exceeds their cost of capital of 20%. Should they invest?
- A Western Canadian producer is considering purchasing a five-year product licence from Sunkist Growers Inc. The product licence will cost $1,500,000, and the required equipment will cost $1 million. Equipment upgrades will be $100,000 at the beginning of the third and fifth years. Expected profits are $1 million in each of the first three years and $750,000 in the last two years. The producer will purchase product licences only if the IRR is greater than 25%. Should the product licence be purchased?
Challenge, Critical Thinking, & Other Applications
- Revisit the robotic machine in question 17 of Section 15.1. What is the highest cost of capital that would still result in a decision to purchase the machine?
- You use the equivalent annual cash flow technique to select between two options satisfying the same need but having different timelines. This technique can also be used even if the timelines are the same. Consider the following two projects, of which only one can be selected: Project A: Immediate investment of $225,000, profits in years four to six of $160,000. Project B: Immediate investment of $112,500, profits in years one to three of $55,000 followed by profits of $20,000 in years four to six.
- At a cost of capital of 12%, calculate the \(NPV\) for both projects and make your recommendation.
- Calculate the equivalent annual cash flow for both projects and make your recommendation.
- Comment on the findings.
- Consider the following two projects with a cost of capital of 15%. Only one can be chosen. Project A: Immediate investment of $550,000; profits starting at $75,000 in the first year and rising by $25,000 for the next six years followed by decreasing profits of $25,000 per year in the subsequent seven years; costs of $50,000 at the beginning of years 4, 10, and 14. Project B: Immediate investment of $800,000; profits starting at $200,000 and rising by $50,000 for the next three years followed by decreasing profits of $75,000 per year in the subsequent four years; costs of $110,000 at the beginning of the fourth and seventh years.
- Calculate the equivalent annual cash flow for each project and recommend which project should be chosen.
- What annual benefit will be realized over the alternative project?
- In this section, it was stressed that the IRR should be not be used when ranking projects or choosing between projects since the analysis does not factor in the cost of capital. Consider the same two projects from question 18.
- Calculate the IRR for both projects and make your recommendation.
- At a cost of capital of 15%, calculate the \(NPV\) for both projects and make your recommendation.
- At a cost of capital of 10%, calculate the \(NPV\) for both projects and make your recommendation.
- Comment on the findings. Which method makes more sense in making the decision—\(NPV\) or IRR?
Chapter Review Exercises
Applications
- A database marketing firm can lease its computer equipment with beginning-of-quarter payments of $10,000 for three years. Alternatively, it can purchase the equipment for $131,200 on a loan at a rate of 9% compounded quarterly with an expected resale value after three years of $33,000. Which option would you recommend, and how much better in today's dollars is your chosen alternative?
- Jeremy is thinking of starting up a candle manufacturing business. The initial outlay for equipment, moulds, and other required production equipment is $15,000. Working part time on this hobby business, Jeremy estimates that he will lose $2,000 in the first year, break even in the second year, and earn annual profits of $5,000, $10,000, and $15,000 in subsequent years. After the five years, he hopes to sell the business to an investor for $17,500. If his cost of capital is 8.25% compounded annually, should he pursue this venture? Provide net present value calculations to support your answer.
- A company has a limited capital budget of $300,000. The following four projects are available. Which projects should be undertaken? What total budget will be spent? What total net present value will be realized?
| Project | Initial Cash Flow | Net Present Value |
|---|---|---|
| Project A | $120,000 | $130,000 |
| Project B | $90,000 | $105,000 |
| Project C | $85,000 | $94,000 |
| Project D | $145,000 | $163,000 |
- You are looking to buy a car and own it for five years. A particular make and model has caught your eye. You could purchase the vehicle brand new for $30,000 and sell the vehicle for $11,000. Regular annual maintenance on the vehicle not covered by the three-year manufacturer warranty is expected to be $200, $800, $1,500, $2,250, and $3,000. Alternatively, you could buy a two-year-old used vehicle for $23,000 and sell it after five years for $6,300. Maintenance costs are expected to be $1,500, $2,250, $3,000, $3,500, and $4,500. The cost of financing is 6.75% compounded monthly. Should you purchase the new or used vehicle? How much will you save in current dollars by picking your chosen alternative?
- A company pursues all projects that exceed its 15% cost of capital. Project "Affinity" is available to the company with an initial investment of $655,000. Forecasted profits are expected to be $200,000 for the first three years and $160,000 for the subsequent three years. Based on the IRR, should the company pursue Project "Affinity"?
- Coca-Cola is considering two new flavours—cherry and vanilla—for expansion of one of its product lines. Based on historical and competitive information, the cherry flavour isn't quite as popular as the vanilla flavour, but it will endure in the market longer. Both options require an investment of $2.25 million in equipment and modifications. The cherry flavour is expected to have annual profits of $750,000 for the first two years and $500,000 for five more years. The vanilla flavour is expected to initially have annual profits of $950,000 for two years, $650,000 for two years, and $250,000 in its last year. The cost of capital is 16%. How much higher is the equivalent annual cash flow from choosing the financially preferable flavour?
- A saleswoman informs the head librarian that investing in her new automated library product is a steal at $83,000. Before purchasing, the head librarian investigates the benefits of the automated product, which is expected to have a useful life of seven years and 15% cost of capital. Each year, $24,000 in labour savings and reduced book shrinkage is projected. However, the automated products require regular maintenance of $1,000 in the first four years and $2,000 in the last three years. Electricity bills will also rise by $1,500 in the first three years and $2,100 in the last four years. Is the saleswoman correct? Should the automated system be purchased? If so, what savings in today's dollars will be realized?
- Hershiser has been researching different methods of management leadership that are designed to increase employee motivation and performance. If he pursues a new leadership style, it will require an investment of $165,000 to take the training. A new executive assistant will be hired at a cost of $55,000 annually with expected raises of 5% each year. The techniques and tactics from the style are expected to have an impact on employees for five years before needing to be refreshed and updated with more modern techniques. Increased motivation and performance will produce net profits of $100,000 in the first year, rising by 10% in each subsequent year.
- Calculate the net present value using a cost of capital of 10%. Should Hershiser take the management leadership course?
- What is the maximum cost of capital that will still produce a decision to proceed with the course?
- Mariners Inc. in Halifax has the option to purchase only one of two available offshore fishing rights. Both rights are available for purchase on a four-year contract before they have to be renewed. Fishing right #1 costs $600,000 to acquire, and $64,000 is needed in new equipment to harvest the fish in the area. For each of the first two years, $21,000 will be spent on equipment maintenance and replacement followed by $33,000 in both of the last two years. Annual profits are expected at $300,000. Fishing right #2 costs $400,000 to acquire, and $82,000 is needed in new equipment, which requires annual costs of $30,000 for each of the first two years and $41,000 for both of the last two years. Annual profits are expected to be $250,000.
- Calculate the net present value for both projects if the cost of capital is 14%. What decision do you recommend?
- Calculate the equivalent annual cash flow for both projects. What decision do you recommend?
- A capital budget of $700,000 has been set. Five different capital projects are available for selection. Which projects should be undertaken? What total budget will be spent? What total net present value will be realized?
| Project | Initial Cash Flow | Net Present Value |
|---|---|---|
| Project #1 | $285,000 | $305,000 |
| Project #2 | $240,000 | $120,000 |
| Project #3 | $146,000 | $135,000 |
| Project #4 | $211,000 | $215,000 |
| Project #5 | $373,000 | $375,000 |
Challenge, Critical Thinking, & Other Applications
- The following projects are available, but only one can be chosen. The cost of capital in all cases is 16%. Project A: An initial investment of $180,000 followed by profits of $30,000 in years one to four, $40,000 in years five to seven, and $50,000 in years eight to ten. Project B: An initial investment of $335,000 followed by profits of $65,000 in years one to three, $85,000 in years four to six, and $110,000 in years seven to eight. Project C: An initial investment of $372,000 followed by profits of $150,000 in years four to nine and a residual value of $70,000 in the ninth year.
- Using an appropriate decision-making technique, recommend which project should be selected. How much better is the chosen alternative over the worst alternative?
- If a new lower cost of capital equal to 11% is used, what decision do you reach?
- Recalculate question 11 with the following modifications: Project A: Add a residual value of $100,000 in year 10. Project B: Add a residual value of $60,000 in year 10. Project C: Move the residual value from the ninth year to the tenth year.
- At a 16% cost of capital and using an appropriate decision-making technique, recommend which project should be selected. How much better is the chosen alternative over the worst alternative?
- If a new lower cost of capital equal to 11% is used, what decision do you reach?
- The Banff Gondola is looking to increase its operational capacity through modifications to its gondola equipment. If it invests $2.3 million it can upgrade the motors, strengthen the necessary supports, and add an additional cable car to its line. The expected life of the project is eight years before the equipment will need to be replaced. Annual increased maintenance costs are $50,000 at the end of every year for four years and then $100,000 at the end of every year during the last four years. Because of construction and down times, Banff Gondola is forecasting a loss of $415,000 in the first year. Afterwards, it projects that the equipment will result in increased profits of $850,000 per year. What is the maximum cost of capital that will result in a break-even scenario?
- For question 13, calculate the net present value (use a cost of capital of 15%), internal rate of return, and the equivalent annual cash flow.
- A capital budget of $1 million has been set. Eight different capital projects are available for selection. Which projects should be undertaken? What total budget will be spent? What total net present value will be realized?
| Project | Initial Cash Flow | Net Present Value |
|---|---|---|
| Project #1 | $295,000 | $203,000 |
| Project #2 | $286,000 | $301,000 |
| Project #3 | $391,000 | $550,000 |
| Project #4 | $172,000 | $226,000 |
| Project #5 | $403,000 | $453,000 |
| Project #6 | $107,000 | $135,000 |
| Project #7 | $212,000 | $101,000 |
| Project #8 | $168,500 | $168,500 |