Firm Financial Decisions: Investment Decisions 2
Choosing Between Projects
- In week 9, decisions involved accepting or rejecting a single, stand-alone project.
- This week considers choosing one project from several possible projects.
- Choosing one project excludes taking other projects, which means facing mutually exclusive projects.
Mutually Exclusive Projects
- For mutually exclusive projects, you can't just pick the project with a positive NPV.
- The projects must be ranked, and the best one chosen.
- Pick the project with the highest NPV.
Mutually Exclusive Projects: Lecture Example 1
- Scenario: You own a small piece of commercial land near a university and are considering its use.
- Offer to sell it for $220,000.
- Alternative uses: a bar, a coffee shop, and a boutique.
- Assume indefinite operation, eventually leaving the business to your children.
- Data Collected:
- Bar: Initial Investment = $400,000, Cash flow in the First Year = $60,000, Growth rate = 3.5%, Cost of capital = 12%.
- Coffee shop: Initial Investment = $200,000, Cash flow in the First Year = $40,000, Growth rate = 3%, Cost of capital = 10%.
- Boutique: Initial Investment = $500,000, Cash flow in the First Year = $75,000, Growth rate = 3%, Cost of capital = 13%.
Mutually Exclusive Projects: Lecture Example 1
- Since you can only do one project (you only have one piece of land), these are mutually exclusive projects.
- To decide which project is most valuable, you must rank them by NPV.
- Each of these projects (except for selling the land) has cash flows that can be valued as a growing perpetuity; the present value of the cash inflows is r−gC.
- The NPV of each investment will be: r−gC−InitialInvestment
Mutually Exclusive Projects: Lecture Example 1
- The NPVs are:
- Bar: \frac{60,000}{0.12 - 0.035} - 400,000 = $305,882
- Coffee shop: \frac{40,000}{0.10 - 0.03} - 200,000 = $371,429
- Boutique: \frac{75,000}{0.13 - 0.03} - 500,000 = $250,000
Mutually Exclusive Projects: Lecture Example 1
- So, the ranking of each alternative (including selling the land today for $220,000) is:
- Coffee shop: $371,429
- Bar: $305,882
- Boutique: $250,000
- Sell the land: $220,000
- Based on the rankings, the coffee shop should be chosen.
Mutually Exclusive Projects: Lecture Example 1
- All of the alternatives have positive NPVs, but you can only take one of them, so you should choose the one that creates the most value.
- Even though the coffee shop has the lowest cash flows, its lower start-up cost coupled with its lower cost of capital (it is less risky), make it the best choice.
Differences in Scale
- Making a direct comparison between mutually exclusive projects of different scales (different initial investments) and different cash flow patterns and picking the highest IRR can lead to mistakes.
- For example: a 10% IRR can have very different value implications for an initial investment of $1 million versus an initial investment of $100 million. This is an important shortcoming of IRR.
- If a project has a positive NPV, and we can double its size (cash flows), then the NPV will double.
- This is not the same in terms of IRR because it only measures the average return of an investment.
Differences in Scale: Lecture Example 2
- We begin by considering two mutually exclusive projects with the same scale.
- Daniel is evaluating two investment opportunities.
- Option 1: If he went into business with his girlfriend, he would need to invest $10,000 and the business would generate incremental cash flows of $6,000 per year for three years.
- Option 2: he could start a two-computer internet café. The computer setup will cost a total of $10,000 and will generate $5,000 for three years.
- The opportunity cost of capital for both opportunities is 12%, and both will require all his time, so Daniel must choose between them.
- How valuable is each opportunity, and which one should Daniel choose?
Differences in Scale: Lecture Example 2
- Option 1: NPV of Daniel’s investment in his girlfriend’s business:
NPV = -10,000 + \frac{6,000}{1.12} + \frac{6,000}{1.12^2} + \frac{6,000}{1.12^3} = $4,411 - Option 2: NPV of Daniel’s investment in the Internet café:
NPV = -10,000 + \frac{5,000}{1.12} + \frac{5,000}{1.12^2} + \frac{5,000}{1.12^3} = $2,009
Differences in Scale: Lecture Example 2
- The NPV of Daniel’s girlfriend’s business is always larger than the NPV of the two-computer internet café.
- The same is true for the IRR: the IRR of his girlfriend’s business is 36.3%, while the IRR for the internet café is 23.4%. NPV and IRR lead to the same decision: Daniel should invest in his girlfriend’s business.
Differences in Scale: Lecture Example 2
- Change in scale
- Daniel realises he can just as easily install five times as many computers in the Internet café.
- Setup costs would be $50,000, and annual cash flows would be $25,000.
NPV = -50,000 + \frac{25,000}{1.12} + \frac{25,000}{1.12^2} + \frac{25,000}{1.12^3} = $10,046 - Daniel should now invest in the 10-computer internet café as it has the highest NPV.
Differences in Scale
- Percentage return versus dollar impact on value
- This result might seem counterintuitive, and you can imagine Daniel having a difficult time explaining to his girlfriend why he is choosing a lower return over going into business with her.
- Why would anyone turn down an investment opportunity with a 36.3% return (IRR) in favour of one with only a 23.4% return? The answer is that the latter opportunity, the internet café, makes more money.
- The IRR is a measure of the average return, which can be valuable information.
- However, when comparing mutually exclusive projects of different scales, you need to know the dollar impact on value – the NPV.
Differences in Scale
- The bottom line on IRR:
- Picking the investment opportunity with the largest IRR can lead to a mistake.
- In general, it is dangerous to use the IRR in choosing between projects.
- Always rely on NPV.
Evaluating Projects with Different Lives
- Often, a firm will need to choose between two solutions to the same problem.
- A complication arises when those solutions last for different periods of time.
- For example:
- A firm could be considering two vendors for its internal network servers. Each vendor offers the same level of service, but they use different equipment.
- Vendor A offers a more expensive server with lower per-year operating costs that it guarantees to last for three years.
- Vendor B offers a less expensive server with higher per-year operating costs, which it will only guarantee for two years.
Lecture Example 3
- The costs are shown below, along with the present value of the costs of each option, discounted at the 10% cost of capital for this project.
- Note that all cash flows are negative. The business needs a server to function (therefore, we are minimising costs here).
| Year | PV at 10% | 0 | 1 | 2 | 3 |
|---|
| A | -12.49 | -10 | -1 | -1 | -1 |
| B | -10.47 | -7 | -2 | -2 | |
Lecture Example 3
- Option A is more expensive on a present value basis (−12,490 vs −10,470) but lasts for 3 years, and Option B lasts for 2 years.
- However, the comparison is not that simple: The decision comes down to whether it is worth paying $2,000 more for option A to get the extra year.
Lecture Example 3
- One method that is used to evaluate alternatives that have different lives is to compute the equivalent annual annuity (EAA) for each project
- The EAA is the level annual cash flow with the same present value as the cash flows of the project.
- The intuition is that we can think of the cost of each solution as the constant annual cost that gives us the same present value as the lumpy cash flows of buying and operating the server.
Lecture Example 3
- Given the present value of −12.49 thousand, the number of years – 3, and the discount rate of 10%, we can solve for the cash flow of an equivalent annuity.
Cash flow = \frac{PV}{\frac{1}{r} (1 - \frac{1}{(1 + r)^n})} = \frac{-12.49}{\frac{1}{0.1} (1 - \frac{1}{1.1^3})} = -$5.02 thousand - So, buying and operating server A is equivalent to spending $5,020 per year to have a network server.
Lecture Example 3
- We can repeat this calculation for server B as a 2-year annuity:
Cash flow = \frac{PV}{\frac{1}{r} (1 - \frac{1}{(1 + r)^n})} = \frac{-10.47}{\frac{1}{0.1} (1 - \frac{1}{1.1^2})} = -$6.03 thousand - Server A is equivalent to spending $5,020 per year and server B is equivalent to spending $6,030 per year to have a network server.
- Seen in this light, server A appears to be the less expensive solution.
Important Considerations when using the EAA
- Required life:
- We computed the equivalent annual cost of server A assuming we would need it for three years.
- But suppose it is likely that we will not need the server in the third year?
- Then we would be paying for something we would not use.
- In that case, server B would be the cheaper option.
Important Considerations when using the EAA
- Replacement cost:
- We assumed that the costs of servers A and B would not change over time.
- But suppose we expect a dramatic change in technology that will reduce the costs of the servers by the third year to an equivalent annual cost of $2,000 per year.
- Then server B has the advantage that we can upgrade to the new technology sooner.
Summary
- Choosing between projects:
- When choosing among mutually exclusive investment opportunities, pick the opportunity with the highest NPV. Do not use the IRR to choose among mutually exclusive investment opportunities.
- Evaluating projects with different lives:
- When choosing among projects with different lives, you need a standard basis of comparison. First, compute an annuity with an equivalent present value to the NPV of each project. The projects can then be compared on their cost or value created per year.
- Equivalent annual annuity:
Cashflow=r1(1−(1+r)n1)PV