A manager is constrained to spend $1,000,000 on projects. The initial costs and net present values (NPVs) of projects she is considering are as follows:
Initial
Cost
NPV
Project A
$500,000
$300,000
Project B
$1,000,000
$400,000
Project C
$250,000
$200,000
Project D
$750,000
$550,000
Project E
$500,000

Which projects should she select?

$250,000

The manager's goal is to maximize the Net Present Value (NPV) of the projects while staying within the budget constraint of $1,000,000. Let's analyze the projects with their costs and NPVs, and find which combination maximizes the total NPV without exceeding $1,000,000.

Here are the projects and their details:

| Project | Initial Cost | NPV    |
|---------|--------------|--------|
| A       | $500,000     | $300,000 |
| B       | $1,000,000   | $400,000 |
| C       | $250,000     | $200,000 |
| D       | $750,000     | $550,000 |
| E       | $500,000     | $250,000 |

The total budget is $1,000,000.

### Step 1: Sort projects by NPV-to-cost ratio
To maximize NPV, it's beneficial to consider the NPV-to-cost ratio:
- Project A: $ \frac{300,000}{500,000} = 0.6 $
- Project B: $ \frac{400,000}{1,000,000} = 0.4 $
- Project C: $ \frac{200,000}{250,000} = 0.8 $
- Project D: $ \frac{550,000}{750,000} \approx 0.73 $
- Project E: $ \frac{250,000}{500,000} = 0.5 $

Thus, the best strategy is to select projects that provide the highest NPV-to-cost ratio first, while staying within the budget.

### Step 2: Select projects that maximize the total NPV within the budget
- Start with **Project C** (Cost: $250,000, NPV: $200,000) since it has the highest NPV-to-cost ratio.
- Next, select **Project D** (Cost: $750,000, NPV: $550,000), as this will maximize the total NPV.

The total cost is $250,000 + $750,000 = **$1,000,000**, which is within the budget.

### Total NPV:
The total NPV for selecting Project C and Project D is:
\[ 200,000 + 550,000 = 750,000 \]

### Conclusion:
The manager should select **Project C and Project D**, giving a total NPV of **$750,000**.

Would you like further details on how this was calculated or have any other questions?

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Here are 5 questions that build on this information:
1. How does changing the budget constraint affect the project selection?
2. What if the NPV for Project A increases to $400,000? Would this change the decision?
3. What impact does the cost of capital have on the NPV in project selection?
4. Can this problem be solved using a linear programming approach?
5. How does risk factor into the decision when comparing NPVs?

**Tip**: Always look at NPV-to-cost ratios when trying to maximize returns within a constrained budget!

A manager is constrained to spend $1,000,000 on projects. The initial costs and net present values (NPVs) of projects she is considering are as follows:

Initial Cost    NPV
Project A       $500,000    $300,000
Project B       $1,000,000  $400,000
Project C       $250,000    $200,000
Project D       $750,000    $550,000
Project E       $500,000    $250,000

Which projects should she select?

Learn how to select projects with the highest net present value (NPV) while staying within a $1,000,000 budget. This problem explains how to use NPV-to-cost ratios and optimization techniques to make the best investment decisions. Suitable for finance and economics students.

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