Your firm has been hired to develop new software for the university's class registration system.
Under the contract, you will receive $502,000 as an upfront payment. You expect the
development costs to be $455,000 per year for the next 3 years. Once the new system is in place,
you will receive a final payment of $903,000 from the university 4 years from now. Assume the
cost of capital is 10%.
a. Calculate the NPV of this opportunity  give me the formula to get the NPV

To calculate the Net Present Value (NPV) of this opportunity, we use the formula:

\[
NPV = \sum \frac{C_t}{(1 + r)^t} - I_0
\]

where:

- $ C_t $ is the cash flow at time $ t $.
- $ r $ is the discount rate (cost of capital).
- $ t $ is the time period.
- $ I_0 $ is the initial investment or upfront payment.

For your scenario:

1. **Upfront payment** (immediate inflow): $502,000.
2. **Development costs** (outflows for the next 3 years): $455,000 each year for 3 years.
3. **Final payment** (inflow at the end of 4 years): $903,000.
4. **Discount rate** $ r $: 10% or 0.10.

The formula for NPV in this case will be:

\[
NPV = 502,000 - \frac{455,000}{(1 + 0.10)^1} - \frac{455,000}{(1 + 0.10)^2} - \frac{455,000}{(1 + 0.10)^3} + \frac{903,000}{(1 + 0.10)^4}
\]

### Steps to Calculate:

1. **Discount each cash flow** to its present value.
2. **Sum** the discounted cash flows, including the initial inflow of $502,000.
3. **Subtract** the development costs from this total.

Would you like a step-by-step calculation with this formula, or any further assistance?

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### Follow-up Questions:
1. How would the NPV change if the cost of capital increased to 12%?
2. What would be the impact on NPV if development costs rose to $500,000 per year?
3. How does extending the payment period affect the NPV?
4. How would changing the final payment amount influence the NPV?
5. Why is discounting cash flows important in NPV calculations?

#### Tip:
Remember, a positive NPV indicates a profitable investment under the given cost of capital.

Your firm has been hired to develop new software for the university's class registration system. Under the contract, you will receive $502,000 as an upfront payment. You expect the development costs to be $455,000 per year for the next 3 years. Once the new system is in place, you will receive a final payment of $903,000 from the university 4 years from now. Assume the cost of capital is 10%. a. Calculate the NPV of this opportunity give me the formula to get the NPV

Learn how to calculate the Net Present Value (NPV) for a software development contract involving upfront payments, annual development costs, and a final payment after 4 years. This example uses a 10% cost of capital and demonstrates the key concepts of discounting cash flows and financial decision-making.

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