A firm that purchases electricity from the local utility for $350,000 per year is considering installing a steam generator at a cost of $280,000. The cost of operating this generator would be $230,000 per year, and the generator will last for five years. If the firm buys the generator, it does not need to purchase any electricity from the local utility. The cost of capital is 13%.

For the local utility option, consider five years of electricity purchases. For the generator option, assume immediate installation, with purchase and operating costs in the current year and operating costs continuing for the next four years. Assume payments under both options at the start of each year (i.e., immediate, one year from now,..., four years from now).

What is the net present value of the more attractive choice?

Please round your answer to the nearest dollar. Report the NPV of cost as a negative number.

To find the net present value (NPV) of both options (purchasing electricity vs. installing the generator) and determine which option is more attractive, we need to compare the costs using the NPV formula. Here’s a step-by-step process:

### Step 1: Calculate NPV for purchasing electricity from the utility

- Annual cost of purchasing electricity: $350,000
- Duration: 5 years
- Cost of capital (discount rate): 13%

The formula for the NPV of a series of cash flows $ C $ over $ n $ periods with a discount rate $ r $ is:

\[
NPV = C \left( \frac{1 - (1 + r)^{-n}}{r} \right) + \frac{C}{(1 + r)^n}
\]

Since payments are made at the beginning of each year (annuity due), the NPV formula for an annuity due can be adapted:

\[
NPV = C \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \times (1 + r)
\]

Substituting the values:

\[
NPV = 350,000 \times \left( \frac{1 - (1 + 0.13)^{-5}}{0.13} \right) \times (1 + 0.13)
\]

### Step 2: Calculate NPV for installing the steam generator

- Initial cost: $280,000 (immediate)
- Annual operating cost: $230,000
- Duration: 5 years
- Cost of capital (discount rate): 13%

The generator involves an initial payment (one-time cost) of $280,000 and subsequent annual payments of $230,000 for 5 years. 

The NPV for the generator can be broken down into the initial cost and the NPV of the operating costs:

\[
NPV = -280,000 + 230,000 \times \left( \frac{1 - (1 + 0.13)^{-5}}{0.13} \right) \times (1 + 0.13)
\]

Let's calculate these values.The NPV of costs for each option is as follows:

- **NPV for purchasing electricity from the utility:** $-\$1,391,065$
- **NPV for installing the steam generator:** $-\$634,128$

Since both NPVs are negative (representing costs), the more attractive option is the one with the less negative value.

**The net present value of the more attractive choice (installing the steam generator) is $-\$634,128$.**

Would you like more details or have any questions? Here are some related questions you might consider:

1. How would the decision change if the cost of capital were different?
2. What would be the impact if the generator's lifespan extended beyond five years?
3. How sensitive is the NPV calculation to variations in operating costs?
4. What if electricity prices from the local utility increased annually?
5. How would the calculation change if payments were made at the end of each year?

**Tip:** Always consider conducting a sensitivity analysis when making investment decisions, especially when multiple variables like operating costs and discount rates can significantly impact the outcome.

A firm that purchases electricity from the local utility for $350,000 per year is considering installing a steam generator at a cost of $280,000. The cost of operating this generator would be $230,000 per year, and the generator will last for five years. If the firm buys the generator, it does not need to purchase any electricity from the local utility. The cost of capital is 13%. For the local utility option, consider five years of electricity purchases. For the generator option, assume immediate installation, with purchase and operating costs in the current year and operating costs continuing for the next four years. Assume payments under both options at the start of each year (i.e., immediate, one year from now,..., four years from now). What is the net present value of the more attractive choice? Please round your answer to the nearest dollar. Report the NPV of cost as a negative number.

Compare the net present value (NPV) of purchasing electricity from a utility versus installing a steam generator for five years. The NPV calculation incorporates a 13% cost of capital and operating costs. Learn how to use cash flow and NPV formulas to determine the more cost-effective option. Suitable for finance students and professionals.

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