Can you help me calculate the EAC of each project if there is a 5% discount rate.  project A has a total operating cost of 40,000 and a project life of eight years, project B has a total operating cost of 35,000 and project last seven years, project C has a total operating cost of 33,000 and a project life of 6 years, project D has a total operating cost of 32,000 and a project life of five years.

To calculate the Equivalent Annual Cost (EAC) of each project, we use the formula:

\[
EAC = \frac{\text{Total Operating Cost}}{\text{Annuity Factor}}
\]

The Annuity Factor (AF) is calculated using the formula:

\[
AF = \frac{1 - (1 + r)^{-n}}{r}
\]

Where:
- $ r $ is the discount rate (5% or 0.05).
- $ n $ is the project life in years.

### Project A: Total Operating Cost = $40,000, Project Life = 8 years

1. Calculate the Annuity Factor:

\[
AF_A = \frac{1 - (1.05)^{-8}}{0.05}
\]

Let's calculate:

\[
AF_A = \frac{1 - \frac{1}{(1.05)^8}}{0.05} \approx \frac{1 - \frac{1}{1.477455}}{0.05} \approx \frac{1 - 0.676839}{0.05} \approx \frac{0.323161}{0.05} \approx 6.4632
\]

2. Calculate the EAC:

\[
EAC_A = \frac{40,000}{6.4632} \approx 6,188.43
\]

### Project B: Total Operating Cost = $35,000, Project Life = 7 years

1. Calculate the Annuity Factor:

\[
AF_B = \frac{1 - (1.05)^{-7}}{0.05}
\]

Let's calculate:

\[
AF_B = \frac{1 - \frac{1}{(1.05)^7}}{0.05} \approx \frac{1 - \frac{1}{1.4071}}{0.05} \approx \frac{1 - 0.7107}{0.05} \approx \frac{0.2893}{0.05} \approx 5.7864
\]

2. Calculate the EAC:

\[
EAC_B = \frac{35,000}{5.7864} \approx 6,048.53
\]

### Project C: Total Operating Cost = $33,000, Project Life = 6 years

1. Calculate the Annuity Factor:

\[
AF_C = \frac{1 - (1.05)^{-6}}{0.05}
\]

Let's calculate:

\[
AF_C = \frac{1 - \frac{1}{(1.05)^6}}{0.05} \approx \frac{1 - \frac{1}{1.3401}}{0.05} \approx \frac{1 - 0.7462}{0.05} \approx \frac{0.2538}{0.05} \approx 5.0757
\]

2. Calculate the EAC:

\[
EAC_C = \frac{33,000}{5.0757} \approx 6,498.45
\]

### Project D: Total Operating Cost = $32,000, Project Life = 5 years

1. Calculate the Annuity Factor:

\[
AF_D = \frac{1 - (1.05)^{-5}}{0.05}
\]

Let's calculate:

\[
AF_D = \frac{1 - \frac{1}{(1.05)^5}}{0.05} \approx \frac{1 - \frac{1}{1.27628}}{0.05} \approx \frac{1 - 0.7835}{0.05} \approx \frac{0.2165}{0.05} \approx 4.3295
\]

2. Calculate the EAC:

\[
EAC_D = \frac{32,000}{4.3295} \approx 7,391.64
\]

### Summary of EACs:
- **Project A:** $6,188.43
- **Project B:** $6,048.53
- **Project C:** $6,498.45
- **Project D:** $7,391.64

These values represent the equivalent annual cost for each project, considering the 5% discount rate.

---

Would you like more detailed explanations on any of these steps, or do you have any other questions?

### Related Questions:

1. What is the significance of the Equivalent Annual Cost (EAC)?
2. How does the discount rate affect the EAC calculation?
3. How would the EAC change if the discount rate were different?
4. What are some common uses of EAC in project evaluation?
5. How does project life impact the EAC of a project?
6. Can EAC be used to compare projects with different lifespans?
7. What are the limitations of using EAC in cost analysis?
8. How is the annuity factor affected by varying discount rates?

### Tip:
When comparing projects with different lifespans, the EAC is a valuable tool as it normalizes costs over time, making it easier to make informed decisions.

Learn how to calculate the Equivalent Annual Cost (EAC) for multiple projects with different operating costs and lifespans using a 5% discount rate. Detailed step-by-step solution provided.

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