To calculate the Equivalent Annual Cost (EAC) for each alternative, we will first compute the Net Present Value (NPV) of the cash flows for each alternative, then convert that into an equivalent annual amount using the formula:

$\text{EAC} = \frac{\text{NPV}}{\text{Annuity Factor}}$

where the Annuity Factor (AF) is calculated as:

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

where:

• $r$ is the discount rate (11% or 0.11),
• $n$ is the number of years (7 years).

Step 1: Calculate the NPV for each alternative.

We will calculate the NPV for both alternatives based on the following cash flows:

• Alternative A:

  • Initial cost (Year 0): $(85,000)
  • Yearly costs (Years 1-7): $(16,000)

• Alternative B:

  • Initial cost (Year 0): $(65,000)
  • Yearly costs (Years 1-7): $(7,000)

We'll first compute the NPV for each project using the formula for NPV:

$\text{NPV} = \sum_{t=0}^{n} \frac{C_t}{(1 + r)^t}$

where $C_t$ represents the cash flow at time $t$.

Let me calculate the NPVs and the EAC for both alternatives. numpy as np

Given data

discount_rate = 0.11 years = 7

Cash flows for both alternatives

cash_flows_A = [-85000] + [-16000] * years # Alternative A cash_flows_B = [-65000] + [-7000] * years # Alternative B

Function to calculate NPV

def calculate_npv(cash_flows, r): return sum(cash_flows[t] / (1 + r) ** t for t in range(len(cash_flows)))

Calculate NPVs for both alternatives

npv_A = calculate_npv(cash_flows_A, discount_rate) npv_B = calculate_npv(cash_flows_B, discount_rate)

Calculate Annuity Factor

annuity_factor = (1 - (1 + discount_rate) ** -years) / discount_rate

Calculate EAC for both alternatives

eac_A = npv_A / annuity_factor eac_B = npv_B / annuity_factor

npv_A, npv_B, eac_A, eac_BHere are the results:

• Alternative A:

  • NPV: $-\$160,395.14$
  • EAC: $-\$34,038.30$

• Alternative B:

  • NPV: $-\$97,985.37$
  • EAC: $-\$20,793.99$

b. Which alternative should Barry select?

Barry should select Alternative B, as it has a lower Equivalent Annual Cost (EAC) of $-\$20,793.99$, which means it is the less costly option over the project's useful life compared to Alternative A, which has an EAC of $-\$34,038.30$.

Would you like more details on how the calculation was done? Let me know if you have further questions.

Related questions:

1. How does the discount rate affect the EAC of each alternative?
2. What would happen if the useful life of the alternatives were longer or shorter?
3. How do cash flow variations influence the choice between two alternatives?
4. What is the difference between NPV and EAC in capital budgeting?
5. How would the choice change if the discount rate were lower than 11%?

Tip: When calculating EAC, always ensure that the discount rate used is consistent with the time value of money and reflects the firm's required return.