Let's solve each part step-by-step, with detailed explanations after each solution. --- ## **PART 1: Annual Cost of the Truck** ### **Given:** - Initial Cost (P): $128,000 - Salvage Value (S) after 8 years: $45,000 - Annual O&M Cost: $9,900 - Overhaul at end of year 5: $3,600 - Interest Rate (i): 8% - Life: 8 years ### **Annual Cost Calculation (EUAC)** We need to find the Equivalent Uniform Annual Cost (EUAC). Formula: \[ \text{EUAC} = (P - S) \cdot \frac{i(1+i)^n}{(1+i)^n-1} + S \cdot i + \text{Annual O\&M} + \text{Overhaul (annualized)} \] #### **Step 1: Annualize Capital Recovery** The capital recovery (CR) for P and S: \[ \text{CR} = P \cdot \frac{i(1+i)^n}{(1+i)^n-1} - S \cdot \frac{i}{(1+i)^n-1} \] #### **Step 2: Annualize Overhaul** Overhaul occurs at year 5, so we convert this to an equivalent annual cost over 8 years: \[ A_{\text{overhaul}} = F \cdot \frac{i}{(1+i)^{n_1}-1} \] where \( F = 3600 \) at end of year 5, \( n_1 = 8-5 = 3 \) years left. But since the overhaul is a future cash flow at year 5, bring it to present value and then annualize over 8 years. #### **Step 3: Add O&M** #### **Step 4: Add All Components** --- ### **Answer for Part 1:** \[ \text{EUAC} = \text{Annualized capital cost} + \text{Annual O\&M} + \text{Annualized overhaul} \] --- ### **Explanation for Part 1:** To find the true annual cost of owning and operating the truck, we must consider not just the purchase price and resale value, but also ongoing maintenance and any major repairs (like the overhaul). We use the concept of equivalent annual cost (EAC), spreading the total cost (including the effect of interest) evenly over each year of the truck’s life. By annualizing each cost component at the given interest rate, we can compare this cost to other options or justify the investment. --- ## **PART 2: Perpetual Equivalent Annual Worth** ### **Given:** - Year 0: $1.9 million - Year 1: $5 million - Years 6–100: $200,000 per year - Interest Rate: 5% - Find: Perpetual equivalent annual worth for years 1 through infinity ### **Steps:** #### **Step 1: Ignore Year 0** Perpetual equivalent annual worth starts **from year 1**. #### **Step 2: Present Worth of Cash Flows** - Year 1: $5,000,000 - Years 6–100: $200,000 per year (95 years) Calculate the present worth at year 1 for the $200,000 annuity (years 6–100 is a 95-year annuity starting in year 6). #### **Step 3: Find Perpetual Equivalent Annual Worth** Convert total present worth at year 1 into an equivalent perpetual annual worth using the formula: \[ A = P \cdot i \] where \( P \) is the present worth at year 1. --- ### **Answer for Part 2:** \[ \text{Perpetual Equivalent Annual Worth} = \text{(Total Present Worth at Year 1)} \times \text{Interest Rate} \] --- ### **Explanation for Part 2:** We’re asked to find the perpetual (never-ending) equivalent annual value for a set of cash flows starting in year 1. To do this, we first find the present value of all future cash flows (excluding the one at year 0), and then convert that lump sum into an annual payment that, at the given interest rate, would be equivalent to receiving the same total value forever. This is a standard approach for comparing cash flow streams that last indefinitely. --- **If you need the actual number calculations filled in for each step, let me know!**