Final Answer:
The annual worth of the generator, considering the purchase price, salvage value, and annual maintenance costs, at an 8% hurdle rate is approximately $698,415.72.
Step-by-step explanation:
To determine the annual worth of the generator, we use the Annual Worth method, which finds the equivalent uniform annual cost over the asset's lifespan. First, calculate the equivalent annual cost of the initial purchase and maintenance. The initial cost of $5 million needs to be converted to an annual equivalent over 10 years using the present worth factor formula: \(A = P(A/P, i, n)\), where \(P = \$5,000,000\), \(i = 8\% = 0.08\), and \(n = 10\) years. Substituting these values, we find \(A = \$865,932.76\).
Next, compute the salvage value of $500,000 at the end of 10 years to its present worth at year 0 using the future worth factor formula: \(P = F(P/F, i, n)\), where \(F = \$500,000\), \(i = 8\%\), and \(n = 10\) years. This gives us a present worth of \(P = \$215,899.81\).
Now, calculate the present worth of the annual maintenance costs from year 4 to year 10. The annual maintenance cost is $20,000 for 7 years. Using the present worth factor formula: \(P = A(A/P, i, n)\), where \(A = \$20,000\), \(i = 8\%\), and \(n = 7\) years, we find \(P = \$113,617.05\).
Finally, sum all three present worth values: \(P_{\text{total}} = P_{\text{initial}} + P_{\text{salvage}} + P_{\text{maintenance}}\). \(P_{\text{total}} = \$865,932.76 + \$215,899.81 + \$113,617.05 = \$1,195,449.62\). This total represents the present worth of all costs and salvage value. To find the equivalent annual worth, we need to find the annual worth of this present worth over 10 years, resulting in an annual worth of approximately \$698,415.72.