Question

A company purchased a machine last year for $150,000. Revenue for the first year was $50,000. Over the total estimated life of 8 years, estimate the remaining equivalent annual revenues (years 2 through 8) to ensure breakeven by recovering the investment and a return of 10.356% per year, compounded daily. Costs are expected to be constant at $42,000 per year and a salvage value of $10,000 is anticipated. (Use the MARR to 3 decimal places. Format: 00.000%)

Answer 1

The remaining equivalent annual revenues (years 2 through 8) required to recover the investment and achieve a return of 10.356% per year, compounded daily, are approximately $64,369.61 each year.

To calculate the remaining equivalent annual revenues (years 2 through 8) required to recover the investment and achieve a return of 10.356% per year, compounded daily, you can follow these steps:

Step 1: Calculate the present value of the investment cost (Year 1 revenue):

`\[PV_{\text{Investment}} = (150,000)/((1 + 0.10356)^1) \]`

Step 2: Calculate the present value of the operating costs (Years 2 through 8):

`\[PV_{\text{Operating Costs}} = (42,000)/(0.10356) \left(1 - (1)/((1 + 0.10356)^8)\right) \]`

Step 3: Calculate the present value of the salvage value (Year 8):

`\[PV_{\text{Salvage Value}} = (10,000)/((1 + 0.10356)^8) \]`

Step 4: Calculate the total present value (PV) of the investment, operating costs, and salvage value:

`\[PV_{\text{Total}} = PV_{\text{Investment}} + PV_{\text{Operating Costs}} + PV_{\text{Salvage Value}}\]`

Step 5: Calculate the required equivalent annual revenue (Years 2 through 8) to recover the investment and achieve the desired return:

`\[EAA = \frac{PV_{\text{Total}}}{(1)/(0.10356)\left(1 - (1)/((1 + 0.10356)^8)\right)} \]`

Now, let's calculate the values step by step:

Step 1:

`\[PV_{\text{Investment}} = (150,000)/((1 + 0.10356)^1) \approx 135,440.29\]`

Step 2:

`\[PV_{\text{Operating Costs}} = (42,000)/(0.10356) \left(1 - (1)/((1 + 0.10356)^8)\right) \approx 258,527.35\]`

Step 3:

`\[PV_{\text{Salvage Value}} = (10,000)/((1 + 0.10356)^8) \approx 4,596.40\]`

Step 4:

`\[PV_{\text{Total}} = 135,440.29 + 258,527.35 + 4,596.40 \approx 398,564.04\]`

Step 5:

`\[EAA = (398,564.04)/((1)/(0.10356)\left(1 - (1)/((1 + 0.10356)^8)\right)) \approx 64,369.61\]`

So, the remaining equivalent annual revenues (years 2 through 8) required to recover the investment and achieve a return of 10.356% per year, compounded daily, are approximately $64,369.61 each year.