A firm is considering replacing the existing industrial air conditioning unit. They will pick one of two units. The first, the AC360, costs $26,347.00 to install, $5,039.00 to operate per year for 7 years at which time it will be sold for $7,048.00. The second, RayCool 8, costs $41,848.00 to install, $2,142.00 to operate per year for 5 years at which time it will be sold for $9,054.00. The firm’s cost of capital is 6.37%. What is the equivalent annual cost of the RayCool8? Assume that there are no taxes.

Answer 1

To determine the Equivalent Annual Cost (EAC) of the RayCool 8, we will follow these steps:

1. Calculate the Present Value (PV) of the costs of the RayCool 8:

   • Installation Cost: This cost will occur at time 0, so it is simply $41,848.
   • Operating Costs: We need to calculate the present value of the operating costs over 5 years.
   • Salvage Value: We will discount the future salvage value back to present value.

2. Calculate the Present Value of Operating Costs: The operating costs of $2,142 per year occur at the end of each year for 5 years. We can use the Present Value of Annuity formula:

   \[ PV(\text{operating costs}) = C \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \]

   Where:

   • \( C = 2,142 \) (annual cost)
   • \( r = 0.0637 \) (cost of capital)
   • \( n = 5 \) (number of years)

   \[ PV(\text{operating costs}) = 2,142 \times \left( \frac{1 - (1 + 0.0637)^{-5}}{0.0637} \right) \]

   \[ PV(\text{operating costs}) = 2,142 \times \left( \frac{1 - (1.0637)^{-5}}{0.0637} \right) \]

   \[ (1.0637)^{-5} \approx 0.74777 \]

   \[ PV(\text{operating costs}) = 2,142 \times \left( \frac{1 - 0.74777}{0.0637} \right) \]

   \[ PV(\text{operating costs}) = 2,142 \times \left( \frac{0.25223}{0.0637} \right) \approx 2,142 \times 3.951 \]

   \[ PV(\text{operating costs}) \approx 8,466.64 \]

3. Calculate the Present Value of the Salvage Value: The salvage value of $9,054 will occur at the end of year 5. We need to discount this amount back to present value:

   \[ PV(\text{salvage value}) = \frac{9,054}{(1 + r)^n} = \frac{9,054}{(1.0637)^5} \]

   \[ PV(\text{salvage value}) = \frac{9,054}{1.36469} \approx 6,634.19 \]

4. Calculate Total Present Value of Costs: Now, combine the present values of the installation cost, operating costs, and salvage value to find the total present value of costs.

   \[ PV(\text{total costs}) = \text{Installation Cost} + PV(\text{operating costs}) - PV(\text{salvage value}) \]

   \[ PV(\text{total costs}) = 41,848 + 8,466.64 - 6,634.19 \]

   \[ PV(\text{total costs}) = 43,680.45 \]

5. Calculate Equivalent Annual Cost (EAC): Finally, we convert the total present value of costs into an equivalent annual cost using the annuity formula:

   \[ EAC = \frac{PV(\text{total costs}) \times r}{1 - (1 + r)^{-n}} \]

   \[ EAC = \frac{43,680.45 \times 0.0637}{1 - (1 + 0.0637)^{-5}} \]

   We already calculated \( (1 + 0.0637)^{-5} \) which is approximately \( 0.74777 \):

   \[ 1 - 0.74777 = 0.25223 \]

   Now substituting these values into the EAC formula:

   \[ EAC = \frac{43,680.45 \times 0.0637}{0.25223} \approx \frac{2,784.65}{0.25223} \approx 11,030.16 \]

Thus, the Equivalent Annual Cost of the RayCool 8 is approximately $11,030.16.

Answer 2

What values do i enter for CF0, C01, F01,C02, F02 to solve on a finance calculator?

Answer 3

To enter the cash flows for the RayCool 8 on a financial calculator, you will set it up as follows:

1. CF0 (Initial Cash Flow at Year 0):

   • This is the installation cost, which is an outflow; hence, you enter it as a negative value.
   • CF0 = -41,848.00

2. C01 (Cash Flow for Year 1):

   • This will be the operating cost for Year 1, which is also an outflow.
   • C01 = -2,142.00

3. F01 (Frequency of C01):

   • This is the total number of years that the cash flow C01 will be received.
   • Since the operating cost is the same for 5 years, you will enter:
   • F01 = 5.

4. C02 (Cash Flow for Year 5):

   • This is the salvage value received at the end of Year 5, which is an inflow. You will enter this as a positive value.
   • C02 = 9,054.00

5. F02 (Frequency of C02):

   • Since the salvage value occurs only at the end of Year 5, you will enter:
   • F02 = 1.

Summary of Inputs:

• CF0 = -41,848
• C01 = -2,142
• F01 = 5
• C02 = 9,054
• F02 = 1

Once you've entered these cash flows, you can then compute the Net Present Value (NPV) using the cost of capital (6.37%) to find the present value of the cash flows. Finally, you'll convert that PV back to an Equivalent Annual Cost (EAC) if your calculator allows for that calculation directly, or manually based on the present value you obtain.