Compare the following alternatives on the basis of their capitalized cost at an interest rate of 10% per year.
Petroleum Based Feedstock
First cost, $ -250000
Annual operating cost, $/year -130000
Annual revenues, $/year 400,000
Salvage value, $ 50,000
Life,years 6
Inorganic-Based Feedstock
First cost, $ -110,000
Annual operating cost, $/year -65,000
Annual revenues, $/year 270,000
Salvage value, $ 20,000
Life, years 4
Is there some reason you can't put this on a spreadsheet and evaluate?
To compare the alternatives on the basis of their capitalized cost, we need to calculate the net present value (NPV) of each alternative. The NPV is the sum of the present values of all the cash flows associated with the alternative, considering the interest rate.
Let's calculate the NPV for each alternative:
Petroleum Based Feedstock:
Step 1: Calculate the present value of the annual operating cost and annual revenues for each year using the formula PV = CF / (1 + r)^n, where CF is the cash flow, r is the interest rate, and n is the number of years.
Year 1:
PV of operating cost = -130000 / (1 + 0.1)^1 = -130000 / 1.1 = -118,181.82
PV of revenues = 400000 / (1 + 0.1)^1 = 400000 / 1.1 = 363,636.36
Year 2:
PV of operating cost = -130000 / (1 + 0.1)^2 = -130000 / 1.21 = -107,438.02
PV of revenues = 400000 / (1 + 0.1)^2 = 400000 / 1.21 = 330,578.51
Year 3:
PV of operating cost = -130000 / (1 + 0.1)^3 = -130000 / 1.331 = -97,526.44
PV of revenues = 400000 / (1 + 0.1)^3 = 400000 / 1.331 = 300,142.84
Year 4:
PV of operating cost = -130000 / (1 + 0.1)^4 = -130000 / 1.4641 = -88,822.84
PV of revenues = 400000 / (1 + 0.1)^4 = 400000 / 1.4641 = 273,378.98
Year 5:
PV of operating cost = -130000 / (1 + 0.1)^5 = -130000 / 1.61051 = -80,398.03
PV of revenues = 400000 / (1 + 0.1)^5 = 400000 / 1.61051 = 249,019.12
Year 6:
PV of operating cost = -130000 / (1 + 0.1)^6 = -130000 / 1.77156 = -73,428.93
PV of revenues = (400000 + 50000) / (1 + 0.1)^6 = 450000 / 1.77156 = 253,944.88 (including the salvage value)
Step 2: Calculate the NPV by summing up the present values.
NPV = First cost + PV of cash flows = -250000 + (-118181.82) + (-107438.02) + (-97526.44) + (-88822.84) + (-80398.03) + (-73428.93) + 253944.88
Inorganic-Based Feedstock:
Repeat the same process for the Inorganic-Based Feedstock alternative:
Year 1:
PV of operating cost = -65000 / (1 + 0.1)^1 = -65000 / 1.1 = -59,090.91
PV of revenues = 270000 / (1 + 0.1)^1 = 270000 / 1.1 = 245,454.55
Year 2:
PV of operating cost = -65000 / (1 + 0.1)^2 = -65000 / 1.21 = -53,719.01
PV of revenues = 270000 / (1 + 0.1)^2 = 270000 / 1.21 = 223,140.50
Year 3:
PV of operating cost = -65000 / (1 + 0.1)^3 = -65000 / 1.331 = -48,836.31
PV of revenues = (270000 + 20000) / (1 + 0.1)^3 = 290000 / 1.331 = 217,855.94
Year 4:
PV of operating cost = -65000 / (1 + 0.1)^4 = -65000 / 1.4641 = -44,470.24
PV of revenues = 270000 / (1 + 0.1)^4 = 270000 / 1.4641 = 184,612.12
NPV = First cost + PV of cash flows = -110000 + (-59090.91) + (-53719.01) + (-48836.31) + (-44470.24) + 217855.94 + 184612.12
Now you can compare the NPVs of both alternatives. The alternative with the higher NPV is more economically favorable.