The Federal government is considering allowing mining on up to three sites in th
ID: 1105842 • Letter: T
Question
The Federal government is considering allowing mining on up to three sites in the Uwharrie National Forest for gold extraction. The cash flows (in millions) associated with each site are given below. Use conventional B/C method to determine which site, if any, is best, if the extraction period is limited to 10 years and the interest rate is 7% per year. Eldorado Site NC 109 Site 180 58 NC 49 Site 400 12 122 4.2 100 Initial Costs $ (in millions) Annual Cost $/year (in millions) Annual benefits $/year (in millions) Annual negative impacts to environment, $/year (in millions) 40 1.0 3.0Explanation / Answer
B/C method is used to measure the benefit and costs associated with the project
B/C is calculate as present value of all the benefits divided by present value of all the costs
B/C suugest a project is feasible if its value is greater than 1
B/C = present value of all benefits/present value of all costs
Present value of benefits is sum of present value of all benefits
Present value of cost is sum of present value of all costs
Present Value = Cash flow/(1+r)n, where r is rate of interest and n is number of years
r = 7%
For NC 49 site,
Initial cost = 100
Annual cost = 6
Annual benefits = 40
Annual negative impacts on environment = 1
negative impact on environment is a kind of cost so we will consider it as cost
Present value of benefits = 40/(1.07)1 + 40/(1.07)2 + .......................... + 40/(1.07)9 + 40/(1.07)10
Present value of benefits = 280.94
Present value of costs = 100+ 7/(1.07)1 + 7/(1.07)2 + .......................... + 7/(1.07)9 + 7/(1.07)10
Present value of costs = 149.17
B/C = 280.94/149.17 = 1.88
For NC 109 site,
Initial cost = 180
Annual cost = 8
Annual benefits = 58
Annual negative impacts on environment = 3
negative impact on environment is a kind of cost so we will consider it as cost
Present value of benefits = 58/(1.07)1 + 58/(1.07)2 + .......................... + 58/(1.07)9 + 58/(1.07)10
Present value of benefits = 407.37
Present value of costs = 180+ 11/(1.07)1 + 11/(1.07)2 + .......................... + 11/(1.07)9 + 11/(1.07)10
Present value of costs = 257.26
B/C = 403.37/257.26 = 1.58
For Eldorado site,
Initial cost = 400
Annual cost = 12
Annual benefits = 122
Annual negative impacts on environment = 4.2
negative impact on environment is a kind of cost so we will consider it as cost
Present value of benefits = 122/(1.07)1 + 122/(1.07)2 + .......................... + 122/(1.07)9 + 122/(1.07)10
Present value of benefits = 856.88
Present value of costs = 400+ 16.2/(1.07)1 + 16.2/(1.07)2 + .......................... + 16.2/(1.07)9 + 16.2/(1.07)10
Present value of costs = 513.78
B/C = 856.88/513.78 = 1.67
Value of B/C for all projects is greater than 1 so all projects are feasible
Value of B/C for NC 49 site is highest so it is best as it is providing most benefits as per the costs.
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