A plant that supplies 1 unit of electricity per year, costs $1 billion to build,

Question

A plant that supplies 1 unit of electricity per year, costs $1 billion to build, lasts 25 years, and has an annual operating cost of $0.2 billion; it costs $0.1 billion to decommission the plant at the end of its lifetime (25 years). (Assume that the construction costs and the operating costs are paid at the beginning of the period, and that the decommissioning cost is paid at the end of the life of the plant.) The annual discount rate is r, with discount factor = 1 1+r . Write the formula for the present value of the cost of providing 1 unit of electricity for 100 years, including the decommissioning costs. (Hint: First Önd the present value of providing one unit of electricity for 25 years. Denote this magnitude as Z. Then find the present value of incurring this cost, Z, 4 times: in periods 0, 25, 50, and 75.)

Explanation / Answer

=(1+0.2)+0.1/(1+r)^25+(1+0.2)/(1+r)^25+0.1/(1+r)^50+(1+0.2)/(1+r)^50+0.1/(1+r)^75+(1+0.2)/(1+r)^75+0.1/(1+r)^100

=1.2*(1+1/(1+r)^25+1/(1+r)^50+1/(1+r)^75)+0.1*(1/(1+r)^25+1/(1+r)^50+1/(1+r)^75+1/(1+r)^100)

=1.2*(1-1/(1+r)^100)/(1-1/(1+r)^25)+0.1*(1-1/(1+r)^100)/((1+r)^25-1)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.