23 A city is offering to install and operate a water pumping station to provide

Question

23 A city is offering to install and operate a water pumping station to provide service to a proposed new production facility. The station will cost $50,000 now plus it will incur $10,000 per year in operating costs for the next 3 years, all measured in year-0 real dollars. To reimburse the city, the new business must pay a fixed uniform annual fee, A, at the end of each year for 3 years to cover the construction and operating costs of the station. It is agreed that the city should receive a 5% real rate of return after taking an inflation rate of 3.8% into account. Determine the equivalent uniform annual cost in actual dollars to the new business. a. EUAC = $9,682 b. EUAC = $19,236 c. EUAC = $29,686 d. EUAC = $30,509 e. EUAC = $77,228

Explanation / Answer

Option (c).

Nominal rate of return = Real rate of return + Inflation rate = 5% + 3.8% = 8.8%

EUAC ($) = 50,000 x A/P(8.8%, 3) + 10,000 = 50,000 x 0.3936** + 10,000 = 19,680 + 10,000

= 29,680

(The slight difference is due to rounding off)

**A/P(r%, N) = r / [1 - (1 + r)-N]

A/P(8.8%, 3) = 0.088 / [1 - (1.088)-3] = 0.088 / (1 - 0.7764) = 0.088 / 0.2236 = 0.3936

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

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