Calculating inflation and project cash flows On July 25 2011

(Calculating inflation and project cash? flows) On July? 25, 2011, the average price of a gallon of gasoline was $3.40. Just 5 years later the price of that same gallon of gas was $2.07. What was the rate of inflation? (deflation) in the price of a gallon of gas over the? period?

a)The annual rate of inflation? (deflation) in the price of a gallon of gasoline over the 5 years was what percent?

Solution

This question requires application of time value of money function, which is FV = PV * (1 + r)ⁿ

Now in this question, PV = $3.40, FV = $2.07, n = 5

2.07 = 3.40 * (1 + r)⁵

(1 + r)⁵ = (2.07/3.40)

(1 + r)⁵ = 0.6088

Taking 5th root of both sides,

(1 + r) = 0.9055

r = - 9.45% --> Annual deflation rate (Deflation since price has reduced over 5 year period).