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Chapter 12

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You must read each slide, and complete any questions on the slide, in sequence.

A. The mayor of your city is considering building a new toll road to reduce congestion. The cost of the toll road is $10 million and is estimated to generate a profit (from tolls collected less expenses collecting the tolls and maintaining the road) of $2 million per year. What is the present value of the first year's profit of $2 million? (Hint: To calculate the present value of the annual profit—for year 1, discount $2 million by 8%.)

Correct! The discounted cash flow of $2 million for one year is $1,851,852.
Incorrect! The discounted cash flow of $2 million for one year is calculated by dividing $2 million by 1.08. Rounding to the nearest dollar results in $1,851,852.

B. If the discount rate is 8%, how many years would it take before the road is paid for? The number of years it will take to recover the initial $10 million investment is years. (Provide the answer as a whole number.)

Correct! It will take 7 years to recover the initial investment.
Incorrect! It would take 7 years. Continue the calculation from the first part of the problem to determine the present value for subsequent years. The present value of $2 million collected for year 2 is $2 million / (1.08)2 = $1,714,678. Continuing these calculations by dividing $2 million by (1.08)n for each year (n = 3, 4, 5…), the present value of total future revenues will exceed $10 million after year 7. (Year 3 = $1,587,664; Year 4 = $1,470,060; Year 5 = $1,361,166; Year 6 = $1,260,339; Year 7 = $1,166,981.)
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