Work It Out

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

Suppose that a major city’s main thoroughfare, which is also an interstate highway, will be completely closed to traffic for two years, from January 2014 to December 2015, for reconstruction at a cost of $535 million. If the construction company were to keep the highway open for traffic during construction, the highway reconstruction project would take much longer and be more expensive. Suppose that construction would take four years if the highway were kept open, at a total cost of $800 million. The state department of transportation had to make its decision in 2014, one year before the start of construction (so that the first payment was one year away). So the department of transportation had the following choices:**(i) **Close the highway during construction, at an annual cost of $267.5 million per year for two years.**(ii) **Keep the highway open during construction, at annual cost of $200 million per year for four years.

Suppose the interest rate is 10%. Calculate the present value of the costs incurred under each plan.

The present value of plan (i) is: $mcztF5Y0nqXglh/Kp8JpixrkQaI= million. (Round your answer to two decimal places.)

Correct! For further review, see section "How to Calculate the Present Value of Multiyear Projects."

Sorry, the present value for plan (i) is $464.25 million. The project costs $267.5 million for each of the first two years. If the interest rate is 10% the cost of the project today is found by taking the discounted present value of $267.5 million in years one and two. Doing so yields a present value of ($267.5 million/1.1 + $267.5 million/(1.1^2)) = $243.18 million + $221.07 million = $464.25 million. For further review see section “How to Calculate the Present Value of Multiyear Projects.”

Suppose the interest rate is 10%. Calculate the present value of the costs incurred under each plan. The present value of plan (i) is:

The present value of plan (ii) is: $wpiKqTqg8NPW3G1A million. (Round your answer to two decimal places.)

Correct! For further review, see section "How to Calculate the Present Value of Multiyear Projects."

Sorry, the present value for plan (ii) is $633.97 million. The project costs $200 million for each of the first four years. If the interest rate is 10% the cost of the project today is found by taking the discounted present value of $200 million in each of the four years. Doing so yields a present value of ($200 million/1.1 + $200 million/(1.1^2) + $200 million/(1.1^3) $200 million/(1.1^4)) = $181.82 million + $165.29 million + $150.26 million + $136.60 million = $633.97 million. For further review see section “How to Calculate the Present Value of Multiyear Projects.”

Suppose the interest rate is 10%. Calculate the present value of the costs incurred under each plan. The present value of plan (ii) is:

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Suppose that a major city’s main thoroughfare, which is also an interstate highway, will be completely closed to traffic for two years, from January 2014 to December 2015, for reconstruction at a cost of $535 million. If the construction company were to keep the highway open for traffic during construction, the highway reconstruction project would take much longer and be more expensive. Suppose that construction would take four years if the highway were kept open, at a total cost of $800 million. The state department of transportation had to make its decision in 2014, one year before the start of construction (so that the first payment was one year away). So the department of transportation had the following choices:**(i) **Close the highway during construction, at an annual cost of $267.5 million per year for two years.**(ii) **Keep the highway open during construction, at annual cost of $200 million per year for four years.

Now suppose the interest rate is 80%. Calculate the present value of the costs incurred under each plan.

The present value of plan (i) is: $gOVsN64lTP2yLGTp million

For further review see section “How to Calculate the Present Value of Multiyear Projects.”

Sorry, the present value for plan (i) is $231.17 million. The project costs $267.5 million for each of the first two years. If the interest rate is 80% the cost of the project today is found by taking the discounted present value of $267.5 million in years one and two. Doing so yields a present value of ($267.5 million/1.8 + $267.5 million/(1.8^2)) = $148.61 million + $82.56 million = $231.17 million. For further review see section “How to Calculate the Present Value of Multiyear Projects.”

Now suppose the interest rate is 80%. Calculate the present value of the costs incurred under each plan. The present value of plan (i) is:

The present value of plan (ii) is: $HrFXY8v/3ptM2Um1t3YNhZtP17E= million

For further review see section “How to Calculate the Present Value of Multiyear Projects.”

Sorry, the present value for plan (ii) is $226.18 million. The project costs $200 million for each of the first four years. If the interest rate is 10% the cost of the project today is found by taking the discounted present value of $200 million in each of the four years. Doing so yields a present value of ($200 million/1.8 + $200 million/(1.8^2) + $200 million/(1.8^3) $200 million/(1.8^4)) = $111.11 million + $61.73 million + $34.29 million + $19.05 million = $226.18 million. For further review see section “How to Calculate the Present Value of Multiyear Projects.”

Now suppose the interest rate is 80%. Calculate the present value of the costs incurred under each plan. The present value of plan (ii) is:

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