Consider a project that costs $5000 and has an expected future cash flow of $1000 per...

Consider a project that costs $5000 and has an expected future cash flow of $1000 per year for 20 years. If we wait one year, the cost will increase to $5500 and the expected future cash flow will increase to $1200. If the required return is 13%, should we accept the project? If so, when should we begin?

Thank you.

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Expert Solution

Let’s compare both the options by computing NPV of each one.

NPV = PV of future cash inflows – Initial investment

Project started now:

NPV = $ 1,000 x PVIFA (13 %, 20) - $ 5,000

= $ 1,000 x [1- (1+0.13)^-20/0.13] - $ 5,000

= $ 1,000 x [1- (1.13)^-20/0.13] - $ 5,000

= $ 1,000 x [(1- 0.0867822948516793)/0.13] - $ 5,000

= $ 1,000 x (0.9132177051483207/0.13) - $ 5,000

= $ 1,000 x 7.024751578064 - $ 5,000

= $ 7,024.75157806401 - $ 5,000

= $ 2,024.75157806401 or $ 2,024.75

Project started after one year:

NPV in one year = $ 1,200 x PVIFA (13 %, 20) - $ 5,500

= $ 1,200 x 7.024751578064 - $ 5,500

= $ 8,429.70189367681- $ 5,500

= $ 2,929.70189367681

NPV now = $ 2,929.70189367681/ (1+0.13)

= $ 2,929.70189367681/1.13

= $ 2,592.65654307682 or $ 2,592.66

Project is acceptable for discount rate of 13 % as NPV is positive.

It is preferable to begin the project next year as NPV is higher if the project started in one year rather than started now.

jeff jeffy answered 1 year ago

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