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Determine the discounted payback period (in years) for a project that costs $1,000 and would yield after-tax cash flows of $525 the first year, $485 the second year, $445 the third year, and $405 for the fourth year. The firm's cost of capital is 11%.

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AyAyCapitan

Answer:

During the 3rd year:

It will be in the 5th month of the Third year

Explanation:

We have to discount each year cash flow at present day using the firm's cost of capital of 11%

[tex]\left[\begin{array}{ccc}\\$Year&$Cash Flow&$Discounted Cash Flow \\\\1&525&472.97 \\2&485&393.63\\3&445&325.38\\4&405&266.78\end{array}\right] \\[/tex]

Adding the discounted cash flow we got that the firm will achieve the payback during the third year.

Now in the attempt of being more precise:

At the end of the 2nd year, we are 133.40 away from payback

By the end of the third year, the company receive 325.38

So in 12 months, we generate 325.38

In how many months do we manage to generate 133.40 and payback the investment?

133.40*12/325.38 = 4.91

So in the 5th month of the Third year, the firm will achieve the payback.

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