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Walt is evaluating an investment that will provide the following returns at the end of each of the following years: year 1, $12,500; year 2, $10,000; year 3, $7,500; year 4, $5,000; year 5, $2,500; year 6, $0; and year 7, $12,500. Walt believes that he should earn an annual rate of 8 percent on this investment. How much should he pay for this investment?

Respuesta :

TomShelby

Answer:

$38,771.44

To achieve at least the 8% rate Walt can pay until this amount.

Explanation:

The goal would be to calcualte the present value for each cashflow using the expected rate of 8%

[tex]\left[\begin{array}{ccc}-&Cash Flow&Discounted\\Year \: 1&12,500&11,574.0740740741\\Year \: 2&10,000&8,573.38820301783\\Year \: 3&7,500&5,953.74180765127\\Year \: 4&5,000&3,675.14926398227\\Year \: 5&2,500&1,701.45799258438\\Year \: 6&0&0\\Year \: 7&12,500&7,293.62994077667\\Total&50,000&38,771.4412820865\\\end{array}\right][/tex]

[tex]\frac{Principal}{(1 + rate)^{time} } = Present \: Value[/tex]

For example year 3

[tex]7,500\div \: 1.08^3  = 5953.74180765127[/tex]

Then we add each cashflow, to get the present value of the project.

To achieve at least the 8% rate Walt can pay until this amount.

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