Question

In: Economics

A company has an investment project that would cost $8 million today and yield a payoff of $10 million in 5 years.

A company has an investment project that would cost $8 million today and yield a payoff of $10 million in 5 years. 

Complete the following table by indicating if the firm should undertake the project for each of the interest rates listed. 

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Which of the following formulas would help you figure out the exact cutoff for the interest rate between profitability and nonprofitability?

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Solutions

Expert Solution

It is given that the cost of the investment project is \(\$ 8\) million, payoff is \(\$ 10\) million, and number of years is \(5 .\)

Use the following formula to calculate the present value of the project at each interest rate:

Cost of the project \(=\frac{\text { Payoff }}{(1+i)^{t}}\)

$$ \begin{aligned} (1+i)^{t} &=\frac{\text { Payoff }}{\text { Cost of the project }} \\ i &=\left(\frac{\text { Payoff }}{\text { Cost of the project }}\right)^{\frac{1}{5}}-1 \end{aligned} $$

Here, \(i\) is the interest rate.

$$ \begin{array}{l} i=\left(\frac{10}{8}\right)^{\frac{1}{5}}-1 \\ i=0.0456 \end{array} $$

\(i=4.56 \%\)

Therefore, any project lower than \(4.56 \%\) is profitable.

Thus, \(4 \%\) is the correct option.

From the first part, it is known that the formula for measuring the exact cutoff is mentioned in third option.


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