Question

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. 

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

Answer 1

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.