Question

A firm is considering an investment that will earn a $6\mathrm{\%}$ rate of return. If it were to borrow the money, it would have to pay $8\mathrm{\%}$ interest on the loan, but it currently has the cash, so it will not need to borrow. Should the firm make the investment? Show your work.

Short answer

The firm should make the investment, as it will earn a $6\mathrm{\%}$ rate of return and save itself from incurring an $8\mathrm{\%}$ interest cost in the future. The net advantage of this decision is the $2\mathrm{\%}$ difference between the two rates.

Step-by-step solution

Understand the problem

First, we need to make sure we understand the problem. The firm has two choices: either (1) invest the money it currently has and earn a 6% rate of return, or (2) not invest and consider how that compares to borrowing money at an 8% interest rate. The goal is to determine whether the firm should make the investment based on the information provided.

Compare the rate of return and interest rate

Next, we compare the investment's rate of return with the interest rate the firm would pay if it were to borrow money. Rate of return on investment: $6\mathrm{\%}$ \ Interest rate on loan: $8\mathrm{\%}$ Since the rate of return on investment is $6\mathrm{\%}$ and the interest rate on the loan is $8\mathrm{\%}$, we notice that the investment's rate of return is less than the interest rate they would have to pay if they borrowed money.

Analyze the difference between the two rates

Given that the investment's rate of return is less than the interest rate on loan, let's analyze why it is important: Investing the money would result in an increase in the firm's value by $6\mathrm{\%}$. On the other hand, not investing and borrowing money would cost the firm an 8% increase in expenses. By investing at a 6% rate of return, the company will have saved itself from incurring an 8% interest cost in the future, resulting in a net advantage of $8\mathrm{\%}-6\mathrm{\%}=2\mathrm{\%}$.

Make a decision based on the comparison

Now that we have compared the two rates, it is clear that making the investment is advantageous for the company. Although the 6% return on investment is less than the 8% interest rate, making the investment saves the firm from future borrowing costs. Therefore, the firm should make the investment in order to earn a 6% rate of return and save itself from incurring an 8% interest cost in the future.