Question

Suppose a handbill publisher can buy a new duplicating machine for \(500, and the duplicator has a 1-year life. The machine is expected to contribute \)550 to the year's net revenue. What is the expected rate of return? If the real interest rate at which funds can be borrowed to purchase the machine is 8 percent, will the publisher choose to invest in the machine? Will it invest in the machine if the real interest rate is 9 percent? If it is 11 percent?

Short answer

The expected rate of return of the duplicating machine is 10%.

The publisher will choose to invest if the borrowing interest rate is 8%.

The publisher will choose to invest at a 9% interest rate.

The publisher will choose not to invest at an 11% interest rate.

Step-by-step solution

Computing the expected rate of return

The cost of duplicating a machine (TC) with 1-year life is 500, and the expected revenue (ER) is 550, which gives the expected rate of return (Err) as:

$$\begin{gathered} E_{rr}=\frac{\left(ER-TC\right)}{TC} \\ =\frac{\left(550-500\right)}{500}\times 100 \\ {E}_{rr}=10\% \end{gathered}$$

Thus, the expected rate of return for the investment is 10%.

Decision to invest if the interest rate is 8%

The handbill publisher will undertake the investment as long as it is profitable to borrow, that is when the real interest rate is less than the expected rate of return.

An 8% interest rate is lower than the E_rr, which is 10%; hence, the publisher will undertake this investment.

Decision to invest if the interest rate is 9%

A 9% interest rate is lower than the E_rr, which is 10%; hence, the publisher will undertake this investment.

Decision to invest if the interest rate is 11%

An 11% interest rate is higher than the E_rr, which is 10%; hence, the publisher will not undertake this investment.