Question

You are considering buying a new laser printer to use in your part-time desktop publishing business. The printer will cost \(\$ 380,\) and you are certain it will generate additional net revenue of \(\$ 100\) per year for each of the next five years. At the end of the fifth year, it will be worthless. Answer the following questions: a. What is the value of the printer if you could lend funds safely at an annual interest rate of 10 percent? Is the purchase of the printer justified? b. Would your answer to part (a) change if the interest rate were 8 percent? Is the purchase justified in that case? Explain. c. Would your answer to part (a) change if the printer cost \(\$ 350 ?\) Is the purchase justified in that case? d. Would your answer to part (a) change if the printer could be sold for \(\$ 500\) at the end of the fifth year? Is the purchase justified in that case? Explain.

Short answer

The answer depends on the interest rate and the comparisons of present value with the costs under the given scenarios. It can differ based on interest rates, printer's cost, and its future resale value. The comparison of these values with $380 (or $350 in one case) will determine if the purchase is justified or not.

Step-by-step solution

Understanding the initial conditions

The printer costs \(380\) and generates a net revenue of \(100\) per year for 5 years. So, this total revenue over 5 years is considered as an Annuity.

Calculating the present value of the Annuity under a 10% interest rate

We apply the formula for present value of annuity: \[PV = A * \frac{1 - (1 + r)^{-n}}{r}\], where PV = Present Value, A = Annual cash inflow = $100, r = Interest Rate = 0.10 (10% expressed in decimal), n = Number of years = 5. The PV then is calculated as \(PV = 100 * \frac{1 - (1 + 0.10)^{-5}}{0.10}\).

Evaluating the purchase decision at a 10% interest rate

If the present value of the annuity (PV) we calculated in step 2 is higher than the initial cost of the printer ($380), then buying the printer is justified. If not, then the printer is not a good investment.

Repeating the calculation for an 8% interest rate

Apply the same method used in step 2, just replace 'r' with 0.08, and then follow the evaluation step (step 3).

Change the initial cost of the printer and recalculate

If the initial cost of the printer changes to $350, redo the calculations from step 2 and then proceed to the evaluation (step 3).

Changing the future value of the printer and recalculate

If the printer could be sold for $500 at the end of the fifth year, this will change the future cash inflows. So, redo calculations from step 2 considering the increase in future cash inflows due to the resale value of the printer, and then proceed to the evaluation (step 3).