Use the table for the question(s)below.
-Visby Rides, a limousine hire company, is considering buying some new luxury cars. After extensive research, they come up with the above estimates of free cash flow from this project. Visby learns that a competitor is thinking of offering similar services, thus reducing Visby's sales. By how much could sales fall before the net present value (NPV)was zero, given that the cost of capital is 10%, and that cost of goods sold is 45% of revenues?

Question

Use the table for the question(s)below. 
-Visby Rides, a limousine hire company, is considering buying some new luxury cars. After extensive research, they come up with the above estimates of free cash flow from this project. Visby learns that a competitor is thinking of offering similar services, thus reducing Visby's sales. By how much could sales fall before the net present value (NPV)was zero, given that the cost of capital is 10%, and that cost of goods sold is 45% of revenues?

Quizplus · Accepted Answer

To find the sales fall before the NPV becomes zero, we need to find the point where the sum of the present values of free cash flows equals the initial investment, which is $2,500,000.

Using a financial calculator or a spreadsheet function such as PV, we can find that the sum of the present values of free cash flows is approximately $2,585,032. Therefore, we need the sales to fall by an amount that would make the sum of the present values of free cash flows equal to $2,500,000.

Let X be the percentage decrease in sales. Then we have:

NPV = -$2,500,000 + ($1,350,000 - $607,500X)/(1+0.1) + ($936,000 - $421,200X)/(1+0.1)^2 + ($1,017,600 - $457,920X)/(1+0.1)^3 + ($1,094,400 - $492,480X)/(1+0.1)^4 + ($1,175,040 - $528,768X)/(1+0.1)^5 = 0

Solving this equation, we get X = 0.281 or 28.1%. Therefore, sales could fall by up to 28.1% before the NPV becomes zero. Thus, choice C is the correct answer.

Use the Table for the Question(s)below