A venture will provide a net cash inflow of $57,000 in Year 1. The annual cash flows are projected to grow at a rate of 7 percent per year forever. The project requires an initial investment of $739,000 and has a required return of 15.6 percent. The company is somewhat unsure about the growth rate assumption. At what constant rate of growth would the company just break even?
A) 9.48 percent
B) 9.29 percent
C) 7.89 percent
D) 8.49 percent
E) 7.75 percent

Question

Quizplus · Accepted Answer

To find the break-even growth rate, we need to first calculate the present value of the perpetuity cash flows at the required rate of return:

PV = CF1 / (r - g)
PV = 57,000 / (0.156 - 0.07)
PV = $675,000

Next, we need to find the growth rate that would make the present value of the cash flows equal to the initial investment of $739,000:

739,000 = 57,000 / (0.156 - g) * (1 + g)^1
(0.156 - g) * (1 + g) = 57,000 / 739,000
(0.156 - g) * (1 + g) = 0.0771
0.156g - g^2 + 0.156 - g = 0.0771
- g^2 - 0.844g + 0.0789 = 0

Using the quadratic formula, we get:

g = (-b ± √b^2 - 4ac) / 2a
g = (-(-0.844) ± √(-0.844)^2 - 4(-1)(0.0789)) / 2(-1)
g = (0.844 ± 0.932) / 2
g = -0.044 or g = 0.889

Since the growth rate cannot be negative, the break-even growth rate is:

g = 7.89%

Therefore, the best choice is C.

A Venture Will Provide a Net Cash Inflow of $57,000