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

The growth rate should be 7.322%

Explanation:

The formula for the present value of such an investment is just like that for the constant growth model of DDM. The present value of all the expected future cash inflows growing at a constant rate can be determined as follows,

Present value = Cash flow in Year 1 * (1+g)  /  (r - g)

To calculate the growth rate that will provide break even, that is the present value of future cash inflows be equal to the initial investment, we need to plug in the Initial cost in place of present value in the formula and solve for g.

739000 = 57000 * (1+g)  /  (0.156 - g)

739000 * (0.156 - g)  =  57000 + 57000g

115284 - 739000g = 57000 + 57000g

115284 - 57000 = 57000g + 739000g

58284 = 796000g

58284 / 796000 = g

g = 0.07322 or 7.322%

This answer is rounded off to 3 decimal places.

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