Question

Don tran has been working on an advanced technology in laser eye surgery. his technology will be available in the near term. he anticipates his first annual cash flow from the technology to be $183,000, received two years from today. subsequent annual cash flows will grow at 4.3 percent in perpetuity. what is the value today of the technology if the discount rate is 11 percent?

Answer 1

The value today of the technology is $32,872,420.66.

Step-by-step explanation:

To calculate the present value of the technology's cash flows, we need to discount each cash flow to its present value. The future cash flow of $183,000 received two years from today will be discounted to its present value using the formula PV = FV / (1 + r)t, where PV is the present value, FV is the future value, r is the discount rate, and t is the number of years. For subsequent cash flows that grow at a rate of 4.3 percent in perpetuity, we can use the formula PV = CF / r - g, where CF is the cash flow, r is the discount rate, and g is the growth rate.

Calculating the present value of the first cash flow of $183,000, we have PV = 183,000 / (1 + 0.11)² = $145,147.93. To calculate the present value of subsequent cash flows, we need to calculate the perpetuity cash flow and then discount it. The perpetuity cash flow can be calculated using the formula CF / r - g = 183,000 / (0.11 - 0.043) = $3,600,000. Discounting the perpetuity cash flow to its present value using the discount rate of 11 percent gives us PV = 3,600,000 / 0.11 = $32,727,272.73.

Adding the present values of the first cash flow and the perpetuity cash flow, we have a total present value of $145,147.93 + $32,727,272.73 = $32,872,420.66. Therefore, the value today of the technology is $32,872,420.66.