Question

Michael Dell is considering investing $4.5 billion today to take Dell Inc. private. If he takes Dell Inc. private, he will not receive any benefits for 4 years. Then he will receive $225 million per year for 4 years starting exactly five years from today. After that, he will receive $275 million per year for the following 3 years. At that point, the cash flows will increase at 4% per year forever. If Michael Dell has a discount rate of 9%, what is the NPV of this investment and should Michael Dell

Answer 1

Present value (PV) = sum of present value of all future cash flows

After end of 3 years there is a perpetuity model with constant dividend growth which can be calculated using the formula Dividend * (1+ dividend growth rate)/ (return rate - growth rate) which needs to be discounted back from year 3 to year 0 (present value)

1 billion = 1000 million

4.5 billion = 4500 million

PV = -4500+ 225/(1+9%)^5+ 225/(1+9%)^6 +225/(1+9%)^7 +225/(1+9%)^8+ 275/(1+9%)^9+275/(1+9%)^10+275/(1+9%)^11+275*(1+4%)/(9%-4%)/(1+9%)^11=$ -1417.56 mn = $ =-1.4 billion

Since the NPV is negative, Dell shouldn't do this