You are considering introducing a new Tex-MexThai fusion restaurant. The initial

Question

You are considering introducing a new Tex-MexThai fusion restaurant. The initial outlay on this new restaurant is $6.3 million and the present value of the free cash flows (excluding the initial outlay) is $5.4 million, such that the project has a negative expected NPV of $0.9 million. Looking closer, you find that there is a 60 percent chance that this new restaurant will be well received and will produce annual cash flows of $812,000 per year forever (a perpetuity), whereas there is a 40 percent chance of it producing a cash flow of only $190,000 per year forever (a perpetuity) if it isnt received well. The required rate of return you use to discount the project cash flows is 10.4 percent. However, if the new restaurant is successful, you will be able to build 10 more of them and they will have costs and cash flows similar to the successful restaurants costs and cash flows.

a. In spite of the fact that the first restaurant has a negative NPV, should you build it anyway? Why or why not?

b. What is the expected NPV for this project if only one restaurant is built but isnt well received? What is the expected NPV for this project if 10 more are built after one year and are well received? (ignore the fact that there would be a time delay in building additional restaurants.

Explanation / Answer

Solution:

a. There is a 60% probability (P1) that the restaurant will be successful, in that case the cash flows per year would be $812,000.
The present value of future cash flows in that case (PV1) = $812,000/10.4% = $7,807,692

Also, there is a 40% probability (P2) that the restaurant will not be successful, cash flows per year would be $190,000
The present value of future cash flows in that case (PV2) = $190,000/10.4% = $1,826,923

Now expected present value = P1 * PV1 + P2 * PV2
                                              = 0.6*7,807,692 + 0.4*1,826, 923
                                              = $5,415,384.62

The initial outlay of the restaurant is $6,300,000

Hence expected NPV = $5,415,384.6 - $6,300,000
                                   = - $884,615

Hence, from probabilistic cash flows also, the net present value is negative, so we should not build the restaurant.

b. If the restaurant is not well received , future cash flows are $190,000 per year

Expected present value = $190,000/10.4%
                                      = $1,826,923

Expected NPV = $1,826,923 - $6,300,000
                         = - $4,473, 077

Hence expected NPV in this case would be -$4.5 million

Now, assuming that the first restaurant has a negative NPV of $884,615 (calculated in 1st part) (NPV1) and still after 1 year, 10 more are built which become successful,

Then, future cash flows of 1 of those 10 would be $812,000
Present value of those cash flows = $812,000/10.4%
                                                       = $7,807,692
Hence expected NPV of 1 of those 10 would be = $7,807,692 - $6,300,000
                                                                             = $1,507,692

So expected NPV for all 10 would be = 10 * 1,507,692
                                                            = 15,076,923 (NPV2)

Hence, expected NPV of the project = NPV1 + NPV 2
                                                          = -884,615 + 15,076,923
                                                          = $14,192, 307

Hence, expected NPV of the project in that case would be ~$14.2 million
                                                             

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