Question

Opening a restaurant is risky. Its success or failure depends on whether customers like it. Often, success does not occur overnight. It may take several years before a robust clientele of neighborhood regulars develops, and the restaurant gains recognition and reputation around the city and among tourists. Much of the success and recognition depends on whether other new restaurants open around the same time. In addition, the current culinary trend plays a significant role. Bottom line is, while average statistics on restaurant successes and failures in specific areas is available, it is difficult to predict ahead of time whether a particular restaurant will be successful, and it may take time and patience to find out. You are assigned with a task to determine whether to pursue a project that involves opening a new restaurant in the North Shore neighborhood of Milwaukee. You were able to collect the following information.

To start operations, you need to renovate an existing restaurant space at the cost of $200,000. The space will be rented from a real estate company at the cost of $60,000 per year. In addition, the fixed cost of running the restaurant, regardless of the success of the restaurant, is estimated at $150,000 per year. If the restaurant is successful during a certain year, it will produce gross earnings (before the fixed cost or rent is subtracted) of $800,000 per year. If the restaurant is not successful, it will produce gross earnings of $50,000 per year during that year.

You also estimated that the likelihood that the restaurant will be successful in the first year of operations is 10%. If the restaurant becomes successful during a particular year, it will remain successful forever. The likelihood that the restaurant will become successful in the second year of operations is 20%. The likelihood that the restaurant will become successful in the third year of operations is 5%. If the restaurant has not become successful by the end of the third year of operations, it will remain unsuccessful.

Should the company open the restaurant? You assume there is no corporate tax, and due to the volatile and risky nature of the restaurant business, you require a discount rate of 20%.

Answer 1

State 1: Restaurant is successful in year 1

Formula	Year (n)	0	Forever
	Initial investment (I)	(200,000)
	Gross earning (G)		800,000
	Rental cost ('R)		(60,000)
	Fixed cost (F)		(150,000)
(G-R-F)	Net cash flow (CF)	(200,000)	5,90,000
CFn/20%	PV of cash flow	(200,000)	2,950,000
	NPV	2,750,000

State 2: Restaurant is successful in year 2

Formula	Year (n)	0	1	Forever
	Initial investment (I)	(200,000)
	Gross earning (G)		50,000	800,000
	Rental cost ('R)		(60,000)	(60,000)
	Fixed cost (F)		(150,000)	(150,000)
(G-R-F)	Net cash flow (CF)	(200,000)	(160,000)	590,000
CFn/(1+20%)^n CFforever/20%	PV of cash flow	(200,000)	(133,333)	2,950,000
	NPV	2,616,667

State 3: Restaurant is successful in year 3

Formula	Year (n)	0	1	2	Forever
	Initial investment (I)	(200,000)
	Gross earning (G)		50,000	50,000	800,000
	Rental cost ('R)		(60,000)	(60,000)	(60,000)
	Fixed cost (F)		(150,000)	(150,000)	(150,000)
(G-R-F)	Net cash flow (CF)	(200,000)	(160,000)	(160,000)	590,000
CFn/(1+20%)^n CFforever/20%	PV of cash flow	(200,000)	(133,333)	(111,111)	2,950,000
	NPV	2,505,556

State 4: Restaurant is unsuccessful forever

Formula	Year (n)	0	Forever
	Initial investment (I)	(200,000)
	Gross earning (G)		50,000
	Rental cost ('R)		(60,000)
	Fixed cost (F)		(150,000)
(G-R-F)	Net cash flow (CF)	(200,000)	(160,000)
CFn/20%	PV of cash flow	(200,000)	(800,000)
	NPV	(1,000,000)

State	Successful in Year 1	Successful in Year 2	Successful in Year 3	Unsuccessful by Year 3
Probability (P)	10%	20%	5%	65%
NPV	27,50,000	26,16,667	25,05,556	(10,00,000)
Weighted NPV (P*NPV)	2,75,000	5,23,333	1,25,278	(6,50,000)
Expected NPV	2,73,611

The expected NPV is positive so the company can open the restaurant.