Question

MUTUALLY EXCLUSIVE PROJECTS WITH DIFFERENT LIVES
You are offered a food concession at the Charros de Jalisco Stadium to sell food during the matches. You expect to have profits of $40,000 every match and there are 20 matches per season (year). There are two options: Pay an initial fee of $2,000,000 for a 10 year contract, or pay an initial fee of $1,000,000 for a 5 year contract (only 5 years, it can’t be renewed). With a MARR of 10% per year:

a) What is the best option with a study period of 10 years? Assume you can invest your capital earning an interest rate equal to the MARR. Use FV
b) What is the best option with a study period of 5 years? Assume that if you choose the 10 year contract, after 5 years you can sell your rights for the remaining 5 years to another company at $1,000,000. Use NPV

Answer 1

1. Study period of 10 Years
	As the Life of two projects is different we have to compare
	using Annualised NPV as following
		Option - 1	Option - 2
	Annual Profits	800000	800000
	No of Years	10	5
	Rate of Return	10%	10%
	PV of Profits	4915654	3032629
	Initial Fee	2000000	1000000
	Net Present Value(NPV)	2915654	2032629
	Discount Factor for above period(DF)	6.1446	3.7908
	Annual NPV (NPV/DF)	474509	536203
	As Anualised NPV is higher, Option-2 is the best option
2. Study Period of 5 Years
	If we choose to sell the rights after 5 years at 1,000,000
	NPV of Option-1 will change as follows:
	a. PV of Sale Value received after 5 Years
	Sale Value	1000000.00
	Received in Year	5
	Rate of Return	10%
	PV of Sale Value (a)	620921
	b. PV of Profits
	Annual Profits	800000
	No of Years	5
	Rate of Return	10%
	PV of Profits (b)	3032629
	Initial Fee (Cash Outflow)(c)	2000000
	NPV (a+b-c)	1653551
	As the Period of Both options now is same(5 yrs)
	we don’t need Annualised NPV,
	we can compare normal NPV for decision making
	NPV of Option-1	1653551
	NPV of Option-2	2032629
	As NPV is higher, Option-2 is the best option.