Question

Riverdale’s Betty Cooper and Jughead are planning to buy Pop’s Chock’lit Shoppe. As knowledgeable investors, they know that the restaurant industry is a little risky and they expect to be compensated with a high return. They have a required return of 8%. They expect to pay $300,000 to buy the shoppe today but they expect $50,000 for the next 8 years afterwards (starting in year 1).

Using the IRR method, should they take on the project?

Answer 1

IRR is the internal Rate of Return of a project. If the IRR of the project is less than the requored rate of return then the project should not be accepted. However if the IRR of the Project is more than the required rate of return (8%) then the project should be accepted.

IRR can be computed using two methods

1) Excel

	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7	Year 8
Intial Investment (Cash Outflow)	-300000
Cash Inflows Every Year		50000	50000	50000	50000	50000	50000	50000	50000
Net Cash Flows	-300000	50000	50000	50000	50000	50000	50000	50000	50000
Formula for Computing IRR	=IRR( Net Cash Flows of the project)
IRR	6.88%

As the IRR of the project is less than 8 % (which is the required rate of return ) the project should not be accepted.

Now, the other methord to compute IRR

2) Without Excel

IRR is also the discount rate where NPV of the project is 0.

NPV = Present Values of Cash Inflows - Initial Investment

Now the Discount rate to compute the present values should be such that the NPV is 0. This discount rate is the IRR of the project.

	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7	Year 8
Intial Investment (Cash Outflow)	-300000
Cash Inflows Every Year		50000	50000	50000	50000	50000	50000	50000	50000
Net Cash Flows (A)	-300000	50000	50000	50000	50000	50000	50000	50000	50000
Discount Rate @ 8% (B)	1	0.925926	0.857339	0.793832	0.73503	0.680583	0.63017	0.58349	0.540269
Derivation of Discount Rate @ 8% (B)	=1/1.08^0	=1/1.08^1	=1/1.08^2	=1/1.08^3	=1/1.08^4	=1/1.08^5	=1/1.08^6	=1/1.08^7	=1/1.08^8
Present Values (C =AxB)	-300000	46296.3	42866.94	39691.61	36751.49	34029.16	31508.48	29174.52	27013.44
A summation of all the present Values would give us the NPV of the project
NPV	-12668.1

Using Hit and trial method using a discount rate of 6.88 % we would have NPV = 0. This discount rate is the IRR of the project

As the NPV of the project is negative therefore we can say that the IRR of the project is less than the discount rate required . Therefore the Project should not be accepted.