Question

Question 1:
Part a: Evaluate a 4 - year project costing $25,000 and returning $8,000 annually using the payback period technique and a 3-year cutoff.

Part b: Evaluate the project above using the NPV method and a 12% required rate.

Part c: Evaluate the project in part "a" using the IRR method and a 10% required rate.

Please show written work (if possible) and formulas used, thank you!

Answer 1

1. Part a.

Payback Period = ( Last Year with a Negative Cash Flow ) + [( Absolute Value of negative Cash Flow in that year)/ Total Cash Flow in the following year)]

= 3+ ( 1000/8000)

= 3.125 years

Evaluation : Since the cutoff for the Project is less than the actual payback period, the project must not be accepted.

Note:

Investment	Cash Inflow	Net Cash Flow
-25,000	-	-25,000	(Investment + Cash Inflow)
-	8,000	-17,000	(Net Cash Flow + Cash Inflow)
-	8,000	-9,000	(Net Cash Flow + Cash Inflow)
-	8,000	-1,000	(Net Cash Flow + Cash Inflow)
-	8,000	7,000	(Net Cash Flow + Cash Inflow)

Part b.

NPV = Present Value of Cash Inflows - Present Value of Cash Outflows

= [ $ 8000 * 1/(1.12) ^ 1 +$ 8000 * 1/(1.12) ^2+$ 8000 * 1/(1.12) ^3+$ 8000 * 1/(1.12) ^4] - $ 25,000

=- $ 701.21

Hence the NPV is - $ 701.21

Evaluation = Since the project has negative NPV, the project must not be accepted. This is because the projects with a positive NPV are beneficial for the company.

Part c.

Let the IRR be x.

Now , Present Value of Cash Outflows=Present Value of Cash Inflows

25000 = 8000/(1.0x) +8000/ (1.0x)^2 +8000/(1.0x)^3+ $ 8000/(1.0x)^4      

Or x= 10.662%

Hence the IRR is 10.662%

Evaluation = Since, the project has higher IRR than the required return, the project must be accepted. This is because the project in which the IRR is greater than the required return is beneficial to the company.