Question

1. Consider the following two projects. The cost of capital for both projects is 15%.

Project	Year 0	1	2	3	4	5
Alpha	-55,000	15,000	14,000	22,000	30,000	35,000
Gamma	-80,000	40,000	30,000	25,000	25,000	20,000

1. Calculate the IRR for each project and determine which one is better.
2. Calculate the NPV for each project and determine which one is better.
3. Based on profitability index method, which project is better?
4. Overall, which project should be accepted assuming they are mutually exclusive? Why?

Answer 1

	Present Value = Future value/ ((1+r)^t)
	where r is the interest rate that is 15% and t is the time period in years.
	Net present value (NPV) = initial investment + sum of present values of future cash flows.
	Use the financial formulas function in excel to find the Internal rate of return (IRR)
	Profitability Index (PI) = sum of present values of future cash flows/initial investment
	PROJECT ALPHA
	Year	0	1	2	3	4	5
	cash flow	-55000	15000	14000	22000	30000	35000
	present value		13043.48	10586.01	14465.36	17152.6	17401.19
	NPV	17648.63
	Internal rate of return	25.73%
	PI	1.32
	PROJECT GAMMA
	Year	0	1	2	3	4	5
	cash flow	-80000	40000	30000	25000	25000	20000
	present value		34782.61	22684.31	16437.91	14293.83	9943.535
	NPV	18142.19
	Internal rate of return	25.55%
	PI	1.23
a)		IRR
	PROJECT ALPHA	25.73%
	PROJECT GAMMA	25.55%
	The IRR is the discount rate for which NPV is zero. Select the project if the cost of capital
	is less than the IRR. The higher the IRR, the more profitable is the project.
	Project Alpha is better because it has a higher IRR.
b)		NPV
	PROJECT ALPHA	17648.63
	PROJECT GAMMA	18142.19
	The higher the NPV, the better the project.
	Project Gamma is better because it has a higher NPV.
c)		PI
	PROJECT ALPHA	1.32
	PROJECT GAMMA	1.23
	The higher the PI, the more profitable the project.
	Project Alpha is better because it has a higher PI.
d)	Based on the IRR and PI rule, project Alpha is better.
	Based on NPV, project Gamma is better.
	Overall, project Alpha is better because project Alpha is
	better according to two of the rules. Project Gamma is
	only better as per the NPV rule.