Question

please show your work and write out your solutions in detail by giving formulas and a short summary at the end. Please do not just post about financial calc or excel without explaining how you got the answer. thank you!

Consider the following mutually exclusive projects:

	T=0	1	2	3
Project X:	-100	20	30	90
Project Y:	-100	80	30	20

1. Find IRRs for both projects.
2. Find the cross-over rate.
3. Construct a graph, where you will show the NPV of each project as a function of its discount rate (i.e NPV on the vertical axis and r on the horizontal axis). Both NPVs should be on the same graph. This graph is the NPV schedule.
4. Please describe as fully as possible which project is the best and under which circumstances.

Answer 1

	A	B	C	D	E	F	G
1		Year 0	Year 1	Year 2	Year 3	Formula	IRR
2	Project X:	-100	20	30	90	IRR(B2:E2)	14.64%	IRR of Project X
3	Project Y:	-100	80	30	20	IRR(B3:E3)	19.23%	IRR of Project Y
4	Project X (-) Project Y:	0	-60	0	70	IRR(B4:E4)	8.01%	Cross-over Rate

• IRR can be manually calculated on paper using the below formula where we will calculate NPV on two rates based on trial and use those figures in the formula to get IRR.
• IRR = Lower Rate(say 10%) + (((NPV@ 10% /(NPV@20%-NPV@10%))*(Higher Rate(say 20%) - Lower Rate(i.e.10%))
• For calculating Cross-over Rate, We can subtract Project Y cashflows from Project X and then calculate IRR of the subtracted cashflows.

3. Preparing NPV Graph :

Rate	NPV -Project X	NPV -Project Y
5%	$24.00	$20.68
10%	$10.59	$12.55
15%	($0.75)	$5.40
20%	($10.42)	($0.93)

D. Project X is better at NPV of less than 8% (cross-over rate) and Project Y is better at NPV of more than 8%.

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