Question

The large furniture retailer "Sofa So Good" is evaluating two mutually exclusive projects: NPV versus IRR. Consider the following projects where the firms may only choose one not both:

The firm's cost of capital/required return equals 9%.

NOTE: The firm's cost of capital K, acts as a hurdle rate, and is based on the costs involved in financing other firm projects. The Cost of capital allows us to decide to accept or reject an investment, using IRR, which additionally allows us to use it as the discount rate, R, in NPV calculations.

Years	Cash Flow Project X	Cash Flow Project Y	The differential (X-Y) or (Y-X)
0	-$69,000	-$69,000	???
1	$13,000	$29,000	???
2	$33,000	$24,000	???
3	$38,000	$27,000	???

a) What would be the Internal Rate of Return for each investment, X and Y?

b) What would be the NPV's of each project, if the cost of capital is 9% for the firm, "Sofa So Good"?

c) What is the crossover point, otherwise known as the discount crossover rate, where both projects cross? (Remember to subtract X-Y cash flows, or Y-X, and then set series equal to zero, and solve for IRR)

d) Sketch the NPV profile for the above data.

e) Finally, which project should you accept, under what circumstances, and why?

**Please include a timeline and show all work for detail**

Answer 1

Years	Cash Flow Project X	Cash Flow Project Y	The differential (X-Y) or (Y-X)
0	$-69,000.00	$-69,000.00	$            -
1	$ 13,000.00	$ 29,000.00	$-16,000.00
2	$ 33,000.00	$ 24,000.00	$   9,000.00
3	$ 38,000.00	$ 27,000.00	$ 11,000.00
IRR	9.03%	7.89%
NPV	$           45.02	$   -1,345.22
Crossover rate	15.68%

NPV formula:
=H7+NPV(0.09,H8:H10) where H7 is the initial cash flow and the rest are other cash flows

Project X shall be chosen at 9% as it provides positive NPV at that rate