Question

Elgin Restaurant Supplies is analyzing the purchase of manufacturing equipment that will cost $62,000. The annual cash inflows are as follows. Use Appendix D.

Year	Cash Flow
1		$31,000
2		29,000
3		24,000

a. Determine the IRR using interpolation. (Round the intermediate calculations to the nearest whole dollar. Round the final answer to 2 decimal places.)

IRR          %

b. With a cost of capital of 16 percent, should the machine be purchased?

• Yes

• No

c. With information from part b, compute the PI. (Round the final answer to 3 decimal places.)

PI            

Problem 12-25

You are asked to evaluate the following two projects for Boring Corporation. Use a discount rate of 13 percent. Use Appendix B.

Project X (DVDs of the Weather Reports) ($18,000 Investment)						Project Y (Slow-Motion Replays of Commercials) ($38,000 Investment)
Year		Cash Flow				Year		Cash Flow
1			$9,000			1			$19,000
2			7,000			2			12,000
3			8,000			3			13,000
4			7,600			4			15,000

a. Calculate the profitability index for project X. (Round "PV Factor" to 3 decimal places. Round the final answer to 2 decimal places.)

PI            

b. Calculate the profitability index for project Y. (Round "PV Factor" to 3 decimal places. Round the final answer to 2 decimal places.)

PI            

c. Using the NPV method combined with the PI approach, which project would you select? Use a discount rate of 13 percent.

• Project Y

• Project X

Answer 1

Answer 1)

Computation of Elgin Restaurant Supplies - IRR & PI
Year	Cash Flow	Discounting Factor @16%	DCF	Discounting Factor @20%	DCF
1	31000	0.862	26,724.14	0.833	25,833.33
2	29000	0.743	21,551.72	0.694	20,138.89
3	24000	0.641	15,375.78	0.579	13,888.89
Present Value (PV)	63,651.65		59,861.11

a) IRR using Interpolation

IRR = Lowest Discount Rate + [NPV at Lower rate * (Higher Rate - Lower Rate) / (NPV at Lower Rate - NPV at Higher Rate)]

IRR = 16% +[63651.65 * (20% - 16%) / (63,651.65 - 59,861.11)]

IRR = 16.672%

b) Yes Machine can be purchased with a cost of capital 16%

NPV=TVECF−TVIC

where: TVECF=Today’s value of the expected cash flows ; TVIC=Today’s value of invested cash

NPV ​= (63,651.65 - 62,000) = 1,651.65

A positive net present value indicates that the projected earnings generated by a project or investment - in present dollars - exceeds the anticipated costs, also in present dollars. It is assumed that an investment with a positive NPV will be profitable.

c) Profitability Index = [PV of Future Cash Flow / Initial Investment]

PI = (63,651.65 / 62,000) = 1.027

Answer 2)

a) 1.314

b) 1.169

c) Project X - $ 5,652.252

Project Y - $ 6,421.353

Workings:

Boring Corporation Project X (DVDs of the Weather Reports) ($18,000 Investment)		Boring Corporation Project Y (Slow-Motion Replays of Commercials) ($38,000 Investment)
Year	Cash Flow	Discounting Factor @13%	DCF	Year	Cash Flow	Discounting Factor @13%	DCF
1	9000	0.885	7,964.602	1	19000	0.885	16,814.16
2	7000	0.783	5,482.027	2	12000	0.783	9,397.76
3	8000	0.693	5,544.401	3	13000	0.693	9,009.65
4	7600	0.613	4,661.222	4	15000	0.613	9,199.78
Present Value	23,652.252	Present Value	44,421.35

Sl No	Particulars	Project X	Project Y
a	Present Value	23,652.252	44,421.35
b	Initial Investment	18,000	38,000
c	Net Present Value (a-b)	5,652.252	6,421.353
d	Profitability Index (a/b)	1.314	1.169