Question

Hangers Corp. is in the process of choosing the better of two equal-risk, mutually exclusive
capital expenditure projects—X and Y. The relevant cash flows for each project are shown in the
following table. The firm’s weighted average cost of capital is 11%.

Year Expected Net Cash Flows
project X project Y
0 -$625,000 -$600,000
1 156,250 250,000
2 156,250 100,000
3 156,250 200,000
4 156,250 100,000

a) Calculate the Payback Period for both the projects.
b) Calculate the NPV and the Profitability Index for each of the projects. Please explain which
project should be selected and why?

Answer 1

Pay Back Period = Last year with negative cumulative cash flow + (Absolute value of cumulative cash flow in the last year in which Cumulative CF is negative / Cash Flow during the year in which cumulative F turns positive)

Profitability Index = Sum of PV of all cash flows / Initial Investment

NPV = Sum of Present value of all years - Initial Investment

Present Value = CF/ (1+k)^t or CF x Discount Factor

where, K = Cost of Capital & t is the time period

Discount Factor = 1/ (1+k)^t

a) Pay Back Period

For Project X, Cumulative cash flow turn positive (or zero) at the end of year 4.

i) Pay Back period for X project = 4 years

ii) Pay Back period for project Y = 3 = 50000/ 100000 = 3.5 years

The following table shows the cumulative cash flows of X & Y project

Year	Project X cash Flows	Project X Cumulative Cash Flows	Project Y cash Flows	Project Y Cumulative Cash Flows
0	(625,000)	(625,000)	(600,000)	(600,000)
1	156,250	(468,750)	250,000	(350,000)
2	156,250	(312,500)	100,000	(250,000)
3	156,250	(156,250)	200,000	(50,000)
4	156,250	-	100,000	50,000

b) For calculating NPV & PI,

NPV for project X

= 156250/(1+11%)^1 + 156250 x 1/(1+11%)^2 + 156250/ (1+11%)^3 + 156250/(1+11%)^4 - 625000

= 156250 x 0.901 + 156250 x 0.812 + 156250 x 0.731 + 156250 x 0.659 - 625000

= 140766 + 126816 + 114249 + 102927 - 625000

= 484,757 - 625000

= - $140243

NPV for Project Y

= 250000/(1+11%)^1 + 100000 x 1/(1+11%)^2 + 200000/ (1+11%)^3 + 100000/(1+11%)^4 - 600000

= 250000 x 0.901 + 100000 x 0.812 + 200000 x 0.731 + 100000 x 0.659 - 600000

= 225225 + 81162 + 146238 + 65873 - 600000

= 518499 - 600000

= - $81501

Profitability Index for X

= PV of all cash inflows / Investment

= 484757 / 625000

= 0.776

Profitability Index for Y

= 518499 / 600000

= 0.864

Since none of the projects have NPV > 0, it would be wise not to go for any of the project.

However , if one were to chose on the basis og PBP, project Y with lesser PBP is better.

Table for calculating NPV & PI

Year	Project X cash Flows (CFx)	Project Y cash Flows (CFy)	Discount Factor (D)	Discounted Cash flows of Project X D x CFx	Discounted Cash flows of Project Y D x CFy
0	-625000	-600000	1.000	-625000	-600000
1	156250	250000	0.901	140766	225225
2	156250	100000	0.812	126816	81162
3	156250	200000	0.731	114249	146238
4	156250	100000	0.659	102927	65873
	Total			-140243	-81501