Question

Q3. Mobile company hired a consultant to propose a way to increase company revenues. The consultant has evaluated two mutually exclusive project with the following information provided for each project. Project X Project Y Capital investment Annual cash flow Estimated useful life 1,105,000 180,000 10 years 625,000 105,000 10 years Mobile uses discount rate of 9% to evaluate both project Instructions: a. Calculate NPV of both projects b. Calculate profitably index for each project C. Which project should be accepted

Answer 1

(a)-The Net Present Value (NPV) of the Projects

Net Present Value (NPV) of Project-X

Year	Annual cash flows ($)	Present Value Factor (PVF) at 9.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	1,80,000	0.9174312	1,65,137.61
2	1,80,000	0.8416800	1,51,502.40
3	1,80,000	0.7721835	1,38,993.03
4	1,80,000	0.7084252	1,27,516.54
5	1,80,000	0.6499314	1,16,987.65
6	1,80,000	0.5962673	1,07,328.12
7	1,80,000	0.5470342	98,466.16
8	1,80,000	0.5018663	90,335.93
9	1,80,000	0.4604278	82,877.00
10	1,80,000	0.4224108	76,033.95
TOTAL		11,55,178.39

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $11,55,178.39 - $11,05,000

= $50,178.39

Net Present Value (NPV) of Project-Y

Year	Annual cash flows ($)	Present Value Factor (PVF) at 9.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	1,05,000	0.9174312	96,330.28
2	1,05,000	0.8416800	88,376.40
3	1,05,000	0.7721835	81,079.27
4	1,05,000	0.7084252	74,384.65
5	1,05,000	0.6499314	68,242.80
6	1,05,000	0.5962673	62,608.07
7	1,05,000	0.5470342	57,438.60
8	1,05,000	0.5018663	52,695.96
9	1,05,000	0.4604278	48,344.92
10	1,05,000	0.4224108	44,353.13
TOTAL		6,73,854.06

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $6,73,854.06 - $625,000

= $48,854.06

(b)-The Profitability Index (PI) for the Projects

Profitability Index (PI) for Project-X

Profitability Index (PI) = Present Value of annual cash inflows / Initial Investment

= $11,55,178.39 / $11,05,000

= 1.05

Profitability Index (PI) for Project-Y

Profitability Index (PI) = Present Value of annual cash inflows / Initial Investment

= $673,854.06 / $625,000

= 1.08

DECISION

-As per the Net Present Value method, the Project-X should be accepted, since it has the highest NPV of $50,178.39.

-As per the PI method, the Project-Y should be accepted, since it has the higher Profitability Index of 1.08.

NOTE

The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)n], where “r” is the Discount Rate/Cost of capital and “n” is the number of years.