Question

Miltons Construction is analyzing its capital expenditure proposals for the purchase of equipment in the coming year. The capital budget is limited to $7,000,000 for the year. Lyssa Bryce, staff analyst at Miltons, is preparing an analysis of the three projects under consideration by Chris Miltons, the company's owner.

(a)

(b&c)

Answer 1

(a)-The Payback Period for the each Projects

Payback Period for the Project-A

Year	Cash inflow ($)	Cumulative net Cash flow ($)
0	-42,00,000	-42,00,000
1	20,00,000	-22,00,000
2	20,00,000	-2,00,000
3	20,00,000	18,00,000
4	20,00,000	38,00,000

Payback Period = Years before full recover + (Unrecovered cash inflow at start of the year/cash flow during the year)

= 2.00 Years + ($200,000 / $20,00,000)

= 2.00 Years + 0.10 Years

= 2.10 Years

Payback Period for the Project-B

Year	Cash inflow ($)	Cumulative net Cash flow ($)
0	-24,00,000	-24,00,000
1	7,00,000	-17,00,000
2	12,00,000	-5,00,000
3	6,00,000	1,00,000

Payback Period = Years before full recover + (Unrecovered cash inflow at start of the year/cash flow during the year)

= 2.00 Years + ($500,000 / $600,000)

= 2.00 Years + 0.83 Years

= 2.83 Years

Payback Period for the Project-C

Year	Cash inflow ($)	Cumulative net Cash flow ($)
0	-50,00,000	-50,00,000
1	26,00,000	-24,00,000
2	26,00,000	2,00,000
3	2,00,000	4,00,000
4	1,00,000	5,00,000

Payback Period = Years before full recover + (Unrecovered cash inflow at start of the year/cash flow during the year)

= 1.00 Years + ($24,00,000 / $26,00,000)

= 1.00 Years + 0.92 Years

= 1.92 Years

DECISION

As per the Payback period method, the PROJECT-C should be accepted, since it has the lowest Payback period of 1.92 Years

(b)-The Net Present Value (NPV) for each project

The Net Present Value (NPV) of Project-A

Year	Annual cash flows ($)	Present Value Factor (PVF) at 6.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	20,00,000	0.943396226	18,86,792.45
2	20,00,000	0.889996440	17,79,992.88
3	20,00,000	0.839619283	16,79,238.57
4	20,00,000	0.792093663	15,84,187.33
TOTAL		69,30,211.23

Net Present Value (NPV) of the Project = Present value of annual cash inflows – Initial investment costs

= $69,30,211.23 - $42,00,000

= $27,30,211.23

The Net Present Value (NPV) of Project-B

Year	Annual cash flows ($)	Present Value Factor (PVF) at 6.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	7,00,000	0.943396226	6,60,377.36
2	12,00,000	0.889996440	10,67,995.73
3	6,00,000	0.839619283	5,03,771.57
TOTAL		22,32,144.66

Net Present Value (NPV) of the Project = Present value of annual cash inflows – Initial investment costs

= $22,32,144.66 - $24,00,000

= -$167,855.34 (Negative NPV)

The Net Present Value (NPV) of Project-C

Year	Annual cash flows ($)	Present Value Factor (PVF) at 6.00%	Present Value of annual cash flows ($) [Annual cash flow x PVF]
1	26,00,000	0.943396226	24,52,830.19
2	26,00,000	0.889996440	23,13,990.74
3	2,00,000	0.839619283	1,67,923.86
4	1,00,000	0.792093663	79,209.37
TOTAL		50,13,954.16

Net Present Value (NPV) of the Project = Present value of annual cash inflows – Initial investment costs

= $50,13,954.16 - $50,00,000

= $13,954.16

DECISION

As per the NPV Method, the PROJECT-A should be accepted, since it has the highest Positive NPV of $27,30,211.23.

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.