Question

Use the following information to answer next three questions:

  IO                    PI        IRR                 LIFE

Project 1       $300,000        1.12     14.38%           15 years

Project 2       $150,000        1.08     13.32%           6 years

Project 3       $100,000        1.20     16.46%           3 years

Assume that the cost of capital is 12%.

If the firm has unlimited capital and each project is independent, which project(s) should be accepted?

A) Project 1 B) Projects 1 and 2 C) Projects 1 and 3 D) Projects 2 and 3 E) Projects 1, 2 and 3

Answer 1

Answer E. Because all the projects NPV is positive

At IRR, Present value of cash outflows = Present value of cash inflows

for computation of annual cash flows;

= Total initial outflows / Annuity value at IRR for respective project years.

All the calculations made below,

Project 1:
Annuity factor for 15 years at 14.38% per year	= (1-(1/(1+r)^n))/r
				= ((1-(1/(1+0.1438)^15))/0.1438,4)
				6.0273
Therefore Annual installment amount		=300000/6.0273
				=49773.53
Year	Particulars	Cash Flows	Present Value Factor @12% [(1/1.12)^n]	Discounted Cash Flows
0	Initial Cost	-3,00,000.00	1.0000	-3,00,000.00
1	Annual Cash Flow	49,773.53	0.8929	44,440.65
2	Annual Cash Flow	49,773.53	0.7972	39,679.15
3	Annual Cash Flow	49,773.53	0.7118	35,427.82
4	Annual Cash Flow	49,773.53	0.6355	31,631.98
5	Annual Cash Flow	49,773.53	0.5674	28,242.84
6	Annual Cash Flow	49,773.53	0.5066	25,216.82
7	Annual Cash Flow	49,773.53	0.4523	22,515.02
8	Annual Cash Flow	49,773.53	0.4039	20,102.69
9	Annual Cash Flow	49,773.53	0.3606	17,948.83
10	Annual Cash Flow	49,773.53	0.3220	16,025.74
11	Annual Cash Flow	49,773.53	0.2875	14,308.70
12	Annual Cash Flow	49,773.53	0.2567	12,775.63
13	Annual Cash Flow	49,773.53	0.2292	11,406.81
14	Annual Cash Flow	49,773.53	0.2046	10,184.65
15	Annual Cash Flow	49,773.53	0.1827	9,093.44
Net Present Value	39,000.77
Project 2:
Annuity factor for 6 years at 13.32% per year		= (1-(1/(1+r)^n))/r
				= ((1-(1/(1+0.1332)^6))/0.1332)
				3.9622
Therefore Annual installment amount		=150000/3.9622
				=37857.76
Year	Particulars	Cash Flows	Present Value Factor @12% [(1/1.12)^n]	Discounted Cash Flows
0	Initial Cost	-1,50,000.00	1.0000	-1,50,000.00
1	Annual Cash Flow	37,857.76	0.8929	33,801.57
2	Annual Cash Flow	37,857.76	0.7972	30,179.97
3	Annual Cash Flow	37,857.76	0.7118	26,946.41
4	Annual Cash Flow	37,857.76	0.6355	24,059.29
5	Annual Cash Flow	37,857.76	0.5674	21,481.51
6	Annual Cash Flow	37,857.76	0.5066	19,179.92
Net Present Value	5,648.67
Project 3:
Annuity factor for 3 years at 16.46% per year		= (1-(1/(1+r)^n))/r
				= ((1-(1/(1+0.1646)^3))/0.1646)
				=2.2291
Therefore Annual installment amount		=100000/2.2291
				=44861.15
Year	Particulars	Cash Flows	Present Value Factor @12% [(1/1.12)^n]	Discounted Cash Flows
0	Initial Cost	-1,00,000.00	1.0000	-1,00,000.00
1	Annual Cash Flow	44,861.15	0.8929	40,054.60
2	Annual Cash Flow	44,861.15	0.7972	35,763.03
3	Annual Cash Flow	44,861.15	0.7118	31,931.28
Net Present Value	7,748.91