4. (15%) Consider the following two mutually exclusive projects, X and Y, and th
ID: 1169994 • Letter: 4
Question
4. (15%) Consider the following two mutually exclusive projects, X and Y, and their cash flows information, Project Year 0 ($2,600) (S2,700) Year 1 $1,000 S500 Cash Flows Year 2 $1,500 S950 Year 3 $600 $1,300 Year 4 $500 $1,400 (a) Assume that the discount rate is 14%, calculate the Payback Period. Modified RR McKinsey's approach), and Profitability Index for Project Y only. Given that the Payback Period and Profitability Index of Project X are, respectively, 2.1667 years and 1.0509, state and concisely justify your choice between these two mutually exclusive projects, X versus Y, according to EACH of the two capital budgeting methods, respectively. Note that the company demands a quick recovery rate of 1.5 years on its projects. (b) (c)Apply the incremental project (IRR) analysis to select between the two mutually exclusive proiects. Explain precisely your selection according to the incremental project analysis. Given that IRRs for Projects X and Y are, respectively, 16.82% and 16.68%!Explanation / Answer
a)
Cumulative cash flow for year 0 = -2,700
Cumulative cash flow for year 1 = -2,700 + 500 = -2,200
Cumulative cash flow for year 2 = -2,200 + 950 = -1,250
Cumulative cash flow for year 3 = -1,250 + 1,300 = 50
1,250 / 1,300 = 0.9615
Payback period for project Y = 2 + 0.9615 = 2.9615 years
Future value of year 1 cash flow = 500 * ( 1 + 0.14)3 = 740.772
Future value of year 2 cash flow = 950 * ( 1 + 0.14)2 = 1,234.62
Future value of year 3 cash flow = 1,300 * ( 1 + 0.14)1 = 1,482
Future value of year 4 cash flow = 1,400 * ( 1 + 0.14)0 = 1,400
Total future cash flow = 740.772 + 1,234.62 + 1,482 + 1,400 = 4,857.392
4,857.392 = 2700 ( 1 + R)4
1.799034 = ( 1 + R)4
1.158137 = 1 + R
R = 0.158137
MIRR is 15.8137%
Profitability index = present value of future cash flows / initial investment
Present value of cash flows = 500 / ( 1 + 0.14)1 + 950 / ( 1 + 0.14)2 + 1,300/ ( 1 + 0.14)3 + 1,400 / ( 1 + 0.14)4
Present value of cash flows = 2,875.966
Profitability index = 2,875.966 / 2,700 = 1.0652
b)
According to payback period, company should reject both the projects as both the projects exceeds the payback target of 1.5 years.
According to profitablily index, company should choose project Y as it has a higher profitability index.
c)
Company should choose project X as it has a higher IRR and also the IRR exceeds the cost of capital of 14%
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