Unit price: However, you recognize that some of these estimates are subject to e
ID: 2654872 • Letter: U
Question
Unit price:
However, you recognize that some of these estimates are subject to error. Suppose that each variable may turn out to be either 10% higher or 10% lower than the initial estimate. The project will last for 10 years and requires an initial investment of $1.5 million, which will be depreciated straight-line over the project life to a final value of zero. The firm’s tax rate is 35% and the required rate of return is 12%.
What is project NPV in the “best-case scenario,” that is, assuming all variables take on the best possible value? AND what is the
"worst case scenrio?
Explanation / Answer
Net present value (NPV) is the difference between the present value of cash inflows and the initial investment.
NPV in the best case:
Initial investment = $1,500,000
Project life (n) = 10 years
MARR (r) = 12% = 0.12
Net income annually = Total sales – Total cost
= ($50 × 110% × 31,000) – ($320,000 + $30 × 90% × 31,000)
= $1,705,000 - $1,157,000
= $548,000
Straight-line depreciation = $1,500,000 / 10 = $150,000
Net income after tax = $548,000 × (1- tax rate)
= $548,000 × 65%
= $356,200
Net cash flow = $356,200 + Depreciation
= $356,200 + $150,000
= $506,200
NPV = (Present value of cash inflows) – (Initial investment)
= {$506,200 × (accumulated 12% rate after 10th year)} - $1,500,000
= ($506,200 × 5.6502) - $1,500,000
= $2,860,131.24 - $1,500,000
= $1,360,131.24 (Answer)
NPV in the worst case:
Initial investment = $1,500,000
Project life (n) = 10 years
MARR (r) = 12% = 0.12
Net income annually = Total sales – Total cost
= ($50 × 90% × 31,000) – ($320,000 + $30 × 110% × 31,000)
= $1,395,000 - $1,343,000
= $52,000
Straight-line depreciation = $1,500,000 / 10 = $150,000
Net income after tax = $52,000 × (1- tax rate)
= $52,000 × 65%
= $33,800
Net cash flow = $33,800 + Depreciation
= $33,800 + $150,000
= $183,800
NPV = (Present value of cash inflows) – (Initial investment)
= {$183,800 × (accumulated 12% rate after 10th year)} - $1,500,000
= ($183,800 × 5.6502) - $1,500,000
= $1,038,506.76 - $1,500,000
= -$461,493.24 (Answer)
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