Vanderheiden Inc. is considering two average-risk alternative ways of producing its patented polo shirts. Process S has a cost of $8,000 and will produce net cash flows of $5,000 per year for 2 years. Process L will cost $11,500 and will produce cash flows of $4,000 per year for 4 years. The company has a contract that requires it to produce the shirts for 4 years, but the patent will expire after 4 years, so the shirts will not be produced after 4 years. Inflation is expected to be zero during the next 4 years. If cash inflows occur at the end of each year, and if Vanderheiden's cost of capital is 10 percent, by what amount will the better project increase Vanderheiden's value?
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A. B. C. D. E.B
0 k = 10%1234
S -
-8,0005,0005,0005,0005,000
-8,000
-3,000
IRR(S) = 16.26%.
NPV(S) = $1,237.76. (extended NPV)
0 k = 10%1234
L -
-11,5004,0004,0004,0004,000
IRR(L) = 14.66%.
NPV(L) = $1,179.46.
To determine the increase in Vanderheiden Inc.'s value from the better project, we need to calculate the net present value (NPV) of each project and compare them.
Let's start by calculating the NPV for Process S:
The cost of Process S is $8,000, and it will produce net cash flows of $5,000 per year for 2 years. The cost of capital is given as 10 percent.
The formula to calculate the NPV is: NPV = CF₁ / (1 + r)¹ + CF₂ / (1 + r)² + ... + CFₙ / (1 + r)ⁿ - Initial Investment
Where: CF₁, CF₂, ..., CFₙ are the cash flows for each period r is the discount rate (cost of capital) Initial Investment is the cost of the project
Using this formula, let's calculate the NPV for Process S:
NPV = $5,000 / (1 + 0.10)¹ + $5,000 / (1 + 0.10)² - $8,000 = $5,000 / 1.10 + $5,000 / 1.10² - $8,000 = $4,545.45 + $4,132.23 - $8,000 = $657.68
Next, let's calculate the NPV for Process L:
The cost of Process L is $11,500, and it will produce cash flows of $4,000 per year for 4 years. The cost of capital is still 10 percent.
NPV = $4,000 / (1 + 0.10)¹ + $4,000 / (1 + 0.10)² + $4,000 / (1 + 0.10)³ + $4,000 / (1 + 0.10)⁴ - $11,500 = $4,000 / 1.10 + $4,000 / 1.10² + $4,000 / 1.10³ + $4,000 / 1.10⁴ - $11,500 = $3,636.36 + $3,305.79 + $3,005.26 + $2,732.05 - $11,500 = $1,179.46
Now, we compare the NPVs of the two projects. The better project will be the one with the higher NPV. In this case, Process L has a higher NPV of $1,179.46 compared to Process S's NPV of $657.68.
To determine the amount by which the better project will increase Vanderheiden's value, we subtract the NPV of Process S from the NPV of Process L:
Increase in Value = NPV(Process L) - NPV(Process S) = $1,179.46 - $657.68 = $521.78
Therefore, the better project will increase Vanderheiden Inc.'s value by $521.78.
None of the given answer choices match the calculated amount of $521.78. There might be a mistake in the calculation or the answer choices provided.