# CMA Study Group

View Only #### Syed Yousuf Jamal01-27-2020 06:00 AM #### Ammar Aldubaisi15 days ago

Posted 01-27-2020 06:00 AM
A company is considering the purchase of a new production machine and is not sure whether the project fulfills its investment objective. The company requires that all investments must have a positive net present value (NPV). The machine costs \$100,000 and will be depreciated for tax purposes on a straight-line basis over its useful life of 5 years. After 5 years the used equipment will be sold. The project requires an initial investment in working capital of \$20,000 and will generate \$30,000 of pretax operating cash inflow annually. The company has a 25% effective income tax rate and uses a 10% discount rate for investment projects. Of the four estimated ranges shown below, which is the approximate minimum sales price that must be realized for the used equipment at the end of Year 5 in order to achieve a positive NPV on this project?

A. \$5,250-\$5,625
B. \$7,000-\$7,500
C. \$10,000-\$13,500
D. \$800-\$1,200

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Syed Yousuf Jamal

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Posted 15 days ago
The NPV must be calculated without a value for the used equipment. The initial outflow is \$120,000 (\$100,000 machine cost plus \$20,000 investment in working capital). The annual cash inflows would be \$30,000, but that would be reduced by the \$2,500 of income taxes. Thus, the net inflows each year would be \$27,500 {[\$30,000 cash inflow × (1 – .25 tax rate)] + (\$20,000 depreciation × .25 tax rate)}. The inflows from termination equal the \$20,000 of working capital recovered, plus the selling price of the used equipment, minus the taxes on the sale of the fully-depreciated equipment. These amounts would then be discounted at 10%, as follows:
\$27,500 × 3.791
=
\$104,252.50
20,000 ×   .621
=
12,420.00
Partial present value
=
\$116,672.50
Less: Initial investment
=
120,000.00
Amount needed at sale
=
\$    3,327.50
The \$3,327.50 represents the present value of the amount needed from the after-tax sale of the used machine. In other words, (S – .25S) × .621 = \$3,327.50. Dividing both sides of the equation by .621 yields .75S = \$5,358.29, or S = \$7,144.39.

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Ammar Aldubaisi
Student
Qatif
Saudi Arabia
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