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# Determinig Net Present Value (NPV) of various Proposals

1.Uneven Cash Flows: Find the NPV (Net Present Value) of a project that requires an investment of \$400 now; and another expense of \$500 at the end of the 1st year. It gives cash inflows of \$300 at the end of year 3, \$400 at the end of year 4, and \$800 at the end of year 5. The required rate of return is 11%. Is the project acceptable?

2.Depreciation and Taxes: Atlas Corp needs a new machine that will cost \$50,000. Using the straight-line method, Atlas will depreciate it over its useful life of 5 yrs. The machine will add \$14,000 annually to the earnings before interest and taxes (EBIT) of Atlas. The WACC of Atlas is 12% and its tax rate is 32%. Should Atlas install the machine?

3.After-Tax cash flows: You have the opportunity to invest \$10,000 in a project that will generate a pretax return of \$4,000 annually for the next 10 yrs. You are in the 28% tax bracket, and your after-tax required rate of return is 15%. Should you make the investment?

4. Uncertain Life: Mercy Hosp is planning to buy an X-ray machine whose total useful life is 4 yrs. However, there is a 25% chance that it may break down completely after 3 yrs. The machine will save \$4,500 annually, and it will cost \$11,000. The hospital is a tax-exempt entity, and its proper discount rate is 7%. Should Mercy buy the machine?

#### Solution Preview

Please refer attached file for better clarity of tables and formulas.
Solution:
1.
Let us see cash flows associated with project
PV of cash flow=Future Value of cash flow/(1+required rate of return)^period

Year End Cash Flow PV
0 -400 -400/(1+11%)^0=-400.00
1 -500 -500/(1+11%)^1=-450.45
2 0/(1+11%)^2=0.00
3 300 300/(1+11%)^3=219.36
4 400 400/(1+11%)^4=263.49
5 800 800/(1+11%)^5=474.76
NPV 107.16
-ve sign indicate cash outflow

We get a positive value of NPV (\$107.16), It is acceptable.

2.
Depreciation per year=(Purchase Value-Salvage Value)/Useful life
Depreciation per year=(50000-0)/5= \$10,000.00
Required rate of return=WACC=12%
Tax rate=32%
Let us see cash flows associated with the project
Taxes=(EBIT-Depreciation)*Tax Rate=(14000-10000)*32%= \$1,280.00

Year End Machine Cost EBIT Taxes ...

#### Solution Summary

There are 4 problems related to capital budgeting techniques. Solutions to these problems explain the methodology to analyze investment proposals based upon NPV method.

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