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# Opportunity costs, net present value, expected returns

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1. A generous university benefactor has agreed to donate a large amount of money for student scholarships.
The money can be provided in one lump-sum of \$10mln, or in parts, where \$5.5mln can be provided in
year 1, and another \$5.5mln can be provided in year 2. Assuming the opportunity interest rate is 6%, what
is the present value of the second alternative? Which of the two alternatives should be chosen and why?
How would your decision change if the opportunity interest rate was 12%? Please, show all your
calculations.

2. Volkswagen is considering opening an Assembly Plant in Chattanooga, Tennessee, for the production of
its 2012 Passat, tailored for the US market. The CEO of the company is considering two potential options
for the size of the plant: one is a large size with a projected annual production of 150,000 cars, and the
other one is a smaller size plant, which is cheaper to build, but can only produce up to 80,000 cars per
year. Depending on the expected level of demand for these cars in the US, Volkswagen has to decide
which option is more profitable. The discount rate is 6% and for simplicity purposes, the CEO is only
evaluating a two-year horizon. The initial factory setup cost, the expected demand scenarios, profit, and
probabilities are shows in the below table. Calculate the Net Present Value in each of the two options.
Which option should the CEO choose and why? Please, show all your calculations.

3. An angel investor is considering investing in one of two start-up businesses and is evaluating the expected
returns along with the risk of each option in order to choose the better alternative.

Business 1 is an innovative protein energy drink, which has ENPV of \$100,000 with a standard deviation of \$40,000.

Business 2 is a unique chicken wings dipping sauce with an ENPV of \$60,000 and a standard deviation of \$25,000.

a) Apply the coefficient-of-variation decision criterion to these alternatives to find out which is preferred
by the angel investor, assuming that he/she is risk-averse.
b) Apply the maximin criterion, assuming that the worst outcome in Business 1 is to lose \$5,000,
whereas the worst outcome in Business 2 is to make only \$5,000 in profit.
c) If you were the angel investor, what is your certainty equivalent for these two projects? Are you risk-
averse, risk-neutral, or risk-lover?

#### Solution Preview

Thanks for your question! Please see the attached Excel sheet for correct formatting of the tables.

1.
First, we calculate the present value of the \$5.5mln payments
Year 1 pmt \$5,500,000.00
Year 2 pmt \$5,188,679.25
Total Present Value of partial payments \$10,688,679.25

Total present value of lump sum payment \$10,000,000.00

Since the present value of partial payments is higher than the lump sum, the partial payments should be chosen

Calculations if the opportunity rate was 12%
First, we calculate the present value of the \$5.5mln payments
Year 1 pmt \$5,500,000.00
Year 2 pmt \$4,910,714.29
Total Present Value of partial payments \$10,410,714.29

Total present value of lump sum payment \$10,000,000.00
The present value of the partial payment option is still higher.

2.
For this problem we must figure out the expected payoff for each year based on the given scenario.
Present Value (millions)
Expected ...

#### Solution Summary

The following posting helps with a problem involving opportunity costs, net present value and expected returns.

\$2.19

## Net Present Value, Modified Internal Rate of Return and Regular Payback

Pure Life (a juice company) owns a building, which is fully depreciated.

Equipment Cost: \$200,000. plus an additional \$40,000. for shipping and installation
Inventories would rise by \$25,000. and accounts payable would go up by \$5,000. All of these costs would be incurred at t =0.

The machinery could be depreciated under the MACRS system as a 3-year property. Applicable depreciation rates are 33%, 45%, 15% and 7%.

The project will operate for 4 years and will then be terminated. Cash flows are assumed to being 1 year after the project is undertaken, or at t=1 and will continue out to t=4. At the end of the project, (t=4), the equipment is expected to have a salvage value of \$25,000.

Unit sales are expected to total 100,000 cans per year and the expected sales price is \$2.00 per can. Cash operating costs are expected to total 60% of dollar sales. Pure Life's tax rate is 10%.

How do I calculate the project's NPV, IRR, MIRR and regular payback?

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