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# Expected return and standard deviation, NPV, IRR

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18) Use the data below and consider portfolio weights of .60 in stocks and .40 in bonds.

Rate of Return
Scenario Probability Stocks Bonds
Recession 0.2 -5% 14%
Normal 0.6 15% 8%
Boom 0.2 25% 4%

a. What is the rate of return on the portfolio in each scenario?
b. What is the expected return and standard deviation of the portfolio?
c. Would you prefer to invest in the portfolio of stocks only or in bonds only?

21) Revenues generated by a new fad product in each of the next 5 years are forecasted as follows:
Year Revenues
1 \$40,000
2 30,000
3 20,000
4 10,000
Thereafter 0

Expenses are expected to be 40 percent of revenues, and working capital required in each year is expected to be 20 percent of revenues in the following year. The product requires an immediate investment of \$50,000 in plant and equipment.
a. What is the initial investment in the product? Remember working capital.
b. If the plant and equipment are depreciated over 4 years to a salvage value of zero using straight-line depreciation, and the firm's tax rate is 40 percent, what are the project cash flows in each year?
c. If the opportunity cost of capital is 10 percent, what is the project NPV?
d. What is the project IRR?

(See attached file for full problem description)

#### Solution Summary

Calculates 1) expected return and standard deviation of a portfolio 2) NPV and IRR of a project.

\$2.19

## I need some help with these question

(See attached file for full problem description)

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Problem 7-9
NPV and IRR. A project that costs \$3,000 to install will provide annual cash flows of \$800 for each of the next 6 years.
Is this project worth pursuing if the discount rate is 10 percent?
Project NPV

How high can the discount rate be before you would reject the project?
Maximum Project Rate

Problem 7-10
Payback. A project that costs \$2,500 to install will provide annual cash flows of \$600 for the
next 6 years. The firm accepts projects with payback periods of less than 5 years.

Will the project be accepted?
Project payback period

Should this project be pursued if the discount rate is 2 percent?
NPV of Project at 2%

What if the discount rate is 12 percent?
NPV of Project at 12%

Will the firm's decision change as the discount rate changes?

Problem 7-19
Here are the cash flows for two mutually exclusive projects:

Project C0 C1 C2 C3
A (\$20,000) \$8,000 \$8,000 \$8,000
B (\$20,000) 0 0 \$25,000

Use the MS Excel NPV function to calculate the NPVs for both projects in the profile below. In part B use the IRR function.
a. At what interest rates would you prefer project A to B?
NPV Profile
Discount
Rate NPVA NPVB
0% FORMULA FORMULA
2% FORMULA FORMULA
4% FORMULA FORMULA
6% FORMULA FORMULA
8% FORMULA FORMULA
10% FORMULA FORMULA
12% FORMULA FORMULA
14% FORMULA FORMULA
16% FORMULA FORMULA
18% FORMULA FORMULA
20% FORMULA FORMULA

b. What is the IRR of each project?

Project A IRR
Project B IRR

Problem 7-23
Profitability Index. Consider the following projects:
Project C0 C1 C2
A (2,100.00) 2,000.00 1,200.00
B (2,100.00) 1,440.00 1,728.00

a. Calculate the profitability index for A and B assuming a 22 percent opportunity cost of capital.
Project A NPV
Project B NPV

Project A Profitability Index
Project B Profitability Index

b. Use the profitability index rule to determine which project(s) you should accept (i) if you
could undertake both and (ii) if you could undertake only one.
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