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# Determining Discount Rate, Return Probability and Expected Return

1. Largent Supplies Corp. has borrowed to invest in a project. The loan calls for a payment of \$17,384 every month for three years. The lender quoted Largent a rate of 8.40 percent with monthly compounding. At what rate would you discount the payments to find amount borrowed by Largent?

2. The expected return for Stock Z is 30 percent. If we know the following information about Stock Z, then what return will it produce in the Lukewarm state of the world?

Return Probability

Poor 0.2 0.25
Lukewarm ? 0.5
Dynamite! 0.4 0.25

3. You have invested 40 percent of your portfolio in an investment with an expected return of 12 percent and 60 percent of your portfolio in an investment with an expected return of 20 percent. What is the expected return of your portfolio?

A)15.2%
B)16.0%
C)16.8%
D)17.6%

4. Given the returns for two stocks with the following information, calculate the covariance of the returns for the two stocks. Assume the expected return is 14.4 percent for Stock 1 and 15.9 percent for Stock 2.

Prob Stock 1 Stock 2

0.5 0.11 0.18
0.3 0.17 0.15
0.2 0.19 0.12

5. Mr. Moore is 35 years old today and is beginning to plan for his retirement. He wants to set aside an equal amount at the end of each of the next 25 years so that he can retire at age 60. He expects to live to about 80, and wants to be able to withdraw \$25,000 per year from the account on his 61st through 80th birthdays. The account is expected to earn 10 percent per annum for the entire period of time. Determine the size of the annual deposits that must be made by Mr. Moore.

6. Modern Federal Bank is setting up a brand new branch. The cost of the project will be \$1.2 million. The branch will create additional cash flows of \$235,000, \$412,300, \$665,000 and \$875,000 over the next four years. The firm's cost of capital is 12 percent. What is the internal rate of return on this branch expansion?

Capital budgeting analysis of mutually exclusive projects A and B yields the following:

Project A Project B
IRR 18% 22%
NPV \$270,000 \$255,000
Payback Period 2.5 yrs 2.0 yrs
Which project Management should choose? And why?

7. The Cyclone Golf Resorts is redoing its golf course at a cost of \$2,744,320. It expects to generate cash flows of \$1, 223,445, \$2,007,812, and \$3,147,890 over the next three years. If the appropriate discount rate for the firm is 13 percent, what is the NPV of this project? Which project should the firm choose

8. Problems (use the following data)
Assume Cost of Capital = 12%
YEAR Project A Project B Project C Project D
0 -\$15,000 -\$15,000 -\$25,000 -\$23,000
1 \$4,000 \$6,500 \$14,742 \$6,641
2 \$15,000 \$7,200 \$14,742 \$6,641
3 \$14,000 \$7,241 \$14,742 \$6,641
4 \$7,241 \$6,641
5 \$7,241 \$6,641
6 \$7,241 \$6,641
7 \$7,241 \$6,641
8 \$7,241 \$6,641
9 \$7,241 \$6,641

9. Using the NPV method, which project is preferred?
A)Project A
B)Project B
C)Project C
D)Project D
E)Project C&D

10. Using the replacement chain method, which project is preferred?
a. Project A
b. Project B
c. Project C
d. Project D
e. Project C&D

11. Using the EAA method, which project is preferred?
a. Project A
b. Project B
c. Project C
d. Project D
e. Project C&D

12. Using the profitability index method, which project is preferred?
a. Project A
b. Project B
c. Project C
d. Project D
e. Project C&D

Use the following table to answer question 13:
Expected Net Cash Flow
Year Project L Project S
0 -100 -100
1 10 70
2 60 50
3 80 20

13. Using the payback method, which project is preferred?
a. Project L
b. Project S
c. Payback periods are identical
d. None of the above

#### Solution Preview

See the attached file for full solutions.

1. .Largent Supplies Corp. has borrowed to invest in a project. The loan calls for a payment of \$17,384 every month for three years. The lender quoted Largent a rate of 8.40 percent with monthly compounding. At what rate would you discount the payments to find amount borrowed by Largent?
The discount rate is 0.70% per month (or per compounding period)
We can calculate the borrowed amount as PV of an annuity \$551,501.48

2.The expected return for Stock Z is 30 percent. If we know the following information about Stock Z, then what return will it produce in the Lukewarm state of the world?

Return Probability

Poor 0.2 0.25
Lukewarm ? 0.5
Dynamite! 0.4 0.25
We have 0.30 = 0.2*0.25+X*0.50+0.40*0.25
Solving we get X=0.30 or 30%
Thus, Z will produce a return of 30% in the Lukewarm state of the world

3. You have invested 40 percent of your portfolio in an investment with an expected return of 12 percent and 60 percent of your portfolio in an investment with an expected return of 20 percent. What is the expected return of your portfolio?

A)15.2%
B)16.0%
C)16.8%
D)17.6%

4. Given the returns for two stocks with the following information, calculate the covariance of the returns for the two stocks. Assume the expected return is 14.4 percent for Stock 1 and 15.9 percent for Stock 2.

Prob Stock 1 Stock2 Stock1-Mean1 Stock2-Mean2

0.5 0.11 0.18 -0.034 0.021
0.3 0.17 0.15 0.026 -0.009
0.2 0.19 0.12 0.046 -0.039
Mean 0.144 0.159
Covariance = -0.000786

5. Mr. Moore is 35 years old today and is beginning to plan for his retirement. He wants to set aside an equal amount at the end of each of the next ...

#### Solution Summary

The solution determines the rate which payments are discounted in order to find amount borrowed, expected return for portfolio, size of annual deposits based on earnings, and uses the replacement chain method to determine which given product is preferred.

\$2.19