Complete the following problems. For assistance, you may want to refer to the attached example:

  1. Use the attached examples and complete the answer for both using both examples.
  2. You are considering buying stock A, which is a large firm with a steady business. If the economy grows rapidly, you may earn 12% on your investment. A declining economy will likely result in a 5% loss. Slow growth will return 5%. If the probability is 15% for rapid growth, 20 % for a declining economy, and 65% for slow growth, what is the expected return of the investment?
  3. You are considering investing in three stocks with the following expected returns:Stock A     2%Stock B     10%Stock C     15%

What is the expected return on the portfolio if an equal amount is invested in each stock? What would the expected return be if 50% of your funds are invested in stock A and the remaining funds divided evenly between stocks B and C?

Present Value

Present Value

0

0

0

)

A

Rate

Nper 5
PMT 0

FV

0

Type 0

PV

Rate

Nper

PMT 0

FV

Type 0

PV Incorrect

Example
Rate 6%
Nper 5
PMT 0
FV $

1
Type
PV ($74.7

3
Example 1
5%
$

15
Incorrect ($117.53)
Example 1B
0.07
10
250
($127.09)

Future Value

Future Value

Example

Rate

Nper

PMT 0

PV

Type 0

FV

A

Rate 5%
Nper 10
PMT 0
PV -$100.00
Type 0

FV Incorrect

Rate

Nper 15

PMT 0

PV

Type 0

FV Incorrect

5.00%
20

$100.00
$265.33
Example 2
162.8894626777
Example 2B
7%
-$250.00
689.7578851788

Interest

using product formula.

Example 1

$100.00

Rate 5%

Interest

Principal

Rate

Interest
New balance Incorrect
Principal

Rate

Interest
New balance Incorrect

Example 2
Interest 5.00%

1

20

PV $100.00

2.6532977051

FV

$265.33

Present Value $100.00
Rate 5.00%

20

Future Value $265.33
interest

plus 1 1

1 plus interest

Power 20

POWER function
PV

(1 + i)n Power Function
FV

Incorrect

Present Value $500.00
Rate 4.00%

Term 20

Future Value Incorrect

interest 5.00%

plus 1 1
1 plus interest
Power 20
POWER function

PV

(1 + i)n Power Function
FV result Incorrect

Present Value $200.00

Rate 5.00%
Term 20

Future Value Incorrect

Simple

interest
Principal
$5.00
New balance $105.00
Sample 3A
$1,000.00
6.00%
Sample 3B
$2,500.00
7.50%
Compound interest using power formula and FV Function
plus 1
1 plus interest 1.05
Power
POWER function 2.6532977051
(1 + i)n Power Function
Result
Example 3
Term
Example 4A
4.00%
$500.00
result
1095.5615715167
Example 4B
$200.00
530.6595410289

PV of Annuity

Example

Rate 6%
Nper 3
PMT

FV 0

0

PV

Rate 7%
Nper 5

PMT ($100)
FV 0
type 0

PV Incorrect

Rate 4.00%
Nper 10
PMT

FV 0
type 0

PV Incorrect

Present Value of an Annuity
($100)
type
$267.30
Example 5A
410.0197435948
Example 5B
($50.00)
405.5447889678

FV of Annuity

Example

Rate 5%

Nper 3
PMT ($100)

PV 0

type 0

Rate 6%
Nper 5
PMT ($100)
PV 0
type 0

Incorrect

Rate

Nper 10

PMT

PV 0
type 0

FV of an ordinary annuity Incorrect

Future Value of an Annuity
FV of annuity $315.25
Example 6A
FV of an ordinary annuity $563.71
Example 6B
4%
($50)
$600.31

Week 03 Example Problems

1. You are considering buying stock A. If the economy grows rapidly, you may earn 30% on your investment, while a declining economy could result in a 20% loss. Slow economic growth may generate a return of 6%.

If the probability is 15% for rapid growth, 20% for a declining economy, and 65% for slow growth, what is the expected return on the investment?

Solution:

The answer is 4.4%. How do we get that?

1. First, the decimal .15 is the same as 15% and .20 is the same as 20%. It is easier to use all decimals, or you can use both.

2. 15 rapid growth probability x .30 return if that happens =.045

3. .20 chance of declining economy x -.20 loss if that happens = -.04

4. .65 chance of slow growth x .06 return if that happens = .039

5. Now sum them up. Make sure the loss is subtracted, not added.

6. A return of .045 plus a return of .039 = .084 – a loss of .04 = .044. Now to get it as a percentage, always move the decimal place to the right two places. 4.4%.

2. You are considering investing in three stocks with the following expected returns:

Stock A
7%

Stock B
12%

Stock C
20%

What is the expected return on the portfolio if an equal amount is invested in each stock? What would the expected return be if 50% of your funds are invested in stock A and the remaining funds divided evenly between stocks B and C?

Solution:

The answer is 12.87%. How do we get that?

1. .07 x .33 = .0231

2. .12 x .33 = .0396

3. .20 x .33 = .066

4. Add them up .1287 or 12.87%.

Then, redo how much stock of each company you buy and you get a much different result. Why?

1. .07 x .50 = .035

2. .12 x .25 = .03

3. .20 x .25 = .05

4. Add them up .115 or 11.5%

All we are doing is we are making sure we give heavy weight to stocks we have invested in heavily and lighter weight to stocks that we invested in more lightly.

Adapted from:

Mayo, H. (2007). Basic finance: An introduction to financial institutions, investments & management. United States: Thomson South-Western.

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