- Use the attached examples and complete the answer for both using both examples.
- 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?
- 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

0

Type 0

PV Rate NperPMT 0

FVType 0

PV IncorrectExample | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

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 ValueExample

Rate NperPMT 0

PVType 0

FVA

Rate 5%

Nper 10

PMT 0

PV -$100.00

Type 0

PMT 0

PVType 0

FV Incorrect5.00% | ||||||

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 InterestNew balance Incorrect

Principal Rate

Interest

New balance Incorrect

Interest 5.00%

1

20

2.6532977051

$265.33

Rate 5.00%

20

interest

plus 1 1

1 plus interestPower 20

POWER functionPV (1 + i)n Power Function

FV

Incorrect

Rate 4.00%

Term 20

Future Value Incorrect interest 5.00% plus 1 1

1 plus interest

Power 20

POWER function

(1 + i)n Power Function

FV result Incorrect

Rate 5.00%

Term 20

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

Nper 5

PMT ($100)

FV 0

type 0

Nper 10

PMT

FV 0

type 0

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)

type 0

Rate 6%

Nper 5

PMT ($100)

PV 0

type 0

Incorrect

RateNper 10

PMT PV 0

type 0

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.