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# Growth Rates, Future value of an Annuity & Portfolio Risk

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1. Growth Rates:
- XYZ Corporation's 2005 sales were \$12 million. Its 2000 sales were \$6 million,
a. At what rate have sales been growing?
b. If someone made the statement: "Sales doubled in 5 years. This represents a growth of 100 percent in 5 years, so, dividing 100 percent by 5, we find the growth rate to be 20 percent per year"...IS THIS STATEMENT CORRECT?

2. Future value of an annuity:
- Your client is 40years old, and she wants to begin saving for retirement, with the first payment to come in one year from now. She can save \$5000 per year, and you advise her to invest it in the stock market, which you expect to provide an average return of 9 percent in the future.
a. If she follows your advice, how much money would he have at 65?
b. How much would she have at 70?
c. If she expects to live for 20 years in retirement if she retires at 65 and for 15 years if she retires at 70, and her investments continue to earn the same rate, how much could she withdraw at the end of each year after retirement at each retirement age?

3. You own a portfolio consisting of \$250,000 of long term US government bonds:
a) Would your portfolio be risk less?
b) Suppose the portfolio consists of \$250,000 of 30-day Treasury bills. Every 30 days our bills mature, and you will reinvest the principal (\$250,000) in a new batch of bills. You plan to live of the investment income from your portfolio, and you want to maintain a constant standard of living. Is the T-bill portfolio truly risk less? Explain
c) What is the least risky security you can think of? Explain

#### Solution Preview

1. Growth Rates:
- XYZ Corporation's 2005 sales were \$12 million. Its 2000 sales were \$6 million,
a. At what rate have sales been growing?

Growth rate = 14.87% =(12/6)^(1/5)-1
Note: ^ stands for raised to the power of

b. If someone made the statement: "Sales doubled in 5 years. This represents a growth of 100 percent in 5 years, so, dividing 100 percent by 5, we find the growth rate to be 20 percent per year"...IS THIS STATEMENT CORRECT?

This statement is incorrect
When we talk of growth rates we are talking about CAGR (compounded annual growth rate)
CAGR is equal to 14.87% as calculated above and not 20%

2. Future value of an annuity:
- Your client is 40years old, and she wants to begin saving for retirement, with the first payment to come in one year from now. She can save \$5000 per year, and you advise her to invest it in the stock market, which you expect to provide an average return of 9 percent in the future.

Note: the abbreviations have the following meanings

PVIFA= Present Value Interest Factor for an Annuity
FVIFA= Future Value Interest Factor for an ...

#### Solution Summary

The solution answers questions on Growth Rates of sales, Future value of an annuity & Portfolio risk.

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