# Time Value of Money Applied

1 Your younger sister, Jennifer, will start college in five years. She has just informed your parents that she wants to go to Penn State U,. which will cost $18,000 per year for four years (cost assumed to come at teh end of each year). Anticipating Jennifer's ambitions, your parents started investing #3,000 per year five years ago and will continue to do so for five more years.

How much more will your parents have to invest each year for the next five years to have the funds for her education? Use 10 percent as the appropriate interest rate throughout the problem (for discounting or compounding).

2. Jennifer (from problem 1) is now 18 years old (five years have passed), and she wants to get married instead of going to college. Your parents have accumulated the necessary funds for her education.

Instead of her schooling, your parents are paying $7,000 for her current wedding and plan to take year-end vacations costing $2,000 per year for the next three years.

How much money will your parents have at the end of three years to help you with graduate school, which you will start then? You plan to work on a master's perhaps a Ph.D. If graduate school costs $18,930 per year, approximately how long will you be able to stay in school based on these funds? Use 10 percent as the appropriate interest rate throughout this problem. (Round all values to whole numbers.)

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#### Solution Preview

Please see attached file

Note: the abbreviations have the following meanings

PVIF= Present Value Interest Factor

FVIF= Future Value Interest Factor

PVIFA= Present Value Interest Factor for an Annuity

FVIFA= Future Value Interest Factor for an Annuity

They can be read from tables or calculated using the following equations

PVIF( n, r%)= =1/(1+r%)^n

FVIF( n, r%)= =(1+r%)^n

PVIFA( n, r%)= =[1-1/(1+r%)^n]/r%

FVIFA( n, r%)= =[(1+r%)^n -1]/r%

"1 Your younger sister, Jennifer, will start college in five years. She has just informed your parents that she wants to go to Penn State U,. which will cost $18,000 per year for four years (cost assumed to come at the end of each year). Anticipating Jennifer's ambitions, your parents started investing #3,000 per year five years ago and will continue to do so for five more years.

How much more will your parents have to invest each year for the next five years to have the funds for her education? Use 10 percent as the appropriate interest rate throughout the problem (for discounting or compounding). "

First find the present value of college fees for 4 years at the start of college (end of 5 years from now)

n= 4

r= 10.00%

PVIFA (4 periods, 10.% rate ) = 3.169865

Annuity= $18,000

Therefore, present value= $57,058 =18,000. x 3.169865

Then find the value today of the $3,000 that the parents have invested for 5 years

n= 5

r= 10.00%

FVIFA (5 periods, 10.% rate ) ...

#### Solution Summary

Answers Time Value of Money Questions.

Financial questions relating to Business Organization, Shareholders' wealth, Cash flow statement, financial ratios, time value of money, CAPM, Bonds, payback, NPV, IRR, IOS and MCC schedule, WACC, Leverage, EBIT-EPS approach, Cash Conversion cycle.

1) Explain the three principal forms of business organization. Outline their respective advantages and disadvantages. How do taxes, risk, scale, and ownership liquidity affect the selection of one of these three methods?

2) Compare the shareholder-wealth-maximization model with the corporate-wealth- maximization model. What is the proxy for shareholder wealth? How does the role of the shareholder conflict with that of other stakeholder? Who are some of the stakeholder and give examples of potential conflicts. Additionally, what is meant by the agency problem, why does it arise, and what may be done to address it?

3) Discuss the three components of a cash flow statement. What is another name for the statement of cash flows and why is the cash flow statement important? How is the statement of cash flows similar or different from a cash budget?

4) Outline the five classes of financial ratios (you do not need to give the formulas). What are the advantages and disadvantage to using ratio analysis? What do you need to be mindful of when doing ratio analysis? What is the DuPont ratio, what are its components, and why is it important?

5) Time value of money

a) What is the difference between compounding and discounting?

b) What are the five variables in a time value calculation?

c) What is the difference between an annuity and a mixed cash flow?

d) What is the difference between an ordinary annuity and an annuity due? Which has a greater future value and why?

e) Give examples where you may use time value in your own life.

6) How do you measure the return and total risk for a single asset? What is the difference between portfolio risk and stand alone risk? What is the difference between systematic risk and unique risk? What is the tradeoff between risk and return? How does risk change (absolutely and incrementally) as you randomly add assets to a portfolio? What effect does

the risk of a single asset and the correlation between assets in a portfolio have on portfolio risk?

7) What is the capital asset pricing model (CAPM); what does it show; why is it important: and how do you use it? What are some of the practical and theoretical limitations of the CAPM?

8) Describe and compare the zero-growth, constant-growth, and multi-stage dividend growth models for equity valuation. What assumptions must you make? How do changes in the growth rate and the cost of capital affect valuation?

11) Bonds

a) Using a bond price yield curve, discuss in detail the relationship between bond prices and the yield to maturity.

b) How do maturity and the size of the coupon affect the shape of the bond price yield curve? Explain. What does the shape of the bond price yield curve mean for interest rate risk?

c) Assuming no change in interest rates, what happens to the price of a bond as it approaches maturity? Show this graphically for a par, premium, and discount bond.

d) If you expect interest rates to rise (decline), what kind of bond should you buy? Why?

12) Compare and contrast the payback, NPV and IRR techniques for capital budgeting. What are their respective advantages and disadvantages of each? Will they ever give you different recommendations? If so, which would you prefer and why?

13) Draw and label an NPV profile? What does the profile show? How can you use it to assess an individual project or multiple projects? What factor(s) explains the shape of the NPV profile? What other curve does it resemble?

14) Explain the IOS and MCC schedules. What are they; how are they computed; and how can you use them? What is a break point? Use a graph to illustrate your work. Carefully label this graph.

15) Describe and discuss the following terms. Be sure to include where/why they are important and/or how you can use them.

a) Risk adjusted return

b) Annualized net present value

c) Scenario analysis

d) Sensitivity analysis

e) Capital rationing

16) Discuss the weighted average cost of capital: what is it, how do you compute it, why it is important, and what it does it mean for new projects. Is the weighted average cost of capital constant over time? Why or why not?

What are the different ways to determine the weights? Why do some firms use a hurdle rate that is higher than the WACC? What are the implications of using a higher hurdle rate to shareholder wealth maximization?

17) Define operating, financial and total leverage as well as the degree of operating, financial, and total leverage. How do you use them and why are they important? Is the degree of operating, financial, and total leverage constant? Explain why or why not. How do operating and financial leverage affect a company's target capital structure and earnings per share? How and why do businesses adjust for the tradeoff between financial and operating

leverage?

18) Conceptually and graphically discuss how you would determine the optimal capital structure for a specific firm. Include a discussion of the EBIT-EPS approach.

19) Describe the cash conversion cycle, its funding requirements, and the strategies for managing it.

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