530Mod3

Session 4 - Time Value of Money, Chapter 4

All page numbers are references to Corporate Finance: A Focused Approach 7th edition by Ehrhardt and Brigham (Cengage South-Western, 2020)

Things to Absorb

Need to know almost everything plus you need to learn how to use your financial calculator and/or spreadsheet. Specifically, you can solve for any of the variables (present value, future value, payment, interest rate, and number of periods) for present value, future value, and annuity problems. You should be able to solve for the present value of; annuities, perpetuities, growing perpetuities, and a stream of uneven cash flows. You should be able to convert simple interest (aka APR, stated rate, quoted rate, and a few other names for an uncompounded annual interest rate) to an effective annual interest rate and/or a periodic rate. You should be able to solve multiple step time value of money problems. You should be able to solve all of the end-of-chapter questions and problems. Note, that some variation all of those questions and problems have appeared in past quizzes and exams. I consider the following problems to be exam level problems 5, 8, 18, 19, 21b, 24, and 27-34.

This chapter develops the valuation techniques that we use for the rest of the course. This is the most important chapter in the course. The rest of the course will apply techniques learned in this chapter.

Do not need to know - Growing Annuity (until we get to the stock valuation chapter).

You will need to be able to use a financial calculator or spreadsheet for the quizzes and exams. It is critical that you "set up" your calculator correctly. Here is a link to simple instructions for most calculators. To help you with spreadsheets, look on our D2L course page, under Chapter 4 Content, I have placed a ToolKit.  These Toolkits are Excel spreadsheet solutions to various end of chapter problems and Excel templates for common Time Value of Money Problems.

Here are the manufacturer web sites, I do not find them to be that useful.

Note, that your calculator is probably set to 12 payments per year and 2 decimal places. You need to change this to 1 payment per year and at least 4 decimal places.

  1. Watch the Chapter Introduction and Overview video. The Powerpoints for all of this chapter's videos are here. An important concept, and the most common loan in your personal life, is the amortized loan. This video discusses Amortized Loans in detail. If you find yourself making lots of errors, watch this video that discusses the most common TVM errors.
  2. Easy Concepts and Calculations. A key part of learning time value of money is recognizing problems. Below are some audio solutions (courtesy of Dr. Ron Best) to simple problems from this chapter. Use these problems to verify your calculator and/or spreadsheet are set up correctly.
    1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? | Audio Solution
    2. What will $247,000 grow to be in 9 years if it is invested today in an account with an annual interest rate of 11%? | Audio Solution
    3. How many years will it take for $136,000 to grow to be $468,000 if it is invested in an account with an annual interest rate of 8%? | Audio Solution
    4. At what annual interest rate must $137,000 be invested so that it will grow to be $475,000 in 14 years? | Audio Solution
  3. More Difficult Concepts and Calculations. Be able to solve all of the chapter examples and end of chapter problems. A key part of learning time value of money is recognizing problems. Below are audio solutions (courtesy of Dr. Ron Best) to more difficult problems from this chapter.
    1. If you wish to accumulate $197,000 in 5 years, how much must you deposit today in an account that pays a quoted annual interest rate of 13% with semi-annual compounding of interest? | Audio Solution
    2. What will $153,000 grow to be in 13 years if it is invested today in an account with a quoted annual interest rate of 10% with monthly compounding of interest? | Audio Solution
    3. How many years will it take for $197,000 to grow to be $554,000 if it is invested in an account with a quoted annual interest rate of 8% with monthly compounding of interest? | Audio Solution
    4. At what quoted annual interest rate must $134,000 be invested so that it will grow to be $459,000 in 15 years if interest is compounded weekly? | Audio Solution
    5. You are offered an investment with a quoted annual interest rate of 13% with quarterly compounding of interest. What is your effective annual interest rate? | Audio Solution
    6. You are offered an annuity that will pay $24,000 per year for 11 years (the first payment will occur one year from today). If you feel that the appropriate discount rate is 13%, what is the annuity worth to you today? | Audio Solution
    7. If you deposit $16,000 per year for 12 years (each deposit is made at the end of each year) in an account that pays an annual interest rate of 14%, what will your account be worth at the end of 12 years? | Audio Solution
    8. You plan to borrow $389,000 now and repay it in 25 equal annual installments (payments will be made at the end of each year). If the annual interest rate is 14%, how much will your annual payments be? | Audio Solution
    9. You are told that if you invest $11,000 per year for 23 years (all payments made at the end of each year) you will have accumulated $366,000 at the end of the period. What annual rate of return is the investment offering? | Audio Solution
    10. You are offered an annuity that will pay $17,000 per year for 7 years (the first payment will be made today). If you feel that the appropriate discount rate is 11%, what is the annuity worth to you today? | Audio Solution
    11. If you deposit $15,000 per year for 9 years (each deposit is made at the beginning of each year) in an account that pays an annual interest rate of 8%, what will your account be worth at the end of 9 years? | Audio Solution
    12. You plan to accumulate $450,000 over a period of 12 years by making equal annual deposits in an account that pays an annual interest rate of 9% (assume all payments will occur at the beginning of each year). What amount must you deposit each year to reach your goal? | Audio Solution
    13. You are told that if you invest $11,100 per year for 19 years (all payments made at the beginning of each year) you will have accumulated $375,000 at the end of the period. What annual rate of return is the investment offering? | Audio Solution
    14. You plan to buy a car that has a total "drive-out" cost of $25,700. You will make a down payment of $3,598. The remainder of the car's cost will be financed over a period of 5 years. You will repay the loan by making equal monthly payments. Your quoted annual interest rate is 8% with monthly compounding of interest. (The first payment will be due one month after the purchase date.) What will your monthly payment be? | Audio Solution
    15. You are considering leasing a car. You notice an ad that says you can lease the car you want for $477.00 per month. The lease term is 60 months with the first payment due at inception of the lease. You must also make an additional down payment of $2,370. The ad also says that the residual value of the vehicle is $20,430. After much research, you have concluded that you could buy the car for a total "driveout" price of $33,800. What is the quoted annual interest rate you will pay with the lease? | Audio Solution
    16. You are valuing an investment that will pay you $12,000 the first year, $14,000 the second year, $17,000 the third year, $19,000 the fourth year, $23,000 the fifth year, and $29,000 the sixth year (all payments are at the end of each year). What it the value of the investment to you now is the appropriate annual discount rate is 11.00%? | Audio Solution
    17. You are valuing an investment that will pay you $27,000 per year for the first ten years, $35,000 per year for the next ten years, and $48,000 per year the following ten years (all payments are at the end of each year). If the appropriate annual discount rate is 9.00%, what is the value of the investment to you today? | Audio Solution
    18. John and Peggy recently bought a house. They financed the house with a $125,000, 30-year mortgage with a nominal interest rate of 7 percent. Mortgage payments are made at the end of each month. What total dollar amount of their mortgage payments during the first three years will go towards repayment of principal? | Audio Solution
    19. You are valuing an investment that will pay you $26,000 per year for the first 9 years, $34,000 per year for the next 11 years, and $47,000 per year the following 14 years (all payments are at the end of each year). Another similar risk investment alternative is an account with a quoted annual interest rate of 9.00% with monthly compounding of interest. What is the value in today's dollars of the set of cash flows you have been offered? | Audio Solution
    20. You have just won the Georgia Lottery with a jackpot of $40,000,000. Your winnings will be paid to you in 26 equal annual installments with the first payment made immediately. If you feel the appropriate annual discount rate is 8%, what is the present value of the stream of payments you will receive? | Audio Solution
    21. You have just won the Georgia Lottery with a jackpot of $11,000,000. Your winnings will be paid to you in 26 equal annual installments with the first payment made immediately. If you had the money now, you could invest it in an account with a quoted annual interest rate of 9% with monthly compounding of interest. What is the present value of the stream of payments you will receive? | Audio Solution
    22. You are planning for retirement 34 years from now. You plan to invest $4,200 per year for the first 7 years, $6,900 per year for the next 11 years, and $14,500 per year for the following 16 years (assume all cash flows occur at the end of each year). If you believe you will earn an effective annual rate of return of 9.7%, what will your retirement investment be worth 34 years from now? | Audio Solution
    23. You plan to retire 33 years from now. You expect that you will live 27 years after retiring. You want to have enough money upon reaching retirement age to withdraw $180,000 from the account at the beginning of each year you expect to live, and yet still have $2,500,000 left in the account at the time of your expected death (60 years from now). You plan to accumulate the retirement fund by making equal annual deposits at the end of each year for the next 33 years. You expect that you will be able to earn 12% per year on your deposits. However, you only expect to earn 6% per year on your investment after you retire since you will choose to place the money in less risky investments. What equal annual deposits must you make each year to reach your retirement goal? | Audio Solution
  4. Additional Support Material. There is some good internet support material for this topic.
    1. If you are completely lost, the Khan Academy has some very low level tutorials, https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial.
    2. Students tend to make the certain errors as they learn about Time Value of Money. If you find yourself making lots of errors, watch this video (same video as above) that discusses the most common TVM errors.

There is a fairly long Quiz for Chapter 4.  The only way to learn this material is to do many, many problems.

 

Updated August 21, 2020
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