Accounting and the Time Value of Money

CHAPTER 6 ACCOUNTING AND THE TIME VALUE OF MONEY Part I

Read pages 269-283 and answer the following questions.

1. What does the term “time value of money” indicate in accounting and finance?

2. Why is a dollar received today worth more than a dollar promised at some time in the future?

3. List nine areas in which present value measurements are used in accounting. (See page 271. The first five are studied in later chapters in this book.)

4. Give three examples of how you might use time value of money concepts in your personal life.

5. What is interest? What three variables are involved in the computation of interest?

6. Why are interest rates typically expressed on an annual basis rather than the monthly or quarterly rate? (See footnote 4 page 272) 2

7. What are the three components of an interest rate? Explain each.

8. What is simple interest? How is it computed?

9. What is compound interest? How is it computed?

10. If you had a choice, would you rather invest your money at simple interest or compound interest? Why?

There are four common ways to make time value of money computations. 1. Formulas 2. Financial calculators 3. Spreadsheets such as Excel 4. Time value of money tables

You will use the formulas in some other classes. In this class, you need to learn to use the tables, financial calculators and spreadsheets to work problems. The appendix to the chapter explains how to use financial calculators and spreadsheets.

11. What are the four fundamental variables to all compound interest problems? (If we know three of these, we can always solve to find the fourth.)

12. When we are computing an unknown (future or present) amount, we either accumulate cash flows or discount the cash flows. Which method is used a. for unknown future amounts?

b. for present value amounts? 3

For each situation below, give the interest rate per period (i) and the number of compounding periods (n).

1. Money is invested for 20 years at 10% compounded semi-annually. i = ______n = ______2. A loan is taken out for 15 years at 12% compounded monthly. i = ______n = ______3. Deposits are made monthly for 10 years at 12% compounded monthly. i = ______n = ______4. Money is invested for 5 years at 9% compounded annually. i = ______n = ______5. A loan is taken out at 12% for 4 years with payments made and interest compounded quarterly. i = ______n = ______

For each situation below, indicate the value for each variable: present value (PV), future value (FV), interest rate ( i), and number of compounding periods (n). 1. Amber invested $1,000 today in an account that earns 6% compounded annually. How much will she have in the account at the end of 3 years?

PV = ______i = _____ n = _____ FV = ______

2. J.R. wants to have $12,000 at the end of 10 years. How much would he have to invest today in an account that earns 12% interest compounded quarterly?

PV = ______i = _____ n = _____ FV = ______

3. Charissa has $2,000 to invest today. She plans to take a cruise when the account has a balance of at least $3,250. If the account earns 10% compounded semi- annually, approximately how long will it be before she takes the cruise?

PV = ______i = _____ n = _____ FV = ______

4. Jamie has $4,000 that he would like to grow to $4,500 in 3 years. What interest rate must she earn on the account if interest is compounded annually?

PV = ______i = _____ n = _____ FV = ______4

CHAPTER 6 ACCOUNTING AND THE TIME VALUE OF MONEY Part II

Read pages 283 – 297 and answer the following questions.

1. What is an annuity?

2. What is the future value of an annuity?

3. What is the difference between an ordinary annuity and an annuity due?

4. Determine whether each series of rents below is an annuity. If not, explain why. Amount Date of rent Compounding period Annuity? A. $1,000 Jan 1, 2003 monthly $1,200 Feb 1, 2003 $1,300 Mar 1, 2003 $1,500 Apr 1, 2003

B. $1,000 Jan 1, 2003 monthly $1,000 Mar 1, 2003 $1,000 Sep 1, 2003 $1,000 Nov 1, 2003

C. $1,000 Jan 1, 2003 monthly $1,000 Apr 1, 2003 $1,000 Jul 1, 2003 $1,000 Oct 1, 2003

D. $1,000 Jan 1, 2003 quarterly $1,000 Apr 1, 2003 $1,000 Jul 1, 2003 $1,000 Oct 1, 2003 5

5. Which annuity will yield a higher future value (all else equal), an ordinary annuity or an annuity due?

6. If you know the future value of an ordinary annuity factor (from the table), how can you convert this to the future value of an annuity due factor?

7. What is the present value of an annuity?

8. If you know the present value of an ordinary annuity factor (from the table), how can you convert this to the present value of an annuity due factor?

Part II continues on the following page. 6

9. For each situation below, indicate whether the unknown variable is (a) the future value of an ordinary annuity; (b) the future value of an annuity due; (c) the present value of an ordinary annuity; or (d) the present value of an annuity due. Then compute the unknown variable.

a. Steve’s parents who live in another state would like to deposit money into a money market account. Steve would then be allowed to withdraw $500 per quarter for spending money for the next two years. The first withdrawal would occur as soon as the account is opened. The account earns 12% interest compounded quarterly. How much would they have to deposit today?

Rents = ______n = ______i = ______

Unknown variable is ______

b. Julissa wants to retire in 30 years. She plans to invest $2,000 per year at the end of each of the next 30 years. The money will earn an estimated 8% compounded annually. How much will she have when she retires?

Rents = ______n = ______i = ______

c. Matt has just purchased a new sports car. He has agreed to pay $1,924 at the end of every three months for the next 5 years. Interest of 10% on the car loan is compounded quarterly. Matt wants to know the cost of the car (without interest).

Rents = ______n = ______i = ______

d. Kimberley wants to save money for a downpayment on a new house. She will invest $300 at the beginning of each month starting March 1, 2002. She has found an investment that pays 24% annual interest compounded monthly. The last deposit will be made on February 1, 2005. How much will she have as a downpayment in three years (i.e., on March 1, 2005)?

Rents = ______n = ______i = ______

Part II ends here. 7

PRICING BONDS PRACTICE PROBLEM

On January 1, 2002, the Winters Company issued bonds. The bonds have a $3,000,000 face value and mature in 10 years. The bonds have a stated annual interest rate of 9.8% and pay interest semi-annually on July 1 and January 1. The company will also pay the $3,000,000 face value to the bondholders on January 1, 2012.

What are the two streams of cash flows promised to investors who purchase these bonds? 1.

How much did the bonds sell for if the market rate of interest on January 1, 2002 was (a) 12% per year? N = ______I = ______

(b) 8% per year? N = ______I = ______

Check figures: (a) Bonds will sell for $2,621,478; (b) Bonds will sell for $3, 366,949. 8

TIME VALUE OF MONEY CLASS EXERCISE

1. You plan to make deposits on January 1, 2002; January 1, 2003; January 1, 2004 and January 1, 2005. If you want to know the amount in the fund on January 1, 2005, which table would you use? ____ present value of an ordinary annuity ____ future value of an ordinary annuity ____ present value of an annuity due ____ future value of an annuity due

2. You want to know how much your rich uncle would have to deposit today (February 15, 2002) in order for you to withdraw $1,000 on February 15, 2002; February 15, 2003; and February 15, 2004. Which table would you use? ____ present value of an ordinary annuity ____ future value of an ordinary annuity ____ present value of an annuity due ____ future value of an annuity due

3. Bonds with a face value of $100,000 and 10-year term pay interest of 5% semi-annually. Match the selling price to the market rate: Market rate Selling price a. 4% ___ $88,530 b. 5% ___ $100,000 c. 6% ___ $113,590

4. If n=26, i=5%, and the table factor is 0.281, which table was used? ____ present value of a single sum ____ present value of an ordinary annuity ____ future value of a single sum ____ future value of an ordinary annuity

5. The present value of an ordinary annuity factor for 48 periods discounted at 2% is 30.673. How would you convert this factor to the present value of an annuity due factor? Do not do the math, just show the work.

6. The table factor for 16 periods at 2% interest is 18.639. Which table was used? ____ present value of a single sum ____ present value of an ordinary annuity ____ future value of a single sum ____ future value of an ordinary annuity

7. The future value of a single sum factor for 30 periods at 7% interest is 7.612. How would you convert this to the present value factor for 30 periods at 7%? Do not do the math, just show the work.

8. The table factor for n=8 and i=1.5% is 7.486. Which table was used? ____ present value of a single sum ____ present value of an ordinary annuity ____ future value of a single sum ____ future value of an ordinary annuity

9. The future value of an ordinary annuity factor is 34.609 with n=32 and i=0.5%. How would you convert this to the future value of an annuity due factor? Do not do the math, just show your work. 9

TIME VALUE OF MONEY EXAMPLES

Example 1: $1,000 is deposited on February 13, 2002, in an account that pays 10% interest, compounded annually. What will the account balance be at the end of 3 years (February 13, 2005)?

Date (a) (b) (c) = (a) + (b) Account balance, Interest Account Balance, Beginning of year (a) * 10% * 1 end of year Feb 13, 2002 $1,000.00 Feb 13, 2003 Feb 13, 2004 Feb 13, 2005

Example 2: $1000.00 is deposited on February 13, 2002 and each February 13 for the next 2 years (3 deposits in total). The account pays 10% interest compounded annually. What will the account balance be immediately after the third deposit on February 13, 2004?

Date (a) (b) (c) (d) Account Balance, Interest Deposit Account Balance, Beginning of year (a) * 10% end of year (a) + (b) + (c) Feb 13, 2002 $1,000.00 $1,000.00 Feb 13, 2003 $1,000.00 Feb 13, 2004 $1,000.00

Example 3: $1,000.00 is deposited on February 13, 2002, and each February 13 for the next 2 years. The account pays 10% compounded annually. What will the account balance be on February 13, 2005 (1 year after the last deposit)?

Date (a) (b) (c) (d) Account Balance, Interest Deposit Account Balance, Beginning of year (a) * 10% end of year (a) + (b) + (c) Feb 13, 2002 $1,000.00 $1,000.00 Feb 13, 2003 $1,000.00 Feb 13, 2004 $1,000.00 Feb 13, 2005 Example 4: $2,486.86 is deposited on February 13, 2002. $1,000.00 withdrawals will be made on February 13, 2003 and each year thereafter for a total of 3 withdrawals. What will the account balance be on February 13, 2005 after the last withdrawal?

Date (a) (b) (c) (d) Account Balance, Interest Withdrawal Account Balance, Beginning of year (a) * 10% end of year 10

(a) + (b) - (c) Feb 13, 2002 $2,486.86 Feb 13, 2003 $1,000.00 Feb 13, 2004 $1,000.00 Feb 13, 2005 $1,000.00

Example 5: $2,735.55 is deposited on February 13, 2002 $1,000.00 withdrawals will be made on February 13, 2002 and each year thereafter for a total of 3 withdrawals. What will the account balance be on February 13, 2004 after the last withdrawal?

Date (a) (b) (c) (d) Account Balance, Interest Withdrawal Account Balance, Beginning of year (a) * 10% end of year (a) + (b) - (c) Feb 13, 2002 $2,735.55 $1,000.00 $1,735.55 Feb 13, 2003 $1,000.00 Feb 13, 2004 $1,000.00

Example 6: On February 13, 2002, $10,515.42 is deposited in an account that pays 8% interest compounded annually. You plan to withdraw $1,000 each February 13 starting February 13, 2003. What will the account balance be on February 13, 2005?

Date (a) (b) (c) (d) Account Balance, Interest Withdrawal Account Balance, Beginning of year (a) * 8% end of year (a) + (b) - (c) Feb 13, 2002 $10,515.42 Feb 13, 2003 $1,000.00 Feb 13, 2004 $1,000.00 Feb 13, 2005 $1,000.00 11

TIME VALUE OF MONEY BUSINESS APPLICATIONS CLASS EXERCISE

Notes: The Morris Corporation purchased equipment by issuing a non-interest-bearing note payable with a face value of $100,000. The equipment had a cash price of $75,132. The note matures in 3 years. What is the implied interest rate on the note (assume annual compounding)?

$100,000 = ______$75,132 = ______n = ______r = ______

Leases: On February 28, 2001, the Proske Company signed a 3-year lease for a car to be driven by the company’s CEO. The lease has a 9% annual interest rate and requires monthly payments of $1,590 beginning March 31, 2001. The car could have been purchased for $53,000 cash. The company wants to know whether this is a capital lease (whether the present value of the payments is at least 90% of the cost of the car). Is this a capital lease?

$1,590 = ______n = ______r = ______

Unknown variable = ______

Is this a capital lease? ______

N r fvf pvf fvf-oa pvf-oa 3 9% 1.29503 .77218 3.27810 2.53130 3 10% 1.33100 .75132 3.31000 2.48685 5 5% 1.15763 .78353 5.52563 4.32948 5 6% 1.19102 .74726 5.63709 4.21236 5 7% 1.40255 .71298 5.75074 4.10020 36 .75% 1.30865 .76415 41.1527 31.4468 36 9% 22.25123 .04494 236.12472 10.61176 15 12% 5.47357 .18270 37.27972 6.81086 25 12% 17.0000 .05882 431.66350 7.84314 12

Bond Premiums/Discounts: On February 1, 2001, the Shaw Company issued bonds. The bonds have a $1,000,000 face value and mature in 5 years. The bonds pay interest of $60,000 every February 1 beginning in 2002. The company will also pay the $1,000,000 face value to the bondholders on February 1, 2006. How much did the bonds sell for if the market rate of interest on February 1, 2001 was (a) 5% per year; (b) 6% per year; (c) 7% per year?

Hint: The bonds will sell for the total of (a) The present value of the $1,000,000 to be received in 5 years + (b) The present value of the $60,000 to be received at the end of every year for the next 5 years

Market Present value of Present value of ordinary Selling price of bonds rate $1,000,000 (a) annuity of $60,000 (b) (a) + (b) i = 5% n = 5, i = 6% $1,000,000 * .747258 $60,000 * 4.21236 = $747,258 n = 5 = $747,258 $252,742 + 252,742 $1,000,000 i = 7% n = 5

Pensions and Other Post-Retirement Benefits: The Robertson Company has 10 employees who are covered by a pension plan. The employees are expected to retire in 15 years (March 1, 2016). After retirement, the employees are expected to receive a total of $250,000 per year beginning March 1, 2017. The expected life duration after retirement is 25 years. If the discount rate (i.e., interest rate) is 12% per year compounded annually, what is the present value of the future retirement benefits on March 1, 2001?

Step 1: Compute the value of the benefits when the employees retire on March 1, 2016.

n = ______i = ______R = ______PVOA = ______

Step 2: Compute the value of the amount determined in step 1 on March 1, 2001.

n = ______i = ______FV = ______PV = ______