## Presentation on theme: "Copyright © 2007 Prentice-Hall. All rights reserved 1 The Time Value of Money: Present Value of a Bond and Effective Interest Amortization Appendix to."— Presentation transcript:

Copyright © 2007 Prentice-Hall. All rights reserved 4 Present Value Depends on three factors: 1.Dollar amounts to be paid in the future 2.Length of time between investment and future payment 3.Interest rate Computing present value is called discounting

Copyright © 2007 Prentice-Hall. All rights reserved 5 Future Value 1 yr ????? \$1,000 10% Interest = \$1,000 x.10 = \$100 Principal =1,000 Future value\$1,100 Or Future value = 1,000 x 1.10 = \$1,100 Present Value Future Value If you invest \$1,000 today and earn 10% interest, you will have \$1,100 at the end of one year

Copyright © 2007 Prentice-Hall. All rights reserved 6 Present Value 1 yr ????? \$1,100 10% Present value x 1.10 = \$1,100 Present value = \$1,100/1.10 Present value = \$1,000 Present Value Future Value Present value is just taking the interest out. If you can earn 10% interest and want to receive \$1,100 in one year, you will have to invest \$1,000 today

Copyright © 2007 Prentice-Hall. All rights reserved 7 Present Value 1 yr ????? \$1,100 10% Present value x 1.10 = \$1,100 Present value = \$1,100/1.10 Present value = \$1,000 Present Value Future Value 2 yrs Present value x 1.10 = \$1,000 Present value = \$1,000/1.10 Present value = \$909 What if you would like to receive \$1,100 in TWO years instead. How much would you have to invest today? 1,000

Copyright © 2007 Prentice-Hall. All rights reserved 8 Present Value of \$1 Table 1 yr ????? \$1,100 10% Present Value Future Value 2 yrs Present Value = Future Value x Table Factor = \$1,100 x 0.826 = \$909 Look on the Present Value of \$1 table. Find the table factor where the percentage rate and the number of periods intersect

Copyright © 2007 Prentice-Hall. All rights reserved 9 Present Value of an Annuity 1 yr ????? \$1,100 10% Present Value Future Value 2 yrs Present Value of \$1,100 in one year: \$1,100 x 0.909 = \$1,000 \$1,100 Present Value of \$1,100 in two years: \$1,100 x 0.826 = \$909 \$1,000 + \$909 = \$1,909 Now, what if you would like to receive \$1,100 at the end of EACH year for 2 years? How much would you have to invest today? If you invest \$1,909 today and earn 10% interest compounded annually, you can withdraw \$1,100 at the end of each year for two years This type of cash flow is called an annuity – equal cash flows over equal periods of time at a constant rate of interest

Copyright © 2007 Prentice-Hall. All rights reserved 10 Present Value of an Annuity Table 1 yr ????? \$1,100 10% Present Value Future Value 2 yrs \$1,100 Present Value of an Annuity = Payments x Table Factor = \$1,100 x 1.736 = \$1,909.60

Copyright © 2007 Prentice-Hall. All rights reserved 11 Present Value of a Bond 123456 \$100,000 One type of cash flow is the principal that will be received when the bond matures. (Present value of \$1)

Copyright © 2007 Prentice-Hall. All rights reserved 12 Present Value of a Bond 123456 \$4,500 Another type of cash flow is the interest payments that will be received every six months. (Present value of an annuity)

Copyright © 2007 Prentice-Hall. All rights reserved 13 Present Value of a Bond P15A-2a What are the future cash flows? –\$88,000 lump sum (present value of \$1) –\$5,280 interest payments based on stated rate (present value of annuity) What is the market rate? –6% (12%/2) How many times is interest compounded? –20 (10 years x 2)

Copyright © 2007 Prentice-Hall. All rights reserved 14 Present Value of a Bond P15A-2a. Present value of \$88,000 to be received in 20 interest payment periods at 6% interest \$88,000 x 0.312\$27,456 Present value of annuity of \$5,280 to be received 20 times at 6% interest \$5,280 x 11.47060,562 Total present value\$88,018 Use the present value of annuity table. Find the factor where the number of interest payment periods = 20 (twice a year for 10 years) and the interest rate = 6% (12%/2 times a year) This is the amount an investor would be willing to pay in order to receive both the principal and interest payments in the future Use the present value of 1 table. Find the factor where the number of interest payment periods = 20 (twice a year for 10 years) and the interest rate = 6% (12%/2 times a year) Note: the present value should be \$88,000. The difference of \$18 is due to rounding to three decimal places in the present value tables

Copyright © 2007 Prentice-Hall. All rights reserved 15 Present Value of a Bond P15A-2b What are the future cash flows? –\$88,000 lump sum (present value of \$1) –\$5,280 interest payments based on stated rate (present value of annuity) What is the market rate? –7% (14%/2) How many times is interest compounded? –20 (10 years x 2)

Copyright © 2007 Prentice-Hall. All rights reserved 16 Present Value of a Bond P15A-2b Present value of \$88,000 to be received in 20 interest payment periods at 7% interest \$88,000 x 0.258\$22,704 Present value of annuity of \$5,280 to be received 20 times at 7% interest \$5,280 x 10.59455,936 Total present value\$78,640

Copyright © 2007 Prentice-Hall. All rights reserved 17 Present Value of a Bond P15A-2c What are the future cash flows? –\$88,000 lump sum (present value of \$1) –\$5,280 interest payments based on stated rate (present value of annuity) What is the market rate? –5% (10%/2) How many times is interest compounded? –20 (10 years x 2)

Copyright © 2007 Prentice-Hall. All rights reserved 18 Present Value of a Bond P15A-2c Present value of \$88,000 to be received in 20 interest payment periods at 5% interest \$88,000 x 0.377\$33,176 Present value of annuity of \$5,280 to be received 20 times at 5% interest \$5,280 x 12.46265,799 Total present value\$98,975

Copyright © 2007 Prentice-Hall. All rights reserved 19 Effective-Interest Amortization Preferred method over straight-line When amounts are materially different, GAAP requires effective-interest method Allocates bond interest expense over life of bonds in a way that yields constant rate of interest

Copyright © 2007 Prentice-Hall. All rights reserved 20 Effective-Interest Method Interest expense = Carrying value x market rate of interest Cash = Face x stated rate of interest Difference is amount of premium or discount to amortize

Copyright © 2007 Prentice-Hall. All rights reserved 21 Amortization Table Semiannual Interest Period (a) Interest Payment (b) Interest Expense (b-a) Discount Amortization Discount Account Balance Bond Carrying Amount

Copyright © 2007 Prentice-Hall. All rights reserved 23 P15A-5P15A-5 Amortization Table Semiannual Interest Period (a) Interest Payment (b) Interest Expense (a-b) Premium Amortization Premium Account Balance Bond Carrying Amount \$220,0005/31/08\$20,000 \$8,000\$6,60011/30/08 5/31/09 \$1,40018,600218,600 8,0006,5581,44217,158217,158 Face x Stated Rate Carrying Value x Market Rate

Copyright © 2007 Prentice-Hall. All rights reserved 26 P15A-8P15A-8 Present value of \$400,000 to be received in 20 interest payment periods at 4% interest \$400,000 x 0.456\$182,400 Present value of annuity of \$14,500 to be received 20 times at 4% interest \$14,500 x 13.590197,055 Total present value\$379,455

Copyright © 2007 Prentice-Hall. All rights reserved 27 P15A-8P15A-8 Amortization Table Semiannual Interest Period (a) Interest Payment (b) Interest Expense (b-a) Discount Amortization Discount Account Balance Bond Carrying Amount \$379,45512/31/01\$20,545 \$14,500\$15,1786/30/02 12/31/02 \$67819,867380,133 14,50015,20570519,162380,838

Copyright © 2007 Prentice-Hall. All rights reserved 28 P15A-8P15A-8 GENERAL JOURNAL DATEDESCRIPTIONREFDEBITCREDIT Dec 31 Cash 379,455 Discount on Bonds Payable 20,545 Bonds Payable 400,000 2002 Jun 30Interest Expense 15,178 Discount on Bonds Payable 678 Cash14,500