D- TIME VALUE OF MONEY D- D Financial Accounting, Seventh Edition Learning Learning Objectives Objectives After studying this chapter, you should be able to: D- Distinguish between simple and compound interest Solve for future value of a single amount Solve for future value of an annuity Identify the variables fundamental to solving present value problems Solve for present value of a single amount Solve for present value of an annuity Compute the present value of notes and bonds Use a financial calculator to solve time value of money problems Basic Basic Time Time Value Value Concepts Concepts Time Value of Money Would you rather receive $1,000 today or in a year from now? Today! “Interest Factor” D- Nature Nature of of Interest Interest Payment for the use of money Excess cash received or repaid over the amount borrowed (principal) Variables involved in financing transaction: D- Principal (p) - Amount borrowed or invested Interest Rate (i) – An annual percentage Time (n) - The number of years or portion of a year that the principal is borrowed or invested LO Distinguish between simple and compound interest Nature Nature of of Interest Interest Simple Interest Interest computed on the principal only Illustration: Assume you borrow $5,000 for years at a simple interest of 12% annually Calculate the annual interest cost Illustration D-1 Interest = p x i x n FULL YEAR = $5,000 x 12 x = $1,200 D- LO Distinguish between simple and compound interest Nature Nature of of Interest Interest Compound Interest D- Computes interest on ► the principal and ► any interest earned that has not been paid or withdrawn Most business situations use compound interest LO Distinguish between simple and compound interest Nature Nature of of Interest Interest Compound Compound Interest Interest Illustration: Assume that you deposit $1,000 in Bank Two, where it will earn simple interest of 9% per year, and you deposit another $1,000 in Citizens Bank, where it will earn compound interest of 9% per year compounded annually Also assume that in both cases you will not withdraw any interest until three years from the date of deposit Illustration D-2 Simple versus compound interest D- Year $1,000.00 x 9% $ 90.00 $ 1,090.00 Year $1,090.00 x 9% $ 98.10 $ 1,188.10 Year $1,188.10 x 9% $106.93 $ 1,295.03 LO Distinguish between simple and compound interest Future Future Value Value of of aa Single Single Amount Amount Future value of a single amount is the value at a future date of a given amount invested, assuming compound interest FV = p x (1 + i )n FV = p = i = n = D- Illustration D-3 Formula for future value future value of a single amount principal (or present value; the value today) interest rate for one period number of periods LO Solve for a future value of a single amount Future Future Value Value of of aa Single Single Amount Amount Illustration: If you want a 9% rate of return, you would compute the future value of a $1,000 investment for three years as follows: Illustration D-4 D- 10 LO Solve for a future value of a single amount Present Present Value Value of of an an Annuity Annuity Illustration: Kildare Company has just signed a capitalizable lease contract for equipment that requires rental payments of $6,000 each, to be paid at the end of each of the next years The appropriate discount rate is 12% What is the amount used to capitalize the leased equipment? $6,000 D- 32 x 3.60478 = $21,628.68 LO Solve for present value of an annuity Present Present Value Value of of an an Annuity Annuity Illustration: Assume that the investor received $500 semiannually for three years instead of $1,000 annually when the discount rate was 10% Calculate the present value of this annuity $500 D- 33 x 5.07569 = $2,537.85 LO Solve for present value of an annuity Present Present Value Value of of aa Long-term Long-term Note Note or or Bond Bond Two Cash Flows: Periodic interest payments (annuity) Principal paid at maturity (single-sum) 100,000 D- 34 $5,000 5,000 5,000 5,000 5,000 5,000 10 LO Compute the present value of notes and bonds Present Present Value Value of of aa Long-term Long-term Note Note or or Bond Bond Illustration: Assume a bond issue of 10%, five-year bonds with a face value of $100,000 with interest payable semiannually on January and July Calculate the present value of the principal and interest payments 100,000 D- 35 $5,000 5,000 5,000 5,000 5,000 5,000 10 LO Compute the present value of notes and bonds Present Present Value Value of of aa Long-term Long-term Note Note or or Bond Bond PV of Principal $100,000 Principal D- 36 x 61391 Factor = $61,391 Present Value LO Compute the present value of notes and bonds Present Present Value Value of of aa Long-term Long-term Note Note or or Bond Bond PV of Interest $5,000 Principal D- 37 x 7.72173 Factor = $38,609 Present Value LO Compute the present value of notes and bonds Present Present Value Value of of aa Long-term Long-term Note Note or or Bond Bond Illustration: Assume a bond issue of 10%, five-year bonds with a face value of $100,000 with interest payable semiannually on January and July Present value of Principal $61,391 Present value of Interest 38,609 Bond current market value $100,000 D- 38 LO Compute the present value of notes and bonds Present Present Value Value of of aa Long-term Long-term Note Note or or Bond Bond Illustration: Now assume that the investor’s required rate of return is 12%, not 10% The future amounts are again $100,000 and $5,000, respectively, but now a discount rate of 6% (12% / 2) must be used Calculate the present value of the principal and interest payments Illustration D-20 D- 39 LO Compute the present value of notes and bonds Present Present Value Value of of aa Long-term Long-term Note Note or or Bond Bond Illustration: Now assume that the investor’s required rate of return is 8% The future amounts are again $100,000 and $5,000, respectively, but now a discount rate of 4% (8% / 2) must be used Calculate the present value of the principal and interest payments Illustration D-21 D- 40 LO Compute the present value of notes and bonds Using Using Financial Financial Calculators Calculators N = number of periods I Illustration D-22 Financial calculator keys = interest rate per period PV = present value PMT = payment FV = future value D- 41 LO Use a financial calculator to solve time value of money problems Using Using Financial Financial Calculators Calculators Present Value of a Single Sum Assume that you want to know the present value of $84,253 to be received in five years, discounted at 11% compounded annually Illustration D-23 Calculator solution for present value of a single sum D- 42 LO Use a financial calculator to solve time value of money problems Using Using Financial Financial Calculators Calculators Present Value of an Annuity Assume that you are asked to determine the present value of rental receipts of $6,000 each to be received at the end of each of the next five years, when discounted at 12% Illustration D-24 Calculator solution for present value of an annuity D- 43 LO Use a financial calculator to solve time value of money problems Using Using Financial Financial Calculators Calculators Useful Applications – Auto Loan The 3-year loan has a 9.5% nominal annual interest rate, compounded monthly The price of the car is $6,000, and you want to determine the monthly payments, assuming that the payments start one month after the purchase Illustration D-25 D- 44 LO Use a financial calculator to solve time value of money problems Using Using Financial Financial Calculators Calculators Useful Applications – Mortgage Loan You decide that the maximum mortgage payment you can afford is $700 per month The annual interest rate is 8.4% If you get a mortgage that requires you to make monthly payments over a 15-year period, what is the maximum purchase price you can afford? Illustration D-26 D- 45 LO Use a financial calculator to solve time value of money problems Copyright Copyright “Copyright © 2013 John Wiley & Sons, Inc All rights reserved Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Copyright Act without the express written permission of the copyright owner is unlawful Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc The purchaser may make back-up copies for his/her own use only and not for distribution or resale The Publisher assumes no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information contained herein.” D- 46 [...]... the variables fundamental to solving present value problems Present Present Value Value of of aa Single Single Amount Amount Illustration D- 9 Formula for present value Present Value = Future Value / (1 + i )n p = principal (or present value) i = interest rate for one period n = number of periods D- 21 LO 5 Solve for present value of a single amount Present Present
Value Value of of aa Single Single... years, discounted at 10% [PV = $1,000 / 1.102], the present value of your $1,000 is $826.45 What table do we use? D- 25 LO 5 Solve for present value of a single amount Present Present Value Value of of aa Single Single Amount Amount What factor do we use? $1,000 Future Value D- 26 x 82645 Factor = $826.45 Present Value LO 5 Solve for present value of a single amount Present Present
Value Value of of... Solve for a future value of a single amount Future Future Value Value of of an an Annuity Annuity Future value of an annuity is the sum of all the payments (receipts) plus the accumulated compound interest on them Necessary to know the 1 interest rate, 2 number of compounding periods, and 3 amount of the periodic payments or receipts D- 15 LO 3 Solve for a future value of an annuity Future Future Value. .. What table do we use? D- 30 LO 6 Solve for present value of an annuity Present Present
Value Value of of an an Annuity Annuity What factor do we use? $1,000 Future Value D- 31 x 2.48685 Factor = $2,486.85 Present Value LO 6 Solve for present value of an annuity Present Present
Value Value of of an an Annuity Annuity Illustration: Kildare Company has just signed a capitalizable lease contract for equipment... annuity Future Future
Value Value of of an an Annuity Annuity When the periodic payments (receipts) are the same in each period, the future value can be computed by using a future value of an annuity of 1 table Illustration: D- 18 Illustration D- 8 LO 3 Solve for a future value of an annuity Future Future Value Value of of an an Annuity Annuity What factor do we use? $2,500 Payment D- 19 x 4.37462 Factor... $10,936.55 Future Value LO 3 Solve for a future value of an annuity Present Present Value Value Concepts Concepts The present value is the value now of a given amount to be paid or received in the future, assuming compound interest Present value variables: 1 Dollar amount to be received in the future, 2 Length of time until amount is received, and 3 Interest rate (the discount rate) D- 20 LO 4 Identify the... Value D- 12 x 1.29503 Factor = $1,295.03 Future Value LO 2 Solve for a future value of a single amount Future Future Value Value of of aa Single Single Amount Amount Illustration: Illustration D- 5 What table do we use? D- 13 LO 2 Solve for a future value of a single amount Future Future Value Value of of aa Single Single Amount Amount $20,000 Present Value D- 14 x 2.85434 Factor = $57,086.80 Future Value. .. Future Value Value of of aa Single Single Amount Amount Alternate Method Illustration: If you want a 9% rate of return, you would compute the future value of a $1,000 investment for three years as follows: Illustration D- 4 What table do we use? D- 11 LO 2 Solve for a future value of a single amount Future Future Value Value of of aa Single Single Amount Amount What factor do we use? $1,000 Present Value. .. payments, discounted assuming compound interest Necessary to know 1 the discount rate, 2 The number of discount periods, and 3 the amount of the periodic receipts or payments D- 29 LO 6 Solve for present value of an annuity Present Present Value Value of of an an Annuity Annuity Illustration D- 14 Illustration: Assume that you will receive $1,000 cash annually for three years at a time when the discount... Future Value Value of of an an Annuity Annuity Illustration: Assume that you invest $2,000 at the end of each year for three years at 5% interest compounded annually Illustration D- 6 D- 16 LO 3 Solve for a future value of an annuity Future Future Value Value of of an an Annuity Annuity Illustration: Invest = $2,000 i = 5% n = 3 years Illustration D- 7 D- 17 LO 3 Solve for a future value of an annuity