The Time Value of Money/ Present Values Appendix C

Transcription

1 The Time Value Money/ Present Values Appendix C THIS IS ABOUT THE BASICS You should become familiar with the concept present values and the basics how they work using the tables. This is NOT intended to be a comprehensive course in business finance covered in 1 hour! C-1 UCSB, Anderson C-2 UCSB, Anderson CONCEPT #1 CONCEPT #2 What is worth more: (A) $1 today The impact compounding interest is EXPONENTIAL!!! OR (B) $1 One year from today? $1 today IF you invested that $1 for one year at only 3% interest compounding monthly, you would have $ at the end the year! What would you rather have in one year $1 or $1.0304? C-3 UCSB, Anderson C-4 UCSB, Anderson

2 Rate 10% Compounding Monthly $1 Invested NON-COMPOUNDING COMPOUNDING $1.1 $1.105 Year 1 Year 2 $1.2 $1.220 Year 3 $1.3 $1.348 Year 4 $1.4 $1.489 Year 5 $1.5 $1.645 Year 6 $1.6 $1.818 Year 7 $1.7 $2.8 Year 8 $1.8 $2.218 Year 9 $1.9 $2.450 Year 10 $2.0 $2.707 Year 11 $2.1 $2.1 Year 12 $2.2 $3.304 Year 13 $2.3 $3.650 Year 14 $2.4 $4.032 Year 15 $2.5 $4.454 Year 16 $2.6 $4.920 Year 17 $2.7 $5.436 Year 18 $2.8 $6.5 Year 19 $2.9 $6.633 Year 20 $3.0 $ NON-COMPOUNDING COMPOUNDING Key Terminology Present Value: Today s value money to be received in the future; Future Value: Value an amount known today which will be received/ paid in the future. Compound: Interest earning interest. Compounding period should be stated, generally monthly Annuity: Payments over a period time in equal amounts. Payment Interval: Frequency annuity pmts. Ordinary annuity: payments made at the end the payment interval Annuity due: payments made at the beginning the payment interval C-5 UCSB, Anderson Year 1 Year 3 Year 5 Year 7 Year 9 Year 11 Year 13 Year 15 Year 17 Year 19 C-6 UCSB, Anderson Time-Value Money basics $1 today is worth more than $1 tomorrow; GAAP seeks to present the economic substance over legal form a transaction. Consequently, PV becomes relevant. Glaring example: Real estate sold to buyer for $10 million, payable as follows: $7,5,0 due in cash at close escrow; $2,5,0 note payable bearing 0% interest payable in one lump-sum in 5 years.» Is the sales price $10 million NO- $2.5 million in 5 years is worth < $2.5 million! The risk is commensurate with the reward- the higher the perceived risk, the higher the interest rate. Key Variables Whether using a table, microst excel formula or a financial calculator, the key variables are: Present value and/ or Future value; Interest Rate Payment (if an annuity) Period (note: depends on compounding period) C-7 UCSB, Anderson C-8 UCSB, Anderson

3 Present Value Present Value? $20,0 in Future Present Value a Single Sum 31/ BE6-2 Itzak Perlman needs $20,0 in 4 years. What amount must he invest today if his investment earns 12% compounded annually? 31/ C-9 UCSB, Anderson C-10 UCSB, Anderson Present Value a Single Sum Present Value Present Value? $20,0 in Future $20,0 x = $12, / /04 Itzak Perlman needs $20,0 in 4 years. What amount must he invest today if his investment earns 12% compounded quarterly? Funds Needed Factor Present Value C-11 UCSB, Anderson C-12 UCSB, Anderson

4 Present Value a Single Sum Periods 3% 4% 6% 9% 12% C-13 UCSB, Anderson Present Value a Single Sum Periods 3% 4% 6% 9% 12% $20,0 x = $12, Funds Needed Factor Present Value C-14 UCSB, Anderson Present Value Present Value Ordinary Annuity Today Interest paid $80,0 repaid Table / /01 Doc Company entered into a three year loan agreement that requires $80,0 to be repaid at maturity plus annual interest payments in the amount $9,6. What is the present value the interest payments assuming a market interest rate 12%? C-15 UCSB, Anderson C-16 UCSB, Anderson

5 Present Value Ordinary Annuity Present Value Table 6-4 Today Interest paid $80,0 repaid $9,6 x ( ) = $23,058 Interest Payment Factor Present Value 31/ /01 Doc Company borrowed $80,0 under a three year loan agreement that requires annual interest payments in the amount $9,6. What is the present value the principle payment assuming a market interest rate 12%? C-17 UCSB, Anderson C-18 UCSB, Anderson Present Value 1 (Single Sum) Present Value 1 (single sum) C-19 UCSB, Anderson $80,0 x.712 (.71178) = $56, Principal Borrowed Factor Present Value C-20 UCSB, Anderson

6 Present Value Ordinary Annuity Summary -- PV Interest $23,058 PV Principle 56, Total PV $80,0 C-21 UCSB, Anderson