Chapter •Introduction to Valuation: The Time Value of Money McGraw-Hill/Irwin Copyright © by The McGraw-Hill Companies, Inc All rights Chapter – Index of Sample Problems • • • • • • • • • • Slide # 02 - 03 Slide # 04 - 06 Slide # 07 - 09 Slide # 10 - 12 Slide # 13 - 15 Slide # 16 - 18 Slide # 19 Slide # 20 Slide # 21 Slide # 22 Simple interest versus compound interest Future value Present value Interest rate for a single period Interest rate for multiple periods Number of time periods Present value and rate changes Future value and rate changes Present value and time changes Future value and time changes 2: Simple versus compound interest First United Bank pays 4% simple interest on their savings accounts Second Federal Bank pays 4% interest compounded annually on their savings accounts If you invest $1,000 in each bank, how much will you have in your accounts after twenty years? Why are the balances different? 3: Simple versus compound interest First United Bank $1,000 × 04 = $40 $40 × 20 = $800 $1,000 + $800 = $1,800 Second Federal Bank FVt = PV × (1 + r) t = $1,000 × 1.04 20 = $2,191.12 Difference $2,191.12 − $1,800 = $391.12 4: Future value You invest $3,000 in the stock market today How much will your account be worth forty years from now if you earn a 9% rate of return? 5: Future value FVt = PV × (1 + r ) t = $3,000 × (1 + 09 ) = $3,000 × 31.40942 = $94,228.26 40 6: Future value Enter Solve for 40 N I/Y ±3,000 PV PMT FV 94,228.26 7: Present value You want to have $7,500 three years from now to buy a car You can earn 6% on your savings How much money must you deposit today to have the $7,500 in three years? 8: Present value FVt PV = t (1 + r ) $7,500 = (1 + 06) $7,500 = 1.191016 = $6,297.14 9: Present value Enter Solve for N I/Y PV -6,297.14 PMT 7,500 FV 10: Interest rate for a single period Last year your investments were worth $369,289 Today they are worth $401,382 No deposits or withdrawals were made during the year What rate of return did you earn on your investments this year? 11: Interest rate for a single period FVt = PV × (1 + r ) t $401,382 = $369,289 × (1 + r ) 1.086905 = + r r = 086905 r = 8.6905% 12: Interest rate for a single period Enter Solve for N I/Y 8.6905 ±369,289 PV PMT 401,382 FV 13: Interest rate for multiple periods The City Museum owns a rare painting currently valued at $1.2 million The museum paid $240,000 to purchase the painting twelve years ago What is the rate of appreciation on this painting? 14: Interest rate for multiple periods FVt = PV × (1 + r ) t $1,200,000 = $240,000 × (1 + r ) = (1 + r ) 12 12 = 1+ r 5.0833333 = + r 1.1435298 = + r r = 1435298 r = 14.35298% 12 15: Interest rate for multiple periods Enter Solve for 12 N ±240,000 I/Y PV 14.35298 PMT 1,200,000 FV 16: Number of time periods Tom originally started to work for Jackson Enterprises at an annual salary of $36,500 Today, Tom earns $68,200 Tom calculated that his average annual pay raise has been 3.4% How long has Tom worked for Jackson Enterprises? 17: Number of time periods FVt = PV × (1 + r ) t 68,200 = 36,500 × (1.034) t 1.8684932 = 1.034t ln 1.8684932 = t × ln 1.034 ln 1.8684932 t= ln 1.034 6251323 t= 0334348 t = 18.697 18: Number of time periods Enter Solve for N 18.697 3.4 I/Y ±36,500 PV PMT 68,200 FV 19: Present value and rate changes Enter N I/Y N I/Y Solve for Enter Solve for PV -94.34 PV -93.46 PMT 100 FV PMT 100 FV 20: Future value and rate changes Enter N I/Y ±100 PV PMT FV 106 I/Y ±100 PV PMT FV 107 Solve for Enter Solve for N 21: Present value and time changes Enter N I/Y Solve for Enter Solve for N PV -95.24 PMT 100 FV I/Y PV -90.70 100 PMT FV 22: Future value and time changes Enter N I/Y ±100 PV PMT Solve for Enter Solve for N I/Y PV ±100 PMT FV 105 FV 110.25 Chapter •End of Chapter McGraw-Hill/Irwin Copyright © by The McGraw-Hill Companies, Inc All rights ... ±240,000 I/Y PV 14.35298 PMT 1,200,000 FV 16: Number of time periods Tom originally started to work for Jackson Enterprises at an annual salary of $36,500 Today, Tom earns $68,200 Tom calculated... Number of time periods FVt = PV × (1 + r ) t 68,200 = 36,500 × (1.034) t 1.8684932 = 1.034t ln 1.8684932 = t × ln 1.034 ln 1.8684932 t= ln 1.034 6251323 t= 0334348 t = 18.697 18: Number of time... stock market today How much will your account be worth forty years from now if you earn a 9% rate of return? 5: Future value FVt = PV × (1 + r ) t = $3,000 × (1 + 09 ) = $3,000 × 31.40942 = $94,228.26