Fundamentals of coroprate finance 7th ross westerfield CH06

Chapter •Discounted Cash Flow Valuation McGraw-Hill/Irwin Copyright © by The McGraw-Hill Companies, Inc All rights reserved Chapter – Index of Sample Problems • • • • • • • • • • Slide # 03 - 04 Slide # 05 - 07 Slide # 08 - 10 Slide # 11 - 13 Slide # 14 - 16 Slide # 17 - 19 Slide # 20 - 22 Slide # 23 - 25 Slide # 26 - 28 Slide # 29 - 30 Financial calculator review Ordinary annuity present value Annuity due present value Ordinary annuity future value Annuity due future value Annuity – annual payments Annuity – monthly payments Annuity – quarterly payments Annuity time periods Annuity interest rate (Index continued on next slide) Chapter – Index of Sample Problems • • • • • • • • Slide # 31 - 33 Slide # 34 - 36 Slide # 37 - 38 Slide # 39 - 41 Slide # 42 - 44 Slide # 45 - 47 Slide # 48 - 49 Slide # 50 - 52 Present value – uneven cash flows Future value – uneven cash flows Perpetuity present value Effective annual rate Continuous compounding Pure discount loan Interest only loan Amortized loans 3: Financial calculator review If you invest $100 today for one year at a 10% rate of return, how much money will you have one year from now? Enter N 10 I/Y Solve for (continued on next slide) ±100 PV PMT FV 110 4: Financial calculator review Enter Solve for N 10 I/Y ±100 PV PMT FV 110 You are spending $100 by investing it You input that as a negative value using the “±” key You are receiving $110 back at the end of one year That is the positive value Positives and negatives are used to denote the direction of the cash flow Generally you use a positive value to indicate a cash inflow and a negative value to indicate a cash outflow All dollar amounts in this type of problem are, in actuality, positive values 5: Ordinary annuity present value You will receive $12,000 a year for the next ten years from a trust fund your grandmother is establishing What is this gift worth today at a 9% discount rate? 6: Ordinary annuity present value [ ] 1 − / (1 + r ) t  APV = C ×   r   1 − /(1 + 09)10  = $12,000 ×   09    5775892  = $12,000 ×    09  = $12,000 × 6.4176578 = $77,011.89 [ ] 7: Ordinary annuity present value Enter Solve for 10 N I/Y PV -77,011.89 12,000 PMT FV 8: Annuity due present value You are buying some land from your parents today You agree to pay them $5,000 a year for six years The first payment is due today What is the actual selling price of the land if your parents are only charging you 3% interest? 9: Annuity due present value [ ] 1 − / (1 + r ) t  A Due PV = C ×   × (1 + r ) r   [ ] 1 − / (1 + 03)  = $5,000 ×   × (1 + 03) 03   ( 162515743) = $5,000 × × 1.03 03 = $5,000 × 5.4171914 × 1.03 = $27,898.54 39: Effective annual rate You have a credit card with a quoted annual percentage rate of 17.9% Interest is applied to your account monthly What is the effective annual rate? 40: Effective annual rate m   quoted rate  EAR = 1 +   − m    12   179  EAR = 1 +   −   12  = [1.014917] − = 19444 = 19.44% 12 41: Effective annual rate Enter Solve for 17.9 NOM EFF 19.44 12 C/Y 42: Continuous compounding What is the effective annual rate of 14.9% compounded continuously? 43: Continuous compounding EAR = e.149 − = 2.71828 = 16067 = 16.07% 149 −1 44: Continuous compounding 149 2nd ex -1 = 16067 Which is rounded to 16.07% 45: Pure discount loan You are borrowing money today at a 9% interest rate You will repay the loan in one lump sum payment of $5,000 two years from today How much are you borrowing today? 46: Pure discount loan PV = C t × t (1 + r ) = $5,000 × (1 + 09) $5,000 = 1.1881 = $4,208.40 47: Pure discount loan Enter Solve for N I/Y PV 4,208.40 ±5,000 PMT FV 48: Interest only loan You are borrowing $2,500 today for five years at a 7% rate of interest This is an interest only loan with payments paid annually How much must you pay each year until this loan is repaid in full? 49: Interest only loan Year payment = $2,500 × 07 = $175 Year payment = $2,500 × 07 = $175 Year payment = $2,500 × 07 = $175 Year payment = $2,500 × 07 = $175 Year payment = ( $2,500 × 07 ) + $2,500 = $2,675 50: Amortized loan You borrow $1,000 at 8% interest This loan is being amortized over five years with payments being made annually What is the amount of each annual payment? 51: Amortized loan   1 − (1 + r ) t   PV = C ×  r   1 − 1.085  $1,000 = C × 08 3194168 $1,000 = C × 08 $1,000 = C × 3.99271 C = $250.46 52: Amortized loan Enter Solve for N I/Y 1,000 PV PMT -$250.46 FV Chapter •End of Chapter McGraw-Hill/Irwin Copyright © by The McGraw-Hill Companies, Inc All rights reserved ... $3,000 at the beginning of each year for four years You are saving this money and earning a 2.5% rate of return on your savings How much money will you have at the end of the four years? 15: Annuity... market every year for your retirement You will make your first investment at the end of this year The average rate of return you expect to earn is 7% How much money you expect to have when you retire... “±” key You are receiving $110 back at the end of one year That is the positive value Positives and negatives are used to denote the direction of the cash flow Generally you use a positive value