公司理财英文版第五章第六章-表格
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6F-10
Example 6.3 Timeline
0 1 2 3 4
200
178.57 318.88 427.07 508.41 1,432.93
400
600
800
6F-11
Multiple Cash Flows Using a Spreadsheet
• You can use the PV or FV functions in Excel to find the present value or future value of a set of cash flows • Setting the data up is half the battle – if it is set up properly, then you can just copy the formulas • Click on the Excel icon for an example
The cash flows in years 40 – 44 are 25,000 (C02 = 25,000; F02 = 5)
6F-14
Quick Quiz – Part I
• Suppose you are looking at the following possible cash flows: Year 1 CF = $100; Years 2 and 3 CFs = $200; Years 4 and 5 CFs = $300. The required discount rate is 7%. • What is the value of the cash flows at year 5? • What is the value of the cash flows today? • What is the value of the cash flows at year 3?
6F-3
Basic Definitions
• Present Value – earlier money on a time line • Future Value – later money on a time line • Interest rate – “exchange rate” between earlier money and later money
– – – – Discount rate Cost of capital Opportunity cost of capital Required return
5F-4
Future Values
• Suppose you invest $1,000 for one year at 5% per year. What is the future value in one year? – Interest = 1,000(.05) = 50 – Value in one year = principal + interest = 1,000 + 50 = 1,050 – Future Value (FV) = 1,000(1 + .05) = 1,050 • Suppose you leave the money in for another year. How much will you have two years from now? – FV = 1,000(1.05)(1.05) = 1,000(1.05)2 = 1,102.50
6F-12
Saving For Retirement
• You are offered the opportunity to put some money away for retirement. You will receive five annual payments of $25,000 each beginning in 40 years. How much would you be willing to invest today if you desire an interest rate of 12%?
6F-15
Annuities and Perpetuities Defined
• Annuity – finite series of equal payments that occur at regular intervals
– If the first payment occurs at the end of the period, it is called an ordinary annuity – If the first payment occurs at the beginning of the period, it is called an annuity due
6F-2
Chapter Outline
• Future and Present Values of Multiple Cash Flows • Valuing Level Cash Flows: Annuities and Perpetuities • Comparing Rates: The Effect of Compounding • Loan Types and Loan Amortization
• Future value interest factor = (1 + r)t
5FBiblioteka Baidu6
Effects of Compounding
• Simple interest • Compound interest • Consider the previous example
– FV with simple interest = 1,000 + 50 + 50 = 1,100 – FV with compound interest = 1,102.50 – The extra 2.50 comes from the interest of .05(50) = 2.50 earned on the first interest payment
6F-13
Saving For Retirement Timeline
0 1 2 … 39 40 41 42 43 44
0 0 0
…
0
25K 25K 25K
25K 25K
Notice that the year 0 cash flow = 0 (CF0 = 0)
The cash flows in years 1 – 39 are 0 (C01 = 0; F01 = 39)
• Be able to compute the future value of multiple cash flows • Be able to compute the present value of multiple cash flows • Be able to compute loan payments • Be able to find the interest rate on a loan • Understand how interest rates are quoted • Understand how loans are amortized or paid off
6F-19
Buying a House - Continued
• Bank loan
– Monthly income = 36,000 / 12 = 3,000 – Maximum payment = .28(3,000) = 840 – PV = 840[1 – 1/1.005360] / .005 = 140,105
Chapter 6
Formulas
Discounted Cash Flow Valuation
McGraw-Hill/Irwin
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Key Concepts and Skills
5F-5
Future Values: General Formula
• FV = PV(1 + r)t
– FV = future value – PV = present value – r = period interest rate, expressed as a decimal – t = number of periods
(1 r ) t 1 FV C r
6F-17
Annuity – Example 6.5
• You borrow money TODAY so you need to compute the present value.
– 48 N; 1 I/Y; -632 PMT; CPT PV = 23,999.54 ($24,000)
• Formula:
1 1 (1.01) 48 PV 632 23,999.54 .01
6F-18
Buying a House
• You are ready to buy a house, and you have $20,000 for a down payment and closing costs. Closing costs are estimated to be 4% of the loan value. You have an annual salary of $36,000, and the bank is willing to allow your monthly mortgage payment to be equal to 28% of your monthly income. The interest rate on the loan is 6% per year with monthly compounding (.5% per month) for a 30-year fixed rate loan. How much money will the bank loan you? How much can you offer for the house?
• Value at year 4 = 21,803.58(1.08) = 23,547.87
6F-9
Multiple Cash Flows – Present Value Example 6.3
• Find the PV of each cash flows and add them
– Year 1 CF: 200 / (1.12)1 = 178.57 – Year 2 CF: 400 / (1.12)2 = 318.88 – Year 3 CF: 600 / (1.12)3 = 427.07 – Year 4 CF: 800 / (1.12)4 = 508.41 – Total PV = 178.57 + 318.88 + 427.07 + 508.41 = 1,432.93
5F-7
Multiple Cash Flows –Future Value Example 6.1
• Find the value at year 3 of each cash flow and add them together
– – – – – Today (year 0): FV = 7000(1.08)3 = 8,817.98 Year 1: FV = 4,000(1.08)2 = 4,665.60 Year 2: FV = 4,000(1.08) = 4,320 Year 3: value = 4,000 Total value in 3 years = 8,817.98 + 4,665.60 + 4,320 + 4,000 = 21,803.58
• Perpetuity – infinite series of equal payments
6F-16
Annuities and Perpetuities – Basic Formulas
• Perpetuity: PV = C / r • Annuities:
1 1 (1 r ) t PV C r
Example 6.3 Timeline
0 1 2 3 4
200
178.57 318.88 427.07 508.41 1,432.93
400
600
800
6F-11
Multiple Cash Flows Using a Spreadsheet
• You can use the PV or FV functions in Excel to find the present value or future value of a set of cash flows • Setting the data up is half the battle – if it is set up properly, then you can just copy the formulas • Click on the Excel icon for an example
The cash flows in years 40 – 44 are 25,000 (C02 = 25,000; F02 = 5)
6F-14
Quick Quiz – Part I
• Suppose you are looking at the following possible cash flows: Year 1 CF = $100; Years 2 and 3 CFs = $200; Years 4 and 5 CFs = $300. The required discount rate is 7%. • What is the value of the cash flows at year 5? • What is the value of the cash flows today? • What is the value of the cash flows at year 3?
6F-3
Basic Definitions
• Present Value – earlier money on a time line • Future Value – later money on a time line • Interest rate – “exchange rate” between earlier money and later money
– – – – Discount rate Cost of capital Opportunity cost of capital Required return
5F-4
Future Values
• Suppose you invest $1,000 for one year at 5% per year. What is the future value in one year? – Interest = 1,000(.05) = 50 – Value in one year = principal + interest = 1,000 + 50 = 1,050 – Future Value (FV) = 1,000(1 + .05) = 1,050 • Suppose you leave the money in for another year. How much will you have two years from now? – FV = 1,000(1.05)(1.05) = 1,000(1.05)2 = 1,102.50
6F-12
Saving For Retirement
• You are offered the opportunity to put some money away for retirement. You will receive five annual payments of $25,000 each beginning in 40 years. How much would you be willing to invest today if you desire an interest rate of 12%?
6F-15
Annuities and Perpetuities Defined
• Annuity – finite series of equal payments that occur at regular intervals
– If the first payment occurs at the end of the period, it is called an ordinary annuity – If the first payment occurs at the beginning of the period, it is called an annuity due
6F-2
Chapter Outline
• Future and Present Values of Multiple Cash Flows • Valuing Level Cash Flows: Annuities and Perpetuities • Comparing Rates: The Effect of Compounding • Loan Types and Loan Amortization
• Future value interest factor = (1 + r)t
5FBiblioteka Baidu6
Effects of Compounding
• Simple interest • Compound interest • Consider the previous example
– FV with simple interest = 1,000 + 50 + 50 = 1,100 – FV with compound interest = 1,102.50 – The extra 2.50 comes from the interest of .05(50) = 2.50 earned on the first interest payment
6F-13
Saving For Retirement Timeline
0 1 2 … 39 40 41 42 43 44
0 0 0
…
0
25K 25K 25K
25K 25K
Notice that the year 0 cash flow = 0 (CF0 = 0)
The cash flows in years 1 – 39 are 0 (C01 = 0; F01 = 39)
• Be able to compute the future value of multiple cash flows • Be able to compute the present value of multiple cash flows • Be able to compute loan payments • Be able to find the interest rate on a loan • Understand how interest rates are quoted • Understand how loans are amortized or paid off
6F-19
Buying a House - Continued
• Bank loan
– Monthly income = 36,000 / 12 = 3,000 – Maximum payment = .28(3,000) = 840 – PV = 840[1 – 1/1.005360] / .005 = 140,105
Chapter 6
Formulas
Discounted Cash Flow Valuation
McGraw-Hill/Irwin
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Key Concepts and Skills
5F-5
Future Values: General Formula
• FV = PV(1 + r)t
– FV = future value – PV = present value – r = period interest rate, expressed as a decimal – t = number of periods
(1 r ) t 1 FV C r
6F-17
Annuity – Example 6.5
• You borrow money TODAY so you need to compute the present value.
– 48 N; 1 I/Y; -632 PMT; CPT PV = 23,999.54 ($24,000)
• Formula:
1 1 (1.01) 48 PV 632 23,999.54 .01
6F-18
Buying a House
• You are ready to buy a house, and you have $20,000 for a down payment and closing costs. Closing costs are estimated to be 4% of the loan value. You have an annual salary of $36,000, and the bank is willing to allow your monthly mortgage payment to be equal to 28% of your monthly income. The interest rate on the loan is 6% per year with monthly compounding (.5% per month) for a 30-year fixed rate loan. How much money will the bank loan you? How much can you offer for the house?
• Value at year 4 = 21,803.58(1.08) = 23,547.87
6F-9
Multiple Cash Flows – Present Value Example 6.3
• Find the PV of each cash flows and add them
– Year 1 CF: 200 / (1.12)1 = 178.57 – Year 2 CF: 400 / (1.12)2 = 318.88 – Year 3 CF: 600 / (1.12)3 = 427.07 – Year 4 CF: 800 / (1.12)4 = 508.41 – Total PV = 178.57 + 318.88 + 427.07 + 508.41 = 1,432.93
5F-7
Multiple Cash Flows –Future Value Example 6.1
• Find the value at year 3 of each cash flow and add them together
– – – – – Today (year 0): FV = 7000(1.08)3 = 8,817.98 Year 1: FV = 4,000(1.08)2 = 4,665.60 Year 2: FV = 4,000(1.08) = 4,320 Year 3: value = 4,000 Total value in 3 years = 8,817.98 + 4,665.60 + 4,320 + 4,000 = 21,803.58
• Perpetuity – infinite series of equal payments
6F-16
Annuities and Perpetuities – Basic Formulas
• Perpetuity: PV = C / r • Annuities:
1 1 (1 r ) t PV C r