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【正文】 ayments per year 427 Continuous Compounding ? The general formula for the future value of an investment pounded continuously over many periods can be written as: FV = C0 erT Where C0 is cash flow at date 0, r is the stated annual interest rate, T is the number of years, and e is a transcendental number approximately equal to . ex is a key on your calculator. 428 Simplifications ? Perpetuity ? A constant stream of cash flows that lasts forever ? Growing perpetuity ? A stream of cash flows that grows at a constant rate forever ? Annuity ? A stream of constant cash flows that lasts for a fixed number of periods ? Growing annuity ? A stream of cash flows that grows at a constant rate for a fixed number of periods 429 Perpetuity A constant stream of cash flows that lasts forever 0 … 1 C 2 C 3 C ???????? 32)1()1()1( rCrCrCPVrCPV ?430 Perpetuity: Example What is the value of a British consol that promises to pay 163。Discounted Cash Flow Valuation Chapter 4 Copyright 169。 2021 by the McGrawHill Companies, Inc. All rights reserved. McGrawHill/Irwin 41 Key Concepts and Skills ? Be able to pute the future value and/or present value of a single cash flow or series of cash flows ? Be able to pute the return on an investment ? Be able to use a financial calculator and/or spreadsheet to solve time value problems ? Understand perpetuities and annuities 42 Chapter Outline Valuation: The OnePeriod Case The Multiperiod Case Compounding Periods Simplifications Loan Amortization What Is a Firm Worth? 43 The OnePeriod Case ? If you were to invest $10,000 at 5percent interest for one year, your investment would grow to $10,500. $500 would be interest ($10,000 .05) $10,000 is the principal repayment ($10,000 1) $10,500 is the total due. It can be calculated as: $10,500 = $10,000 () ? The total amount due at the end of the investment is call the Future Value (FV). 44 Future Value ? In the oneperiod case, the formula for FV can be written as: FV = C0 (1 + r) Where C0 is cash flow today (time zero), and r is the appropriate interest rate. 45 Present Value ? If you were to be promised $10,000 due in one year when interest rates are 5percent, your investment would be worth $9, in today’s dollars. 000,10$,9$ ?The amount that a borrower would need to set aside today to be able to meet the promised payment of $10,000 in one year is called the Present Value (PV). Note tha
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