Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill/Irwin

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Chapter 5

Discounted Cash Flow Valuation

Discounted Cash Flow Valuation

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Chapter Outline

• Future and Present Values of Multiple Cash Flows

• Valuing Level Cash Flows: Annuities and Perpetuities

• Comparing Rates: The Effect of Compounding Periods

• Loan Types and Loan Amortization

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Time line - Chapter 4

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T = 0 1 2 3 4 5

PV FV

PV = Present ValueFV = Future Valuet = Numbers of periodr = Interest rate

•Single cash flow: FV=PV(1+r)t

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Time line - Chapter 5

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T = 0 1 2 3 4 5

CF1 CF2 CF3 CF4 CF5

CF1= Cash Flow in Yr1CF2= Cash Flow in Yr2CF3= Cash Flow in Yr3CF4= Cash Flow in Yr4CF5= Cash Flow in Yr5

•Multiple cash flows valuation: PV or FV

PV FV

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Uneven Cash Flows – Future Value Example

• You can deposit $4000 at the end of the next three years in a bank account paying 8% interest. You currently have $7000 in the account. How much will you have in three years? In four years?

• Find the future value of each cash flow and add them together.

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Uneven Cash Flows – Present Value Example

• You are offered an investment that will pay you $200 in one year, $400 the next year, $600 the next year, and $800 at the end of the next. If you can earned 12%, what is the most this investment is worth today?

• Find the PV of each cash flow and add them

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• Suppose you are looking at the following possible cash flows: Year 1 CF = $100; Years 2 and 3 CFs = $200; Years 4=0 and Year 5 CFs = $300. The required discount rate is 7%

• What is the value of the cash flows at year 5? (FV5 = $905.07)

• What is the value of the cash flows today?(PV= $645.3)

• What is the value of the cash flows at year 3? (FV3= $790.52)

Quick Quiz: Part 1

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Level Cash Flows: Annuities and Perpetuities

• 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

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Annuities– Basic Formulas

• Annuities (ordinary):

rr)(1

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CPVt

C = equal cash flow (PMT)

r

1r)(1CFV

t

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Annuities– Tables

• Annuities (ordinary):

PV = C * PVIFA (r%, t)

App. A3 (pg.584)

FV = C * FVIFA (r%, t)

App. A4 (pg.586)

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Present Value of Annuity • You won a lottery. The money is paid in

equal annual installments of $100,000 over 3 years. If the appropriate discount rate is 5%, how much is the lottery actually worth today?

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Future Values for Annuities• Suppose you begin saving for your retirement by

depositing $2000 per year in an trust. If the interest rate is 8%, how much will you have in 40 years?

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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?

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Buying a House - Continued

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Quick Quiz: Part 2

• You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value?

• You want to receive $5000 per month in retirement. If you can earn .75% per month and you expect to need the income for 25 years, how much do you need to have in your account at retirement?

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Finding the Payments• Suppose you want to borrow $20,000 for a

new car. You can borrow at 8% per year compounded monthly. If you take a 4 year loan, what is your monthly payment?

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Finding the Number of Payments • You have $1000 balance debt on your

credit card. You can only make a payment of $20 per month. The interest rate is 1.5% per month. How long will you need to pay off the $1000.

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Finding the Rate

– Financial Calculator

– Table

– Trial and error

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Finding the rates-ExampleSuppose you borrow $10,000 from your parents to buy a car. You agree to pay $2504.56 per year for 5 years. What is the interest rate?

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Quick Quiz: Part 3

• Suppose you have $200,000 to deposit and can earn 0.75% per month.

– How many months could you receive the $5000 payment? (t=47.73mths)

– How much could you receive every month for 5 years? (c=$4151.67)

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Annuity Due• First payment occurs at the beginning of the period• Annuity due value=ordinary annuity value*(1+r)

)r1(r

1)r1(CFV

)r1(r

)r1(

11

CPV

t

t

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Annuity Due TimelineYou are saving for a new house and you put $10,000 per year in an account paying 8% for 3 years. The first payment is made today. How much will you have at the end of year 3?

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Perpetuity – Example • Infinite series of equal payments

– Perpetuity formula: PV = C / r

• A preferred stock offers dividend of $2 per year, What is the price of that stock is going to sell if the required rate of return is 8%?

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Quick Quiz: Part 4

• You want to have $1 million to use for retirement in 35 years. If you can earn 1% per month, how much do you need to deposit on a monthly basis if the first payment is made in one month?

• You are considering preferred stock that pays a quarterly dividend of $1.50. If your desired return is 12% per year, how much would you be willing to pay?

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Tutorial

• Problem 6, 21, 26, 28, 30, 35, 47 and 49 from page 153

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