Chapter 6
Discounted Cash Flow Valuation
6-0
McGraw-Hill/Irwin
Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter Outline
• Multiple Uneven Cash Flows
• Multiple Even Cash Flows:
Annuities and Perpetuities
• Effective Rates and Quoted Rates
• Continuous Compounding
• Loan Types
1
Multiple Uneven Cash Flows
• Calculate the PVs (or FVs) of each
cash flow and add them up
or
use the CF & NPV function keys.
(Note: it is helpful to use a timeline)
2
Example
(PV of Uneven Multiple CF)
• You are offered an investment that will pay
you $400 in one year, $600 in two years,
$1,000 in three years, and $500 in four
years. If you can earn 11% on a similar
investment how much would you pay for
the investment at the most?
3
Example
(FV of Uneven Multiple CF)
• You deposit $2,000 in one year $4,000 in
two years $1,000 in three years and $900
in four years. How much money will you
have in five years? Assume you earn 8%
interest!
4
Multiple Even Cash Flows:
Annuities and Perpetuities
• Annuity – finite series of equal
payments (PMT) that occur at regular
intervals
- If the first payment occurs at the end of
the period, it is called a
- If the first payment occurs at the
beginning of the period, it is called an
• Perpetuity – infinite series of equal
payments
5
Annuities & Perpetuities
• Annuity Formulas:
PVA
1

1


(1  r ) t
 C
r









FVA
 (1  r ) t  1 
 C

r


where :
r= I/Y, t= N, PV = PV, FV = FV and
C = PMT on the fin calculator
note : PV & PMT have opposite signs
or FV & PMT have opposite signs
• Perpetuity: PV = C / r
• (note: growing perpetuity: PVt=Ct+1/(r-g)
6
Example: PV of Annuity
• You want to buy a car by borrowing from
your bank. You can afford to spend $540
a month for four years. The bank charges
interest rate of 2% per month for 48
months. The first payment is due one
month from today. How much can you
borrow to buy your car?
• How much can you borrow if the first
payment is due today?
7
Example
• Your interest rate is .5% per month, you
borrow $20,000 and make 48 payments to
repay the loan. How high are your
payments?
8
Example
• Your interest rate is 1% per month, you
borrow $10,000 and you can afford $600
per month. How long does it take to repay
your loan?
9
Example: FV of Annuity
• You make 20 payments of $1,000 at the
end of each period at 15% per period, how
much will your account grow to be?
10
Example: Perpetuity
• Suppose a firm sells a share of preferred
stock for $200/share. What dividend does
the firm have to offer per quarter if a
comparable preferred stock offers 3% per
quarter?
• A company pays a $10 dividend per
quarter. If the quarterly rate is 4%, what is
the value of the preferred stock?
11
Effective Rates &
Quoted Rates
• Effective Rates: rate compounded once
per period
• Effective Annual Rate (EAR): annual rate
compounded once per year
• Quoted Rate: rate compounded more than
once per period
• Annual Percentage Rate (APR): annual
rate compounded more than once per
year
• Always use effective rates for TVM
12
calculations.
EAR Formula
APR= Effective rate per period x #of periods per year
Effective rate per period = APR/ # of periods per year
m
 APR 
EAR  1 

1

m


Where m = # of compounding times per year
Note: You can use the ICONV function instead to
convert the APR (NOM) into the EAR (EFF) and
vice versa.
13
Example
• A bank is charging 3% per month,
compounded monthly, on a car loan.
Transform this rate to a quoted rate per
year (APR).
14
Example
• If the annual interest rate is 18%,
compounded monthly, what is the EAR?
15
Example
• You want to actually earn 15% per year on
a loan. If you want to quote the rate as an
APR compounded quarterly what rate do
you quote?
16
Example
• You invest $5,000 at 6% APR,
compounded monthly. How much will you
have in 4 years?
17
Example
• You borrow $10,000. The loan calls for
monthly payments for 3 years. The APR is
9%, compounded monthly, what are the
monthly payments?
18
Continuous Compounding
• Sometimes investments or loans are
figured based on continuous
compounding (m=)
• EAR = eAPR – 1
19
Example
• What is the largest EAR for a 12% quoted
rate (APR) with continuous compounding?
• What is the future value of $1,000 in 2
years if you invest at 12% under
continuous compounding?
20
Example
• What is the APR if the EAR is 14% under
continuous compounding?
21
Loan Types
• Pure Discount
• Interest Only
• Amortized Loans
- fixed principal
- or fixed total payments
22