Multiple Cash Flows
Chapter 4
Dr. Gillette
FIN 3100
1
Multiple Cash Flows - FV
Suppose you invest $500 in a mutual
fund today and $600 in one year,
$750 in three years. If the fund pays
4.5% annually, how much will you
have in three years?
How much will you have in 8 years if
you make no further deposits?
2
Multiple Cash Flows – PV
You are considering an
investment that will pay you
$1,000 in one year, $2,000 in two
years and $8,000 in seven years. If
you want to earn 7.25% on your
money, how much would you be
willing to pay?
Answer: PV0 = $7,572.416
3
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
Perpetuity – infinite series of equal payments
4
5
Annuities and Perpetuities –
Basic Formulas
 Perpetuity:
PV = FV / r
 Ordinary Annuities:
 FV = PMT * FVAF
 PV = PMT * PVAF
1

1


(1  r ) n
PV  PMT 
r









 (1  r ) n  1 
FV  PMT 

r


6
Annuity – Sweepstakes
Suppose you win the Publishers
Clearinghouse $10 million sweepstakes.
The money is paid in equal annual
installments of $333,333.33 over 30 years.
If the appropriate discount rate is 5%,
how much is the sweepstakes actually
worth today?
Answer: PV0=$5,124,150.29
7
Finding the Payment
Suppose you want to borrow
$20,000 for a new car. You can
borrow at 8% per year. If you take a
4-year loan, what is your annual
payment?
Answer: Pmt =$6,038.416
8
Finding the “monthly” Payment
Suppose you prefer monthly over annual
payments. Another bank will let you
borrow the $20,000 for your new car. You
can still borrow at 8% per year. If you take
the 4-year loan, what is your monthly
payment?
Answer: Monthly Pmt = $488.258/mth
Is that more or less than the annual
payment?
Which does the lender prefer? Why?
9
Finding the Number of Payments
Suppose you borrow $2000 at 5% and you
are going to make annual payments of
$734.42. How long before you pay off the
loan?
Answer: 2.999 years
10
Interest
 Suppose you borrow $35,000 and you
are going to make annual payments of
$5,000 for nine years. What interest rate
are you paying on the loan?
R = 5.345%
11
Future Values for Annuities
Suppose you begin saving for your
retirement by depositing $2,000 per year
in an IRA. If the interest rate is 7.5%, how
much will you have in 40 years?
Answer: FV40 = $454,513.039
12
Perpetuity
Perpetuity formula: PV = PMT / r
What is the dividend for new preferred
stock per quarter if the value is $100 today
and the quarterly interest rate is 2.5% per
quarter?
Answer: D = $2.50 per quarter
Saving For Retirement
13
You are offered the opportunity to put some money away for
retirement. You will receive five annual payments of $25,000
each (A) staring this year, and (B) in 30 years. How much
would you be willing to invest today, if you desire an interest
rate of 8.5%?
(A) PV0 = $98,516.052
(B) PV0 = $9,247.93 where, (PV in Yr29 = $98,516.052)
14
Decisions, Decisions
Your broker calls you and tells you
that he has this great investment
opportunity. If you invest $100
today, you will receive $40 in one
year and $75 in two years. If you
require a 15% return on investments
of this risk, should you take the
investment?
Answer: No thanks!
15
Multiple Cash Flows
Suppose you plan to deposit $100
into an account in one year and
$300 into the account in three
years. How much will be in the
account in six years if the interest
rate is 5%?
Answer: FV6 = $474.916
16
Three basic Loan Types
1) Pure Discount - e.g. T-bills
2) Interest Only - e.g. bonds
3) Amortized - e.g. cars & homes
17
Pure Discount Loans
Treasury bills are excellent examples of
pure discount loans.
The principal amount is repaid at some
future date, without any periodic interest
payments.
18
Interest-Only Loan
Consider a 5-year, interest only loan with
a 7% interest rate. The principal amount
is $10,000. Interest is paid annually.
What would the stream of cash flows
be?
Answer: Interest payments of $700 each
year for five years and $10,000 returned
at end of fifth year.
19
Amortized Loan with Fixed
Payment
Each payment covers the interest
expense plus reduces principal
Consider a 4-year loan with annual
payments. The interest rate is 8% and the
principal amount is $5000.
What is the annual payment?
The Amortization Table
Year
Beg.
Balance
Total
Payment
1
5,000.00
1509.60
400.00 1109.60 3890.40
2
3890.40
1509.60
311.23 1198.37 2692.03
3
2692.03
1509.60
215.36 1294.24 1397.79
4
1397.79
1509.60
111.82 1397.78
6038.40
1038.41 4999.99
Totals
Interest
Paid
Princip
End.
al Paid Balance
.01