Download Ch 6

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts
no text concepts found
Transcript
Ch 6. Discounted cash flow
valuation
1. FV and PV with multiple cash flows
1) FV with multiple cash flows: Two methods
(1) Rolling over FV year by year
(2) FV=FV1+FV2+FV3….
Ex) Deposit $100 every year for 3 yrs. And 10%
interest rate. FV?
2) PV with multiple cash flows: Two
method
(1) Rolling back year by year
(2) PV=PV1+PV2+…..
Ex) You are supposed to need $1000 in one year
and $2000 in the second year. If you can
earn 9% on your money, how much you have
to put up today?
2. Annuities and Perpetuities
1) Def of Annuity:
Constant cash flows for a fixed period of time
Ex) car loan
Ex) Assets with promised to pay $500 at the end
of the each of the next three years. What is
the price of the asset now if a discount rate
is 10%?
Answer:
500/(1.1)+500/(1.1^2)+500/(1.1^3)= 1243.43
2) Formula for Annuity Present Value
C  [1  1 /(1  k ) ]
PV 
k
t
C
C
C
PV 

 ..... 
2
(1  k ) (1  k )
(1  k ) t
C
C
C
PV  (1  k )  C 

 ..... 
2
(1  k ) (1  k )
(1  k ) t 1
C
PV  PV  (1  k ) 
C
t
(1  k )
1
PV ( k )  C[
 1]
t
(1  k )
1
C[1 
]
t
(1  k )
Therefore PV 
k
Ex) You stop by a car dealer shop and find a
really good car. The sticker price of the car is
$15000. But you don’t have money now. So,
want installment payment over 4 yrs. Over
conversation, the dealer suggests $632 per
month for 48 month at 1% per month.
How much is going to be your PV of total
installments?
2-2) Finding C
Ex) You stop by a car dealer shop and find a
really good car. The sticker price of the car is
$15000. But you don’t have money now. So, if
you want installment payment over 4 yrs, how
much you have to pay monthly? (Here interest
rate is 12%)
2-3) Finding rate
Ex) an insurance company offers to pay you
$1000 per year for 10 years if you pay $6710
up front. What rate is used in this annuity?
3) Def of perpetuities:
An annuity in which the cash flow continues
forever
4) Formula for PV of perpetuities
PV=C/k
Ex) Preferred stock – promised fixed dividend every
period forever.
A company want to sell preferred stock at $100 per
share. How much of dividend it has to pay.
Currently the similar preferred stock is sold at $40
with $1 dividend.
i) Calculate r:
R= 1/40 = 0.025
ii) Calculate C:
100 = C/0.025. Then, C=2.5
5) FV for Annuities
FV  C  [(1  k )  1] / k
t
FV  C  C (1  k )  C (1  k )  ......  C (1  k )
2
t 1
FV  (1  k )  C (1  k )  C (1  k ) 2  C (1  k )3  .....  C (1  k )t
FV  FV (1  k )  C  C (1  k )t
FV (k )  C[1  (1  k ) ]
t
C[(1  k )t  1]
FV 
k
Ex) $2000 annuity for 30 years and k= 0.08. What is
the annuity future value?
6) Annuities due
Def: annuity for which the cash flows occur at the
beginning of the period
Annuity due value =
ordinary annuity value * (1+k)
• 7) Uneven Cash Flows;
• Summing PV and FV of each cash flows
• Using the cash flow patterns to apply formula
• 8) Growing annuities: payment growth by g%.
1 g t
1[
]
1 k ]
PV  C  [
kg
• 9) Growing perpetuity: payment grows by g%
forever.
PV  C /( k  g )
3. Rate
Q1. 10% compounded semi-annually is the same as
10% per year in compounding?
No! here, 10% is APR, (annual percentage rate) and
actually, 10.25% (=(1+0.05)*(1+0.05)-1) is the
effective annual rate.
To compare to other rates, we need to convert APR
into the effective rates
3-1) APRs (Annual Percentage Rate)
Def: interest rate charged per period (periodic rate)
multiplied by the number of periods per year
APR =EAR?
No!!!!
So, APR is a quoted rate and need to be converted
to the EAR
EAR(Effect ive Annual Rate)
 [1  (APR/m)] m  1
unlimited interest calculatio n
EAR  e k  1
e  2.71828
Ex)
One credit card company selling a card by telemarketing. The company said the card will
benefit its cardholders with semi-annual
15%APRs, compared to the other credit card
with 16% EAR.
Do you agree or not?
6.Loan types and loan Amortization
1) Pure discount loan:
Receive money today and repay a single lump sum
in future
What is the price of loan that you will pay $25,000 in 5
years? A lender wants to apply 12% interest rate.
14,186 = 25000/(1.12)^5
2) Interest only loan:
Pay interest each period and repay the entire
principal at some point in the future
• A three year, 10% interest only loan of $1000.
• A borrower has to pay $100 at the end of first
and second year. At the end of third year, he
or she has to pay $100 and $1000.
• 3) Amortized loan:
Repay parts of the loan amount over time
• Borrow $5000 for 5 years. An interest rate is
9%. Annual payment happens.
• 3-1) constant principal payment
Year
Begin
Pay
Interest
paid
Principa End
l
1
5000
1450
450
1000
4000
2
4000
1360
360
1000
3000
3
3000
1270
270
1000
2000
4
2000
1180
180
1000
1000
5
1000
1090
90
1000
0
6350
1350
5000
total
3-2) Fixed payment
• 5000 = c*[1-1/(1+0.09)^5]/0.09
• C=1285.46
Year
begin
pay
interest
principal End
1
5000
1285.46
450
835.46
4164.54
2
4164.54
1285.46
374.81
910.65
3253.88
3
3253.88
1285.46
292.85
992.61
2261.27
4
2261.27
1285.46
203.51
1081.95
1179.32
5
1179.32
1285.46
106.14
1179.32
6427.30
1427.31
5000
total