FIN 614: Financial Management
Larry Schrenk, Instructor
1. Discounted Cash Flow (DCF) Method
2. Bond Valuation
3. Bond Yields
1. Yield to Maturity (YTM)
2. Yield to Call (YTC)
3. Current Yield
Asset Value = PV(Cash Flows)
Examples:
Stock Price = PV(Dividends)
Project Value = PV(Net Annual Cash Flows)
Bond Value = PV(Cash Flows)
Two Cash Flows:
(Semi-Annual) Fixed Coupons
Par Value (at Maturity)
Bond Value
= PV(Coupons) + PV(Par Value)
Coupons are an Annuity
Par Value is One Time Payment
Formula for Bond Valuation
PVbond




C
1
Par Value


1

tm
tm
r  

r 
r 

m   1  m    1  m 


PV(Coupons)
PV(Par Value)
PVbond = Value/Price of Bond; C = Period Cash Flow; r = Discount Rate;
m = Periods per Year; t = Time
What is the present value of a four year, semiannual bond with a par value of $1,000.00
and a coupon rate of 8% if the discount rate
is 6%?
PVbond




40 
1
1,000


1

 $1,070.20
0.06   0.06  42   0.06  42
2   1  2    1  2 


What is the present value of a four year, semiannual bond with a par value of $1,000.00 and a
coupon rate of 8% if the discount rate is 6%?
N=8
(= 4 x 2)
I%=6
PV=0 ◄ Select @, then [ALPHA] [ENTER]
PMT=-40
(= (1000 x 0.08)/2)
FV=-1000
P/Y=2
C/Y=2
PMT: END BEGIN
PV = 1070.20
Note: Negatives
Discount rate such that Price = PV(cash
flows)
T
YTM s.t. 0  
t 1
T
Ct
1  YTM 
t
 Investment  
t 0
Ct
1  YTM 
t
YTM = Yield to Maturity; C t = Cash Flow in Year t
Expected return if the bond purchased at
a fair value
What is the YTM of a five year, semi-annual bond
with a par value of $1,000 and a coupon rate of
9% if the bond is selling for $990?
N=10
(= 5 x 2)
I%=0 ◄ Select @, then [ALPHA] [ENTER]
PV=-990
PMT=45
(= (1000 x 0.09)/2)
FV=1000
P/Y=2
C/Y=2
PMT: END BEGIN
PV (YTM) = 9.25%
Note: Negatives
YTM = expected return only when just
purchased.
YTM versus realized/actual yield
The yield of a bond if it is called, i.e., you
were to buy and hold the security until
the call date.
Calculation: Same as YTM except:
N = Periods to the Call Date (not Maturity)
FV = Call Price (not Par Value)
What is the YTC of a five year, semi-annual bond
with a par value of $1,000 and a coupon rate of
9% if the bond is selling for $990, the call price is
$1,100 and the call date is two years?
N=4
(= 2 x 2; N is Periods to Call)
I%=0 ◄ Select @, then [ALPHA] [ENTER]
PV=-990
PMT=45
(= (1000 x 0.09)/2)
FV=1100
(FV is Call Price)
P/Y=2
C/Y=2
PMT: END BEGIN
PV (YTM) = 14.09%
Note: Negatives
Interest payment relative to price
Current Yield = Annual Interest Payment /
Bond Price
It is not the bond’s expected return (that
is YTM).
YTM = Current Yield + Capital Gains Yield
Find the current yield for a 9% annual
coupon bond that sells for $887 and has a
par value of $1,000.
Current Yield = $90 / $887
= 0.1015 = 10.15%
FIN 614: Financial Management
Larry Schrenk, Instructor