Test Two
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Time value of money
o
Valuation requires the use of TVM operations
Compounding
Discounting
o
Future value: what a given amount of money in the present period is worth
as a specified time in the future
Pn = Po (1+r)^n
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N – number of periods
•
Pn – future value n periods from now
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Po – original price
•
R – int rate per period
If interest is paid semiannually
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Both the interest rate and the number of periods used to
compute the future value must be adjusted
o
R = annual int rate/number of times int is paid per
year
o
N = number of times int is paid per year * number
of years
o
Annuity – when the same amount of money is invested periodically
Ordinary annuity – when the first investment occurs one period
from now
Annuity due – when the first investment is immediate
Future value of an annuity – one way of calculating this would be
to find the future value of each investment at the end of the
investment horizon and then add these future values
•
Pn = A[((1+r)^n – 1)/r]
o
A – amount of annuity
o
N – number of periods
o
R – int rate per period
o
Discounting
The appropriate discount rate is the rate at which the money, in
hand now, could be invested in order to produce the desired future
value at a later date
The “opportunity cost” rate, or the rate of return that you could
earn on an alternative investment of similar risk
PV = Pn [1/(1+r)^n]
Present value of an ordinary annuity
•
PV = A [(1 – {1/(1+r)^n})/r]
o
Pricing financial instruments
Price of any financial instrument is equal to the PV of the expected
CF’s
Determining the price requires…

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An estimate of the expected CF’s
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An estimate of the required yield
Pricing a zero coupon bond
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Zero coupon bonds do not make any periodic coupon
payments, so the price is determined as follows…
o
P = M/(1+r)^n
R = ½ the annual yield
N = 2x the number of years
In pricing bonds that pay semi-annual coupons, we assume that…
when might these be violated???
•
The next coupon is exactly six months away
o
Purchased bond in the secondary market with first
coupon coming less than 6 months from now
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The cash flows are known
o
Callable bonds – continuation of cash flows will
depend on the level of current int rates relative to
the coupon rate
o
Floating rate bonds – coupon rate is equal to a
reference rate + quoted margin
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The appropriate required yield can be determined
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One rate is used to discount all cash flows
o
Accrued Interest
Coupon interest earned from the time of the last coupon payment
until the settlement date of the bond
Computation of accrued interest
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Treasury coupon security – based on actual number of days
the bond is held
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Corporate and municipal bond – based on 360 day year,
with each month having 30 days
Clean price – w/o accrued interest
Dirty price – w/ accrued interest
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Measuring Yield
o
Internal rate of return

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