Valuation Models
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Transcript of Valuation Models
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Valuation Models
BondsCommon stock
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Key Features of a Bond
Par value: face amount; paid at maturity. Assume $1,000.
Coupon interest rate: stated interest rate. Multiply by par value to get dollar interest payment. Generally fixed.
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Maturity: years until bond must be repaid. Declines over time.
Issue date: date when bond was issued.
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Value = + . . . .
How can we value assets on the basis of expected future cash flows?
CF1
(1 + k)1
CF2
(1 + k)2
CFn
(1 + k)n
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The discount rate k is the opportunity cost of capital and depends on: riskiness of cash flows. general level of interest rates.
How is the discount rate determined?
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An annuity (the coupon payments).A lump sum (the maturity, or par, value to
be received in the future).
Value = INT(PVIFAi%, n ) + M(PVIFi%, n).
The cash flows of a bond consist of:
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0 1
1001,000
Value = = $1,000.
Find the value of a 1-year 10% annual coupon bond when kd = 10%.
$1,1001.10
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0 10
1001,000
1 2
100 100
Find the value of a similar 10-year bond.
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Way to Solve
Using tables:Value = INT(PVIFA10%,10)+ M(PVIF10%,10).
= 100*6.1446 + 1000*0.3855 = 1000 (approx.)
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Rule: When the required rate of return (kd) equals the coupon rate, the bond value (or price) equals the par value.
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What would the value of thebonds be if kd = 14%?
1-year bondUsing tables:Value = INT(PVIFA14%,1)+ M(PVIF14%,1).
= 100*0.8772 + 1000*0.8772 = 964.92
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10-year bond
When kd rises above the coupon rate,bond values fall below par.They sell at a discount.
Using tables:Value = INT(PVIFA14%,10)+ M(PVIF14%,10).
= 100*5.2164 + 1000*0.2697 = 791.34
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What would the value of the bonds be if kd = 7%?
1-year bond
Using tables:Value = INT(PVIFA7%,1)+ M(PVIF7%,1).
= 100*0.9346 + 1000*0.9346 = 1028.06
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10-year bond
When kd falls below the coupon rate,bond values rise above par.They sell at a premium.
Using tables:Value = INT(PVIFA7%,10)+ M(PVIF7%,10).
= 100*7.0236 + 1000*0.5083 = 1210.66
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Value of 10% coupon bond over time:
13721211
1000
791 775
Mkd = 10%
kd = 7%
kd = 13%
30 20 10 0Years to Maturity
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Summary
If kd remains constant: At maturity, the value of any bond must
equal its par value. Over time, the value of a premium bond
will decrease to its par value. Over time, the value of a discount bond
will increase to its par value. A par value bond will stay at its par valu
e.
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Semiannual Bonds
1. Multiply years by 2 to get periods = 2n.2. Divide nominal rate by 2 to get
periodic rate = kd/2.3. Divide annual INT by 2 to get PMT
= INT/2.
INPUTSOUTPUT
2n kd/2 OK INT/2 OK N I/YR PV PMT FV
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2(10) 14/2 100/220 7 50 1000N I/YR PV PMT FV
788.10
Find the value of 10-year, 10% coupon, semiannual bond if kd = 14%.
INPUTS
OUTPUT
Using tables:Value = INT(PVIFA7%,20)+ M(PVIF7%,20).
= 50*10.5940 + 1000*0.2584 = 788.10
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0 1 2 3 . . . 8
100 100 100 . . . 100
What is the cash flow stream of aperpetual bond with an annual
coupon of $100?
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A perpetuity is a cash flow stream of equal payments at equal intervals into infinity.
Vperpetuity = .PMTk
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V10% = = $1000.
V13% = = $769.23.
V7% = = $1428.57.
$1000.10
$1000.13
$1000.07
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P0 = + + . . . . ^ D1
(1 + k)D2
(1 + k) 2
Dn
(1 + k)n
Stock value = PV of dividends
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D1 = D0(1 + g)D2 = D1(1 + g)
...
Future Dividend Stream:
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P0 = = .^ D1
ks - gD0 (1 + g)
ks - g
If growth of dividends g isconstant, then:
Model requires: ks > g (otherwise results in negative
price).g constant forever.
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D0 = 2.00 (already paid).
D1 = D0(1.06) = $2.12.
P0 = = =$21.20.
Last dividend = $2.00; g = 6%.
What is the value of Bon Temps’ stock given ks = 16%?
^ D1
ks - g$2.12
0.16 - 0.06
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P1 = D2/(ks - g) = 2.247/0.10 = $22.47.
^
What is Bon Temps’ value one year from now?
Note: Could also find P1 as follows:
P1 = P0 (1 + g) = $21.20(1.06) = $22.47.
^
^
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ks = + g
= + 0.06 = 16%.
D1
P0
$2.12$21.20
Constant growth model can berearranged to solve for return:
^
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V =
= = $13.25.
Pmtk
If a stock’s dividends are not expected to grow over time (g = 0), then it is a perpetuity.
$2.12 0.16
Zero growth
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Subnormal or Supernormal Growth
Cannot use constant growth model
Value the nonconstant & constant growth periods separately
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If we have supernormal growth of 30% for 3 years, then a long-run constant
g = 6%, what is P0?^
0 ks=16% 1 2 3 4g = 30% g = 30% g = 30% g = 6%
D0 = 2.00 2.60 3.38 4.394 4.658 2.241 2.512 2.815 P3 = = 46.5829.84237.41 = P0
4.658 0.10
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0 1 2 3 4
$2.00 $2.00 $2.00 $2.12
0% 0% 0% 6% . . .
Suppose g = 0 for 3 years, then g is constant at 6%.
n
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(1) PV 3-year, $2 annuity, 16% PV = PMT(PVIFA 16%,3)
= 2 * 2.2459 = $4.492.
(2)P3 = = $21.20.
PV(P3) = $13.58.
P0 = $4.49 + $13.58 = $18.07.
$2.120.10
What is the price, P0?