Finance Review
Essay by ferger65 • April 18, 2016 • Study Guide • 3,678 Words (15 Pages) • 1,061 Views
Final Review Class
Foundations of Finance
Overview
- For first half of semester, see review class recording online
- Today:
- Go through key points of second part of course
- Not exhaustive
- Do a few sample questions
- Answer any questions you may have.
Outline
- Balance sheet valuation concepts
- Backward looking, easy to manipulate
Fundamental value / intrinsic value
Dividend Discount Model (DDM)
- Zero dividend growth
- Constant dividend growth
• = Gordon Growth Model
- Valuation ratios
- Two-stage dividend growth
3
DDM Case 2: constant dividend growth
Gordon’s Growth Model (GGM)
- Suppose that expected dividends grow at a rate g, that is,
E(D1 ) =(1+g)D0, E(D2 ) =(1+g)2D0, etc.
- Use the Dividend-Discount Model:
V0 =
E(D1 ) +
1+ R[pic 1]
E(D2 )
(1+ R)2[pic 2]
+ E(D3 )
(1+ R)3[pic 3]
2[pic 4]
+ ...
3
= D0 (1+ g) +[pic 5]
D0 (1+ g)
+ D0 (1+ g)
+...
1+ R[pic 6]
(1+ R)2
(1+ R)3
= D0 (1+ g) =[pic 7][pic 8]
E(D1 )
R − g
R − g
Assumption: R > G
4
Using GGM to study Valuation Ratios
- Price-dividend ratio. If GGM applies then:
P0 = 1+ g [pic 9][pic 10]
D0
- Price-earnings ratio.
R − g
- How much do you have to pay for every dollar of earnings generated?
- How do we go between dividends and earnings?
- D0=(1-b)E0 with “earnings retention ratio” – “plowback ratio”of b.
- Inverse of the “dividend payout ratio”
P0 = (1+ g)(1−b)[pic 11]
E0 R− g
5
Other things discussed
How to go from stock prices to implied expected growth rate.
- Microsoft vs. Apple exercise in class
- Twitter IPO example
- When should firms pay out dividends?
- Apple dividend battle
- Bond Pricing
Fixed Income
- Forward Rate / Yield Curve
- Duration/Immunization
Yield to Maturity (YTM) on Annual-
Pay Coupon Bonds
-Po c c………F + c[pic 12]
- Multiple payment security
0 1 2 T
- For an annual-pay coupon bond, the YTM is
calculated as the Internal Rate of Return.
- Hence, YTM is the rate that solves:
[pic 13]
8
Yield to Maturity on
Semi-Annual-Pay Coupon Bonds
For a semi-annual-pay coupon bond, the
YTM is computed in 2 steps:
- Find the semi-annual IRR, that is, the rate r
that solves:
P0
= ∑ _ Ct
- _ FT
t =1[pic 14]
(1+
r)t
(1+
r)T
- The YTM is the corresponding annual percentage rate (APR): YTM = 2 r
- The corresponding effective annual yield
is (1+YTM /2 )2 –1
9
Example: YTM on a
Semi-Annual-Pay Coupon Bond
- Suppose that a 3-year bond has a face value of 1000 and pays semi-annual coupons of 40. If the price is 900 then what is the YTM?[pic 15][pic 16][pic 17][pic 18][pic 19][pic 20][pic 21]
-900 | 40 | 40 | 40 | 40 | 40 | 1040 |
t=0 | t=1 | t=2 | t=3 |
- Step 1 use calculator to find that r = 6.036% solves:
900 =
_ 40
(1+ r )1
+... +
_ 40
(1+ r )5
+ 1040
(1+ r )6
• Step 2: YTM = 2r = 12.072%
...
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