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NPV Profiles for Growth, Maintain, and Difference Strategies
-100000
0
100000
200000
300000
400000
500000
600000
700000
0.00 0.05 0.10 0.15 0.20 0.25
Discount Rates
Ne
t P
rese
nt
Valu
es
Maintain
Growth
Du Pont Titanium Dioxide - Sensitivity Analysis
Variable (% of Projection) NPV (10%) Maintain NPV (10%)Growth
Base Case (100%) 62,458 140,037
Costs (140%) -616 10,217
Sales Price (75% ) -1 7,769
Market Share (87%) -1,417 61,554
NWC Recovery (0%) 49,965 108,994
Plant Recovery (0%) 36,702 80,573
NWC & Plant (0%) 24,209 49,530
NWC & Plant (0%) andCost of Capital (150%, or 15%/10%)
5,540 5,686
Antitrust Concerns?
• Herfindahl-Hirshman Index (HHI)
– The sum of the squared market shares of firms in the industry
• Department of Justice (DOJ) 1984 merger guidelines
– Range of HHI Category Challenge Change
Less than 1,000 Low NA
1,000 to 1,800 Moderate 100
Greater than 1,800 High 50
• Unfair Competition?
Du Pont’s Strategy
• Build Capacity to deter Competition
• Price Titanium Dioxide to Capture the Market
• Restrict Licenses of its Ilmenite Process
Bond and Stock Valuation
• The market value of the firm is the present value of the cash flows generated by the firm’s assets:
• The cash flows generated by the firm’s assets are divided among the investors who pay for the assets. If these investors include only debt and equity holders, the market value of the firm can be expressed as:
PVfirm = PVdebt+ PVStock
N
tt
t
rCF
PV0 )1(
Bond (Debt) Valuation
• The price of bonds in the market place is the present value of the cash flows that bondholders have claim to:
• These cash flows consist generally of two components, interest and principal. They are generally divided as follows:
• That is, interest is paid every period, and the principal is paid at maturity, when the bond comes due.
N
tt
d
tdd r
CFPV
1
,
)1(
Nd
N
tt
dd r
P
r
IPV
)1()1(1
Bond Valuation (Continued)
Terms:– Coupon Payment: the interest paid annually, or semiannually (I).
Typically, these payments are fixed so that the interest paid each year is the same.
– Principal: the amount borrowed, and repaid at maturity (P). – Coupon Rate: the annual interest payment divided by the
principle (I/P)– Current Yield: the annual interest payment divided by the price
(I/PV)– Capital Gains Yield: the change in price (over one year) divided
by the price at the beginning of the year [(PV1-PV0)/ PV0]– Yield to Maturity: the return investors expect if they buy the
bond and hold it until it matures. If the market is in equilibrium, the yield to maturity is also the return investors require given the bond’s risk (rd).
Bond Valuation (Continued)
• Numerical Example: Suppose a bond with 10 years to maturity has a coupon rate of 10%, a principal amount of $1,000, and a yield-to-maturity of 10%. Assuming interest is paid annually and the bond is in equilibrium,– What is the price of the bond?
– What is its current yield?
• Current Yield = I/PV =
– What is its expected capital gains yield?
• Capital Gains Yield = [(PV1-PV0)/ PV0] =
?)10.1(
000,1
)10.1(
10010
10
1
ttdPV
Bond Valuation (Continued)
• Suppose now that everything else remains constant, but the yield to maturity is 12%. What are the price, the current yield, and the expected capital gains yield?
Current Yield = I/PV =
Capital Gains Yield = [(PV1-PV0)/ PV0] =
• What would cause the yield to maturity to be 12% instead of 10%?
?)12.1(
000,1
)12.1(
10010
10
1
ttdPV
Bond Valuation (Continued)
• The yield to maturity, the return investors expect, is linked to the return investors require, rd.
• The required return, rd , is a function of– The real rate of return - the return investors require for deferring
consumption (that is, the time value of money)– The expected rate of inflation - the compensation investors require to guard
against losses in their purchasing power.– The risk premium - the compensation investors require to accept the
possibility that their return will be lower than what they were promised.
• If rd is 12%, not 10%, one or more of the three components of the required rate of return must be higher in the second instance than in the first.
• Why is yield to maturity linked to rd?
Bond Valuation (Continued)
• Suppose the expected rate of return does not equal the required rate of return. If the bond above should be priced at $887 because the required rate of return is 12%, but it is priced at $1,000 to give an expected return of 10%, investors are not being compensated for the risk that they bear. – The NPV from buying the bond will be negative (887-1,000), so new
investors will not buy.
– The NPV from selling the bond will be positive (1,000-887), so existing investors will want to sell.
– The combination of new investors not buying and existing investors wanting to sell will cause the price of the bond to fall.
– How far? Why?
Bond Valuation (Continued)
Risk Return Relationship
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
20.00%
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Risk
Re
turn
Bond Valuation (Continued)Sensitivity of Bond Prices to Changing Interest Rates
0.00
50.00
100.00
150.00
200.00
250.00
300.00
4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00%
Yield to Maturity
Pric
e of
Bon
d R
elat
ive
to $
100
Beg
inni
ng P
oint
Bond Valuation (Continued)
0
200
400
600
800
1000
1200
Bas
is P
oint
Spr
eads
Aa2/AA A2/A Baa2/BBB Ba2/BB B2/B
S1
S4
S7
Ratings
Years to Maturity
Spreads Between Corporate and Government Bonds
Stock Valuation
• The price of stocks in the market place is the present value of the cash flows that stockholders have claim to:
• These cash flows consist generally of two components, dividends and capital gains. They are generally divided as follows:
N
tt
s
tss r
CFPV
1
,
)1(
Ns
NsN
tt
s
ts r
PV
r
DivPV
)1()1(,
10,
Stock Valuation (Continued)
• What are the differences between bond and stock cash flows?– Interest vs Dividends
• Interest is paid before dividends.
• Interest is generally fixed ; dividends are variable.
• Interest is a contractual obligation; dividends are discretionary.
– Principal vs. Future Stock Prices • Principal is contractually binding to the firm; future stock prices are not.
• In liquidation, claims to both principle and interest must be satisfied before payments can be made to stockholders
• What do these differences imply about potential differences between rs
and rd?
Stock Valuation (Continued)
Risk Return Relationship
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
20.00%
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Risk
Re
turn
Stock Valuation (Continued)
• If, for simplicity, we assume that dividends grow forever at a constant rate, g, and that that rate is lower than the required rate of return on the stock, rs, then the present value of the dividends and future stock price can be expressed as
• This says that the price of the stock today equals the expected dividend one year from today (Div1) divided by the difference between the required rate of return and the constant growth rate (rs-g)
• Under these same assumptions, the required return on the stock could be estimated as
gr
DivPV
ss
10,
gPV
Divr
ss
0,
1
Stock Valuation (Continued)
• Suppose the expected dividend next period (D1) is $1.50, the expected constant growth rate (g) is 8%, and the required return (rs)on the stock is 15%. What is the price of the stock today
– P0 = D1/(rs-g) = $1.50/(.15-.08) = $21.43
• What are the expected current (or dividend) yield and capital gains yield?
– Current Yield = D1/P0 = $1.50/$21.43 = .07 or 7%
– Capital Gains Yield = ?
• How does the stock price relate to the NPV of projects undertaken by the firm?
Stock Valuation (Continued)
• How does the stock price relate to capital budgeting decisions of the firm? The NPV of projects undertaken by firms is reflected in stock prices as follows
• The first component, EPS1/rs, is the price of the stock if equity cash flows (or earnings) remain constant forever. The second component is the expected NPV from future growth opportunities.
• What determines whether NPVGO is positive or negative?
NPVGOr
EPSPV
ss 1
0,
Stock Valuation (Continued)
• By setting the two stock pricing relationships equal to each other and recognizing that (Div1/EPS1) equals 1-b, where b is the firm’s retention ratio, and g is the ROE*b, we can express NPVGO as
• The above relationship tells us that NPVGO will be positive so long as the ROE on the investment exceeds the required rate of return,rs
)(*
)(*1 grr
rROEbEPSNPVGO
ss
s
Stock Valuation (Continued)
AssumptionsROE 20.00%Retention Ratio 40.00%Payout Ratio 60.00%Required Return 15.00%Growth 8.00%Expected Earnings without Investment 2.50$
Time 0 1 2 3 4 5 6 …. ….Earnings with No New Investment 2.50$ 2.50$ 2.50$ 2.50$ 2.50$ 2.50$ 2.50$ 2.50$ Present Value of Earnings 16.67$
Amount Retained (1.00)$ Additional Earnings from Investment 0.20$ 0.20$ 0.20$ 0.20$ 0.20$ 0.20$ 0.20$ PV of Additional Earnings 1.33$ NPV of Additional Earnings 0.29$
Total Earnings 2.50$ 2.70$ 2.70$ 2.70$ 2.70$ 2.70$ 2.70$ 2.70$ Amount Retained (1.08)$ Additional Earnings from Investment 0.22$ 0.22$ 0.22$ 0.22$ 0.22$ 0.22$ PV of Additional Earnings 1.44$ NPV of Additional Earnings 0.27$
Total Earnings 2.50$ 2.70$ 2.92$ 2.92$ 2.92$ 2.92$ 2.92$ 2.92$ Amount Retained (1.17)$ Additional Earnings from Investment 0.23$ 0.23$ 0.23$ 0.23$ 0.23$ PV of Additional Earnings 1.56$ NPV of Additional Earnings 0.26$
Stock Valuation (Continued)
• What would happen if the firm could make these investments indefinitely by retaining 40% of its earnings and producing ROEs of 20%?
• What would the price of the stock be?
• EPS1/rs + NPVGO = $2.5/.15 + $4.76 = $21.43
76.4$)08.15(.*15.
)15.20(.*4.*50.2$
)(*
)(*1
grr
rROEbEPSNPVGO
ss
s
• How does that coincide with the earlier model
• How does the model we have just discussed relate to EVA, if it does?