Valuation of Long Term SecuritiesValuation of Long Term Securities (bonds and stocks)

邦保罗邦保罗

What has Mickey Mouse got to do with this?

• In february 2004 Comcast put a hostile take over bid on In february 2004 Comcast put a hostile take over bid on DisneyDisney

• Comcast offered about $ 54 billion for DisneyComcast offered about $ 54 billion for Disney• Many professionals said the bid was far too low and Many professionals said the bid was far too low and

therefore could not be successfultherefore could not be successful• Comcast claimed it offered a 10% premium for the Comcast claimed it offered a 10% premium for the

shareholdersshareholders• But since it was a share for share deal Comcast paid for But since it was a share for share deal Comcast paid for

it with its own sharesit with its own shares• After the bid Disney shares raised 10% and Comcast After the bid Disney shares raised 10% and Comcast

shares fell about 10% at that time the premium shares fell about 10% at that time the premium evaporated and Comcast actually offered a price for evaporated and Comcast actually offered a price for Disney at a discount…Disney at a discount…

• The deal did not effectuate as you imagineThe deal did not effectuate as you imagine• The board of Disney refused to accept it and the The board of Disney refused to accept it and the

shareholders of course also refused…shareholders of course also refused…• In the meantime a fight at the top was taking place In the meantime a fight at the top was taking place

between the cousin of Walt Disney and the CEO Michael between the cousin of Walt Disney and the CEO Michael Eisner…(see the picture)Eisner…(see the picture)

• Eisner won then but agreed to leave Disney per 2006 for Eisner won then but agreed to leave Disney per 2006 for early retirement…goodbye Mr. Eisner…who saved early retirement…goodbye Mr. Eisner…who saved Disney when it was about to go bankrupt…Disney when it was about to go bankrupt…

Bye bye Mr. Eisner…Bye bye Mr. Eisner…

Look at the valueline doc.

And the remainder…(you can enlarge to read or download the doc.)

Disney today…

And has Disney bonds outstanding?

Type Issue Price Coupon(%) YTM(%)

Current

Rating CallableYield(%)

Corp DISNEY WALT CO

105.99 6.75 30-Mar-06 2.602 6.369 BBB No

Corp

DISNEY WALT CO MTNS BE 104.7 5.5 29-Dec-06 3.29 5.253 BBB No

Corp

DISNEY WALT CO MTNS BE 105.39 5.375 01-Jun-07 3.235 5.1 BBB No

Corp

DISNEY WALT CO MTNS BE 111.16 6.375 01-Mar-12 4.579 5.735 BBB No

Corp

DISNEY WALT CO MTNS BE 110 6.2 20-Jun-14 4.893 5.637 BBB No

Corp

DISNEY WALT CO MTNS BE 113.98 7 01-Mar-32 5.958 6.141 BBB No

Maturity

Valuation

• Liquidation value: Sell as separated Liquidation value: Sell as separated asset from ongoing operations (low) asset from ongoing operations (low) for instance when a company is for instance when a company is bankruptbankrupt

• Book Value: Shareholders equity in Book Value: Shareholders equity in the balance sheet of a companythe balance sheet of a company

• Market Value: Share Price * number Market Value: Share Price * number of (common) shares outstandingof (common) shares outstanding

• Intrinsic Value: Long Term Free Intrinsic Value: Long Term Free Cash Flow/Cost of CapitalCash Flow/Cost of Capital

Valuation of Bonds• A Bond is a confession of debt paper A Bond is a confession of debt paper

from the government or a companyfrom the government or a company

• Each Bond has :Each Bond has :– A face value (say $ 1,000)A face value (say $ 1,000)– A Coupon rate (say 10% per year)A Coupon rate (say 10% per year)– A maturity ( for example 9 years)A maturity ( for example 9 years)– A cost of capital (return that the investor A cost of capital (return that the investor

wants for this specific paper (say 12%) wants for this specific paper (say 12%) This is called the cost of debt (Kd)This is called the cost of debt (Kd)

• Calculating the value of a bond means Calculating the value of a bond means calculating the cash flows that the bond calculating the cash flows that the bond will generate over its life and will generate over its life and discounting at 12%discounting at 12%

Put a value on mickey?

So the value is:• V=$100/(1+12%)+$100/(1+12%)^2+… V=$100/(1+12%)+$100/(1+12%)^2+…

+$100/(1+12%)^9+$1000/(1+12%)^9= $ 893.80 (discount: $ +$100/(1+12%)^9+$1000/(1+12%)^9= $ 893.80 (discount: $ 106.20)106.20)

• So an investor should pay not more then $ 893.80 to buy So an investor should pay not more then $ 893.80 to buy this bondthis bond

• The bond is sold at a discount (lower then its face value The bond is sold at a discount (lower then its face value of $ 1000)of $ 1000)

• Note that all the coupons are discounted at 12% and at Note that all the coupons are discounted at 12% and at the end of the life time the amount of the the end of the life time the amount of the ““debtdebt”” ($ 1000) ($ 1000) will be paid backwill be paid back

But if Kd= 8% instead of 12%

• V=$100/(1+8%)+$100/(1+8%)^2+… V=$100/(1+8%)+$100/(1+8%)^2+… +$100/(1+8%)^9+$1000/(1+8%)^9= $ 1124.79 (premium $ 124.79)+$100/(1+8%)^9+$1000/(1+8%)^9= $ 1124.79 (premium $ 124.79)

• The bond is sold at a premium: So now the The bond is sold at a premium: So now the bond has a value higher then its face bond has a value higher then its face value…value…

Perpetual bonds

• Perpetual means that they will give coupon Perpetual means that they will give coupon income forever…income forever…

• If the coupon is 10% and Kd=12%If the coupon is 10% and Kd=12%• The value of such a bond is:V= I/Kd with I=the The value of such a bond is:V= I/Kd with I=the

amount of the couponamount of the coupon

• Value= $100/12%= $ 833,33Value= $100/12%= $ 833,33

• Perpetuity: V= $ Coupon/Kd%Perpetuity: V= $ Coupon/Kd%

Zero coupon bond

• Some bonds do not pay a couponSome bonds do not pay a coupon• They simply mature after several yearsThey simply mature after several years• What is the value of such a bond?What is the value of such a bond?• Say Kd=12% and maturity is 10 yrs.Say Kd=12% and maturity is 10 yrs.

• Value= $1000/(1+12%)^10= $ 322Value= $1000/(1+12%)^10= $ 322• You should pay only pay $ 322 for such a bondYou should pay only pay $ 322 for such a bond

Most bonds issued in the US

• Pay coupon interest twice a year (semi annually) Pay coupon interest twice a year (semi annually) – A 10% bond with half year coupons and 12 years A 10% bond with half year coupons and 12 years

maturity with Kd=14% and a face value of $ 1000 can maturity with Kd=14% and a face value of $ 1000 can be valued at:be valued at:

– V=$50/(1+ 14%/2)^1 +50/(1+14%/2)^2+…..+……. +V=$50/(1+ 14%/2)^1 +50/(1+14%/2)^2+…..+……. +$50/(1+14%/2)^24+$1000/(1+14%/2)^24= $ 770,45$50/(1+14%/2)^24+$1000/(1+14%/2)^24= $ 770,45

Note that a bond valuation is…

• Vb= C1/(1+i)+ …..+Cn/(1+i)^n+P/(1+i)^n• Vb= Coupon*Annuity (i,n) + Principal/(1+i)^n

Annuity(i,n)= (1- 1/(1+i)^n)/I (see the Primer on Time Value of Money)• Thus for 30 year bond with 60 coupon payments of $25 and

i=3% per half year:• Vb=$25*(1-1/(1+3%)^60)/3% + $1000/(1.03)^60

• Growing Annuity(i,g,n)= $A*(1+g)*(1-((1+g)^n/(1+i)^n))/(i-g)

Inverse relationship

How to use Excel…

Change in Bond Price as a Function of YTM…interest rate risk for investors in Bonds

We can observe:• Bond prices and yields are inversely related

• An increase in a bond’s yield to maturity results in a smaller bond price change than a decrease in yield (of equal magnitude)

• Prices of Long Term bonds tend to be more sensitive to interest rate changes than Prices of short term bonds (compare bond A and B)

• The sensitivity of bond prices to changes in yields increases at a decreasing rate as maturity increases (compare bond A and B)

• Interest rate risk is inversely related to a bond’s coupon rate (low coupon bond prices are more sensitive for interest rate changes)

Preferred stock valuation

• Preferred stock offers preferred dividendPreferred stock offers preferred dividend• A perpetual stream of fixed dividends A perpetual stream of fixed dividends

will make the valuation look like a will make the valuation look like a perpetual bond:perpetual bond:

• Value= Dp (yearly amount of Value= Dp (yearly amount of dividends)/Kp ( the return the investor dividends)/Kp ( the return the investor wants on this preferred stock)wants on this preferred stock)

• So if the dividend is $ 9 per share of So if the dividend is $ 9 per share of $1000 and Kp= 14% then Value per $1000 and Kp= 14% then Value per preferred share= Dp/Kp=$9/14%=$ preferred share= Dp/Kp=$9/14%=$ 64,2964,29

• Note this is a Perpetuity!Note this is a Perpetuity!

The most important valuation is the one for common stock

• If a share will be hold forever the value is the If a share will be hold forever the value is the DCF of all future dividendsDCF of all future dividends

• Assumed that the yearly dividends are the Assumed that the yearly dividends are the same and that Ke= the return that an investor same and that Ke= the return that an investor wants on these common shares:wants on these common shares:

• Value per share= D1/(1+Ke)+D2/(1+Ke)^2…Value per share= D1/(1+Ke)+D2/(1+Ke)^2…+Dn/(1+Ke)^n+Dn/(1+Ke)^n

• So if D1=D2=D3=…=Dn= $10So if D1=D2=D3=…=Dn= $10• And Ke is 10% Value/share= $10/10%=$ 100And Ke is 10% Value/share= $10/10%=$ 100• However most likely Di is different …so this However most likely Di is different …so this

becomes a growing Perpetuitybecomes a growing Perpetuity

But in reality

• Companies pay different Companies pay different dividends every yeardividends every year

• Shareholders hold shares for Shareholders hold shares for a short time (not forever)a short time (not forever)– In this case value/share is In this case value/share is

(assume the shareholder hold (assume the shareholder hold the shares 2 years :the shares 2 years :

– Value/share=D1/(1+Ke)+D2/Value/share=D1/(1+Ke)+D2/(1+Ke)^2+ P2/(1+Ke)^2 where (1+Ke)^2+ P2/(1+Ke)^2 where P2= the value of the share at P2= the value of the share at the end of the second yearthe end of the second year

Be bullish!

Dividend constant growth• If dividend grows every year by If dividend grows every year by

a certain % then D2=D1(1+g%) a certain % then D2=D1(1+g%) where g% is the growth where g% is the growth percentage and D1=D0(1+g%)percentage and D1=D0(1+g%)

• Now Now value/share=D0(1+g%)/(1+ke%)value/share=D0(1+g%)/(1+ke%)+D0(1+g%)^2/(1+Ke%)^2+…+D0(1+g%)^2/(1+Ke%)^2+…+Dn(1+g%)^n/(1+Ke)^n+Dn(1+g%)^n/(1+Ke)^n

• This can be simplified to: This can be simplified to: • Value/share=D1/(Ke%-g%) Value/share=D1/(Ke%-g%)

proof!proof!• Note: assume Ke%>g% and Note: assume Ke%>g% and

D0(1+g)^n/(1+Ke)^n converges D0(1+g)^n/(1+Ke)^n converges to 0 (nil) for this reasonto 0 (nil) for this reason

• This is a growing Perpetuity:This is a growing Perpetuity:Bear market?

How to…dividend growth model

• Vs(ultimo 2011)= D12/(1+ks)+D13/(1+ks)^2…+D15/(1+ks)^4+P/(1+ks)^4

• If the first 4 dividends/annum are estimated (D12-D15): D(2012)=$$0.32; D(2013)=$0.41; D(2014)=$$0.50 and D(2015)=$ 0.60

• Ks= 11% and growth rate%=9.375%.

• Note that : D15/(1+ks)^4+P/(1+ks)4=(D15+P)/(1+ks)^4

• With P= D15(1+g)/(ks-g)• So do not forget to after you calculate P take the present value of P since P is

the “Price” of the cash flows after 2015 calculated at the end of 2015…and we calculate value per 1st january 2012…so discount at (1+ks)^4

• The Price in 2015 follows from: P(2015)= D(2015)*(1+g)/(11%-g%) P(2015)= $0.60*(1.09375)/(11%-9.375%)= $40.38

• From the equation under a) it follows: V(2011)= $0.32/1.11+$0.41/(1.11)^2+$0.50/(1.11)^3+$0.60+$40.38(from a)/(1.11)^4= $ 27.98

Assignment Dividend Model• Go to Yahoo FinanceGo to Yahoo Finance• Find out if your teamFind out if your team’’s company pays s company pays

dividend and how much per sharedividend and how much per share• What are the earnings per share (latest What are the earnings per share (latest

figures)figures)• What is the pay out ratio (dividends per What is the pay out ratio (dividends per

share/earnings per share) share/earnings per share) • Find out how much dividend the company Find out how much dividend the company

has paid in the past per sharehas paid in the past per share• Find g% (the dividend growth)Find g% (the dividend growth)• Assume the Cost of equity as dcfAssume the Cost of equity as dcf• Use the dividend growth model to Use the dividend growth model to

calculate the value per share and compare calculate the value per share and compare it with todayit with today’’s share price of your s share price of your companycompany

• Does the share market values your Does the share market values your company shares higher or lower then the company shares higher or lower then the dividend growth model?dividend growth model?

• Why do you think this is the case?Why do you think this is the case?

Earnings Multiplier approach• If b= the retention rate (% of earnings that If b= the retention rate (% of earnings that

the company wants to retain i.e. does not the company wants to retain i.e. does not want to pay out as dividends)want to pay out as dividends)

• Then (1-b)= the pay out ratio (% the Then (1-b)= the pay out ratio (% the company will pay out in dividends)company will pay out in dividends)

• Assume: (1-b)=D1/E1 D1= expected Assume: (1-b)=D1/E1 D1= expected dividend per share of period 1 and dividend per share of period 1 and E1=expected earnings per share of period 1E1=expected earnings per share of period 1

• Rewrite: D1=(1-b)*E1Rewrite: D1=(1-b)*E1• Then if: Value/share=D1/(Ke%-g%) Then if: Value/share=D1/(Ke%-g%)

substitute D1=(1-b)*E1substitute D1=(1-b)*E1• And Value/Share V= (1-b)*E1/(Ke%-g%)And Value/Share V= (1-b)*E1/(Ke%-g%)• And V/E1 (earnings multiplier) or P/E= (1-And V/E1 (earnings multiplier) or P/E= (1-

b)/(Ke%-g%)b)/(Ke%-g%)• Say the retention rate is 40% g%=6% and Say the retention rate is 40% g%=6% and

Ke%=14% and E1=$ 6.67 then the Ke%=14% and E1=$ 6.67 then the value/share is: V=0.60*$6.67/(14%-6%)= $ 50value/share is: V=0.60*$6.67/(14%-6%)= $ 50

• Earnings Multiplier=(1-40%)/(14%-6%)= 7.5 Earnings Multiplier=(1-40%)/(14%-6%)= 7.5 timestimes

• Value/share=Expected Value/share=Expected earnings/share*Earnings Multiplier (PE earnings/share*Earnings Multiplier (PE ration)= $ 6.67*7.5= $ 50ration)= $ 6.67*7.5= $ 50

Stock market talk…

Rate of Return (yield)

• The Yield to Maturity (YTM) for bonds The Yield to Maturity (YTM) for bonds is:is:

• Say you know todaySay you know today’’s price of a bonds price of a bond• You know also the coupon rate and You know also the coupon rate and

how many times the coupon will pay how many times the coupon will pay per yearper year

• But you would like to calculate at But you would like to calculate at which Kd (yield) the present value of which Kd (yield) the present value of all coupons and the $ 1000 at maturity all coupons and the $ 1000 at maturity will result in todays price; this Kd is will result in todays price; this Kd is the the ““Yield Yield ““

Illustration

• A Bond can be bought today A Bond can be bought today for $ 761for $ 761

• The coupon is $80 (8%) per The coupon is $80 (8%) per yearyear

• Maturity is 12 yearsMaturity is 12 years• So we want to find Kd in:So we want to find Kd in:• $761=$80/(1+Kd)^1+$80/$761=$80/(1+Kd)^1+$80/

(1+Kd)^2+…+$80/(1+Kd)^12(1+Kd)^2+…+$80/(1+Kd)^12• We can find it with trial and We can find it with trial and

error or with the IRR% error or with the IRR% function in Excel…(treat $761 function in Excel…(treat $761 as initial cash out)as initial cash out)

• Kd=11.828%Kd=11.828%

Jump!

Assignment: Value Debt

• Estimate the Market Value of Estimate the Market Value of Debt of your companyDebt of your company

• Select Debt from the last Select Debt from the last Balance sheetBalance sheet

• Value each component:Value each component:• Bonds (quotation)Bonds (quotation)• Other debt “intrinsic value”Other debt “intrinsic value”• Refine the WACC% of your Refine the WACC% of your

company based on your company based on your findingsfindings

Climb!

End of chapter

So where are you with your assignments?