Introduction to Financial Management FIN 102 – 8 th Week of Class Professor Andrew L. H. Parkes “A practical and hands on course on the valuation and financial management of corporations”

Valuation of Long Term Securities Chapter 4: Financial Management Fall 2007 Shanghai 卜安吉

Intro. to Financial Managment - 9th Week of Class3 Valuation Liquidation value: Sell as separated asset from ongoing operations (low) Liquidation value: Sell as separated asset from ongoing operations (low) Book Value: Shareholders equity in the balance sheet of a company Book Value: Shareholders equity in the balance sheet of a company Market Value: Share Price * number of (common) shares outstanding Market Value: Share Price * number of (common) shares outstanding Intrinsic Value: Long Term Free Cash Flow/Cost of Capital Intrinsic Value: Long Term Free Cash Flow/Cost of Capital

Intro. to Financial Managment - 9th Week of Class4 Valuation of Bonds A Bond is a confession of debt paper from the government or a company A Bond is a confession of debt paper from the government or a company Each Bond has 4 points: Each Bond has 4 points: –A face value (1,000) –A Coupon rate (say 10% per year) –A maturity ( for example 9 years) –A cost of capital [return that the investor wants for this specific paper (say 12%)]. This is called the cost of debt (K d ) Calculating the value of a bond means calculating the cash flows that the bond will generate over its life and discounting at 12%. Calculating the value of a bond means calculating the cash flows that the bond will generate over its life and discounting at 12%. Put a value on mickey?

Intro. to Financial Managment - 9th Week of Class5 So the value is: V=$100/(1+12%)+$100/(1+12%)^2+ … +$100/(1+12%)^9+$1000/(1+12%)^9= $ V=$100/(1+12%)+$100/(1+12%)^2+ … +$100/(1+12%)^9+$1000/(1+12%)^9= $ So an investor would not pay more than $ to buy this bond. So an investor would not pay more than $ to buy this bond. The bond is sold at a discount (lower than its face value of $ 1000). The bond is sold at a discount (lower than its face value of $ 1000). Note that all the coupon payments are discounted at 12% and at the end of the life time the amount of the debt or “ face value ” (of $ 1000) will be paid back. Note that all the coupon payments are discounted at 12% and at the end of the life time the amount of the debt or “ face value ” (of $ 1000) will be paid back. Thanks!

Intro. to Financial Managment - 9th Week of Class6 But if K d = 8% instead of 12% V=$100/(1+8%)+$100/(1+8%)^2+ … +$100/(1+8%)^9+$1000/(1+8%)^9 = $ V=$100/(1+8%)+$100/(1+8%)^2+ … +$100/(1+8%)^9+$1000/(1+8%)^9 = $ The bond is sold at a premium: So now the bond has a value higher than its face value … The bond is sold at a premium: So now the bond has a value higher than its face value … Donald’s Uncle

Intro. to Financial Managment - 9th Week of Class7 “When will this bond sell at face value (at par)?” If the coupon rate offered by the issuer of the bond (10%) is equal to the return (K d ) the investor demands; so if K d =10%. If the coupon rate offered by the issuer of the bond (10%) is equal to the return (K d ) the investor demands; so if K d =10%. The return offered (coupon rate) is equal to the required K d so the investor is willing to pay the full amount of $ The return offered (coupon rate) is equal to the required K d so the investor is willing to pay the full amount of $ 1000.

Intro. to Financial Managment - 9th Week of Class8 Perpetual bonds Perpetual means that they will give coupon income forever … Perpetual means that they will give coupon income forever … If the coupon is 10% and K d =12% If the coupon is 10% and K d =12% The value of such a bond is: V= I/K d with I=the amount of the coupon The value of such a bond is: V= I/K d with I=the amount of the coupon Value= $100/12%= $ Value= $100/12%= $ Investor: Have lunch or be lunch!

Intro. to Financial Managment - 9th Week of Class9 Zero coupon bond Some bonds do not pay a coupon Some bonds do not pay a coupon They simply mature after several years. They simply mature after several years. What is the value of such a bond? What is the value of such a bond? Say K d =12% and maturity is 10 yrs. Say K d =12% and maturity is 10 yrs. Value= $1000/(1+12%)^10= $ 322 Value= $1000/(1+12%)^10= $ 322 You should pay only pay $ 322 for such a bond. You should pay only pay $ 322 for such a bond. Zero Coupon Bond ?

Intro. to Financial Managment - 9th Week of Class10 Most bonds issued in the U.S. 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 maturity with K d =14% and a face value of $ 1000 can be valued at: –V=$50/(1+ 14%/2)^1 +50/(1+14%/2)^2+ …..+ ……. +$50/(1+14%/2)^24+$1000/( 1+14%/2)^24= $ Demo; 2 coupons per year!

Intro. to Financial Managment - 9th Week of Class11 Preferred stock valuation Preferred stock offers preferred dividend. Preferred stock offers preferred dividend. A perpetual stream of fixed dividends will make the valuation look like a perp[etual bond: A perpetual stream of fixed dividends will make the valuation look like a perp[etual bond: Value= D p (yearly amount of dividends)/K p ( the return the investor wants on this preferred stock). Value= D p (yearly amount of dividends)/K p ( the return the investor wants on this preferred stock). So if the dividend is $ 9 per share of $1000 and K p = 14% then Value per preferred share= D p /K p =$9/14%=$ So if the dividend is $ 9 per share of $1000 and K p = 14% then Value per preferred share= D p /K p =$9/14%=$ 64.29

Intro. to Financial Managment - 9th Week of Class12 The most important valuation is the one for common stock If a share will be held forever the value is the DCF of all future dividends. If a share will be held forever the value is the DCF of all future dividends. Assumed that the yearly dividends are the same and that K e = the return that an investor wants on these common shares: Assumed that the yearly dividends are the same and that K e = the return that an investor wants on these common shares: Value per share= D 1 /(1+K e )+D 2 /(1+K e )^2 … +D n /(1+K e )^n Value per share= D 1 /(1+K e )+D 2 /(1+K e )^2 … +D n /(1+K e )^n So if D 1 =D 2 =D 3 = … =D n = $10 So if D 1 =D 2 =D 3 = … =D n = $10 And K e is 10% Value/share= $10/10%=$ 100 And K e is 10% Value/share= $10/10%=$ 100

Intro. to Financial Managment - 9th Week of Class13 But in reality Companies pay different dividends every year Companies pay different dividends every year Shareholders hold shares for a short time (not forever) Shareholders hold shares for a short time (not forever) –In this case “ value/share ” is (assume the shareholder hold the shares 2 years : –Value/share=D 1 /(1+K e )+D 2 /(1+ K e )^2+ P 2 /(1+K e )^2 where P 2 is the value of the share at the end of the second year Be bullish!

Intro. to Financial Managment - 9th Week of Class14 Dividend constant growth If dividend grows every year by a certain % then D 2 =D 1 (1+g%) If dividend grows every year by a certain % then D 2 =D 1 (1+g%) where g% is the growth percentage and D 1 =D 0 (1+g%) Now value/share=D 0 (1+g%)/(1+k e %) Now value/share=D 0 (1+g%)/(1+k e %) +D 0 (1+g%)^2/(1+K e %)^2+ … + D n (1+g%)^n/(1+K e )^n D n (1+g%)^n/(1+K e )^n This can be simplified to: This can be simplified to: Value/share=D 1 /(K e %-g%) proof! Note: assume K e %>g% and Note: assume K e %>g% and D 0 (1+g)^n/(1+K e )^n converges to 0 (nil) for this reason Bear market?

Intro. to Financial Managment - 9th Week of Class15 Homework assignment Go to Yahoo Finance Go to Yahoo Finance Find out if your team’s company pays dividend and how much per share Find out if your team’s company pays dividend and how much per share What are the earnings per share (latest figures) What are the earnings per share (latest figures) What is the pay out ratio (dividends per share/earnings per share) What is the pay out ratio (dividends per share/earnings per share) Find out how much dividend the company has paid in the past per share Find out how much dividend the company has paid in the past per share Find g% (the dividend growth) Find g% (the dividend growth) Assume that K e =10% Assume that K e =10% Use the dividend growth model to calculate the value per share and compare it with today’s share price of your company. Use the dividend growth model to calculate the value per share and compare it with today’s share price of your company. Does the share market values your company shares higher or lower then the dividend growth model? Does the share market values your company shares higher or lower then the dividend growth model? Why do you think this is the case? Why do you think this is the case?

Intro. to Financial Managment - 9th Week of Class16 Earnings Multiplier approach If b= the retention rate (% of earnings that the company wants to retain i.e. does not want to pay out as dividends). If b= the retention rate (% of earnings that the company wants to retain i.e. does not want to pay out as dividends). Then (1-b)= the payout ratio (% the company will pay out in dividends). Then (1-b)= the payout ratio (% the company will pay out in dividends). Assume: (1-b)=D 1 /E 1 D 1 = expected dividend per share of period 1 and E 1 =expected earnings per share of period 1. Assume: (1-b)=D 1 /E 1 D 1 = expected dividend per share of period 1 and E 1 =expected earnings per share of period 1. Rewrite: D 1 =(1-b)*E 1 Rewrite: D 1 =(1-b)*E 1 Then if: Value/share=D 1 /(K e %- g%) substitute D 1 =(1-b)*E 1 Then if: Value/share=D 1 /(K e %- g%) substitute D 1 =(1-b)*E 1 Stock market talk…

Intro. to Financial Managment - 9th Week of Class17 Earnings Multiplier approach Continued And Value/Share V= (1- b)*E 1 /(K e %-g%) And Value/Share V= (1- b)*E 1 /(K e %-g%) So V/E 1 (earnings multiplier) or So V/E 1 (earnings multiplier) or P/E= (1-b)/(K e %-g%) Say the retention rate is 40% g%=6% and K e %=14% and E 1 =$ 6.67 then the value/share is: V=0.60*$6.67/(14%-6%)= $ 50 Say the retention rate is 40% g%=6% and K e %=14% and E 1 =$ 6.67 then the value/share is: V=0.60*$6.67/(14%-6%)= $ 50 Earnings Multiplier = (1- 40%)/(14%-6%)= 7.5 times Earnings Multiplier = (1- 40%)/(14%-6%)= 7.5 times Value/share=Expected earnings/share*Earnings Multiplier (PE ratio)= $ 6.67*7.5= $ 50 Value/share=Expected earnings/share*Earnings Multiplier (PE ratio)= $ 6.67*7.5= $ 50 Stock market talk…

Intro. to Financial Managment - 9th Week of Class18 Rate of Return (yield) The Yield to Maturity (YTM) for bonds is: The Yield to Maturity (YTM) for bonds is: Say you know today’s price of a bond, Say you know today’s price of a bond, You know also the coupon rate and how many times the coupon will pay per year, You know also the coupon rate and how many times the coupon will pay per year, But you would like to calculate at which K d (the yield). The present value of all coupons and the $ 1000 face value at maturity will result in today’s price; this K d is the “Yield” or YTM. But you would like to calculate at which K d (the yield). The present value of all coupons and the $ 1000 face value at maturity will result in today’s price; this K d is the “Yield” or YTM.

Intro. to Financial Managment - 9th Week of Class19 Illustration A Bond can be bought today for $ 761. A Bond can be bought today for $ 761. The coupon is $80 (8%) per year. The coupon is $80 (8%) per year. Maturity is 12 years. Maturity is 12 years. So we want to find K d in: So we want to find K d in: $761=$80/(1+K d )^1+$80/(1+ $761=$80/(1+K d )^1+$80/(1+ K d )^2+ … +$80/(1+K d )^12 We can find it with trial and error or with the IRR% function in Excel … (treat $761 as initial cash out). We can find it with trial and error or with the IRR% function in Excel … (treat $761 as initial cash out). K d =11.828% K d =11.828% Jump!

Intro. to Financial Managment - 9th Week of Class20 Note that If interest rates rise bond prices fall If interest rates rise bond prices fall If interest rates fall bond prices increase If interest rates fall bond prices increase So interest rates and bond prices move in opposite directions So interest rates and bond prices move in opposite directions Climb!

Intro. to Financial Managment - 9th Week of Class21 End of the chapter Jump and Climb!