Fin 305 Exam 2

6. Consider a bond that is currently priced at $1100. If the face value of the bond is $1000, coupon payments are made semiannually, the bond matures in 5 years, and the YTM is 3%, what is the coupon rate?

$1100 = (C/.015)*(1-1.015^10) + 1000/1.015^10 = C*9.22 + 861.67 →9.22C = 238.33 →C = $25.84 →c=2*$25.84/$1000 = .0517 = 5.17%

3% per year forever afterward. After that, dividends will increase by 2.5% per year indefinitely

(4*1.2^2*1.4^5*1.03/((.15 - .03)*1.15^7) = 149.32 ( 2*1.25^5*1.025/((.18 - .025)*1.18^13 = 8.39 (D*1+g^years *1+new g)/( r-new g)*(1+g^Total years)

Treasury bills are currently paying 8 percent and the inflation rate is 3.50 percent. What is the approximate real rate of interest? What is exact real rate of interest?

4.5%=approx 8-3.5=4.5 4.35%=exact 1.08/1.035=.04347

Sinking fund

Account managed by bond trustee for purpose of repaying the bonds. Company makes annual pmts to the trustee, who then uses the funds to retire portion of the debt.

Call Premium

Amount by which the call price exceeds the par value of the bond 1. The dollar amount over the par value of a callable fixed-income debt security that is given to holders when the security is called by the issuer. 2. The amount the purchaser of a call option must pay to the writer. 1. The call premium is somewhat of a penalty paid by the issuer to the bondholders for the early redemption. 2. In order to receive the rights associated with a call option, the premium must be paid to the seller.

6. Consider a bond with a coupon rate of 8%, YTM of 5%, face value is $1500. The bond matures in 18 years. a. What is bond value today? What is the current yield? What is the capital gains yield?

C = .08*1500 = 120 Coupon Payment= Rate x face value BV0 = (120/.05)*(1-1/1.05^18) + 1500/1.05^18 = $2026 (Coupon/YTM) x (1-1/1+r)^years + (face/(1+r)^years CY0 = 120/2026 = .0592 (coupon/BVo)=Current yield CGY0 = .05 - .0592 = -.0092 (YTM - Current Yield)

7. Consider a bond that promises to make coupon payments of $150 per year for the next 7 years and coupon payments of $350 per year for the remaining lifetime of the bond. The face value is $1200. The bond matures in 20 years and YTM is 9%. What is the value of the bond? CHEAT SHEET

BV0 = (150/.09)*(1-1/1.09^7) + (350/.09)*(1-1/1.09^13)/1.09^7 + 1200/1.09^20 = $2402.53 (C first 7/YTM)* (1-1/1+YTM)^years + (Cremainder/YTM) * (1-1/1+YTM)^(Remaining 13 years)/(1+YTM)^7 years) + (Face value/1+YTM) ^Total years (1666.66)*(.453) + (3888.88)*(.6738)/(1.828) + (214.11) 754.997 + 1433.44 + 214.11 = $2402.53

Bonds

BV=Bond Value CY=Current Yield CGY=Capital Gains Yield C=Coupon payment

Convertible bond

Can be swapped for a fixed number of shares of stock at anytime before maturity at the holders option. Very common, but decreasing lately.

b. Trace the dividend and capital gains component of the required return for this stock over time.

DY0 = 1.25*1.2/16.01 = .094; CGY0 = .16 - .094 = .066 P1 = 16.01*1.066 = 17.07 DY1 = 1.25*1.2^2/17.07 = .1241; CGY1 = .16 - .1241 = .0359

Term Structure of int rates

Dividend Growth Model Po=(D1)/(r-g)= Do(1+g)/(r-g) r=Dyt + CGyt CGyt = ((Pt + 1)/(Pt))-1 Dy=Dt+1/Pt Pt= Stock price at beginning of year t Po=Stock Price today g=growth in dividends r=Required return on stock Do=Last dividend Paid D1=Next dividend Paid Dt=Dividend paid in year t Multi stage dividend growth model? Won't have to solve for YTM Higher YTM=More risk Nothing from 8.2

Exam

Exam

Bond Features

Face/Par Value Coupon Date Maturity Date YTM Frequency of PMT Coupon pmt= C= c x face value/m

c. If the required return is 10% and the stock price is $33.25, what is the implied growth rate in dividends?

G = (33.25*.1 - 2.5)/(33.25 + 2.5) = .023 (Stock price * r - Div)/(stock price + Div)= growth rate

Collateral

General term that frequently means securities, that are pledged as security for payment of debt. Collateral trust bonds often involve a pledge of common stock held by the corporation. However, the term collateral is commonly used to refer to any asset pledged on a debt. A bond that is secured by a financial asset - such as stock or other bonds - that is deposited and held by a trustee for the holders of the bond. If the issuing company were to default on the debt obligation, the debt holders would receive the securities held in trust, like collateral for a loan. For example, say Company A issues a collateral trust bond, and as collateral for the bond it includes the right to Company A shares held by a trust company. If Company A were to default on the bond payments, the bondholders would be entitled to the shares held in trust

8. What is the relationship between coupon rates, YTM, and bond values?

If coupon rate = YTM, then bond value = par value and does not change If coupon rate > YTM, then bond value > par value and declines as time goes by to approach par value at time of maturity If coupon rate < YTM, then bond value < par value and increases as time goes by to approach par value at time of maturity

9. What happens to the value of a bond as time goes by?

It approaches par value, assuming nothing else changes

Bond J is a 4 percent coupon bond. Bond K is a 10 percent coupon bond. Both bonds have 17 years to maturity, make semiannual payments, and have a YTM of 7 percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? What if they fall by 2%?

J: FV=1000, N=34, PMT=20, I/Y=3.5, PV=?--->704.49 Rise by 2% FV=1000, N=34, PMT=20, I/Y=4.5, PV=?-->568.83 704.49 - 568.83 = 135.66/704.49= -19.26% change Fall by 2% FV=1000, N=34, PMT=20, I/Y=2.5, PV=?--->886.38 886.38 - 704.49 = 181.89/704.49 = 25.82% change K: FV=1000, N=34, PMT=50, I/Y=3.5, PV=?--->1295.51 Rise by 2% FV=1000, N=34, PMT=50, I/Y=4.5, PV=?--->1086.23 1295.51 - 1086.23 = 209.28/1295.51= -16.15% change Fall by 2% FV=1000, N=34, PMT = 50, I/Y= 2.5, PV=?--->1568.09 1568.09 - 1295.51 = 272.58/1295.51 = 21.04% Change

Vocab

Longer-term bonds have more interest rate risk. This means that their values change more dramatically in response to changes in interest rates. The examples above illustrate this concept numerically. Interest rate risk is higher for bonds with lower coupon rates. This means that bonds with lower coupon rates experience more dramatic value/price changes when interest rates change. The examples above illustrate this concept.

Ninja Co. issued 14-year bonds a year ago at a coupon rate of 8.6 percent. The bonds make semiannual payments. If the YTM on these bonds is 6.9 percent, what is the current bond price?

Nper = 13*2 = 26 (indicates the remaining maturity period of bonds) Rate = 6.9%/2 (indicates semi-annual YTM) PMT = 1000*8.6%*1/2 = 43 (indicates the amount of semi-annual interest payment) FV = 1000 (indicates the face value of bonds) PV = ? (indicates the current price of the bond) Current Price of the Bond = PV(Rate,Nper,PMT,FV) = PV(6.9%/2,26,43,1000) = 1144.38 Answer is 1144.38.

Other stuff

Optional Bond features (Call provision, Convertible, Collateral, seniority, s fund)

3. Consider a company that most recently paid a dividend of $4 and dividends are expected to grow 20% per year for 2 years, 40% per year for 5 years after that, and 3% per year forever afterward. If the required return for this stock is 15%, what is the value of the stock?

P0 = (4*1.2/1.15) + (4*1.2ˆ2/1.15^2) + (4*1.2^2*1.4/1.15^3) + (4*1.2^2*1.4^2/1.15^4) + (4*1.2^2*1.4^3/1.15^5) + (4*1.2^2*1.4^4/1.15^6) + (4*1.2^2*1.4^5/1.15^7) + (4*1.2^2*1.4^5*1.03/((.15 - .03)*1.15^7) = 149.32

Yield to call....

is the annual yield an investor would receive if a callable bond is held from purchase date until the earliest possible call date.

1. Consider a stock that most recently paid a dividend of $2.50. a. If you expect this company to grow dividends by 2% annually for the foreseeable future and require a 10% return on stock in this company, what are you willing to pay for the stock today?

P0 = 2.50*1.02/(.1-.02) = 31.875 (Div PMT * 1+g)/(r-g)= Price willing to pay today Po=(D1)/(r-g)= Do(1+g)/(r-g)

Po Problems

Po Problems

Buy stock today will receive D=2, P=100 r=.1

Po= 102/1.1=92.73

Consider a stock Div=2.5 g=.02 r=.1 Find Po, Dy, CGy

Po= 2.5(1.02)/(.1-.02) = 31.876 Dyo=2.5 (1.02)/(31.876)= .08 CGyo= .02

b. If you expect this company to grow dividends by 2% annually for the foreseeable future and the current stock price is $28.50, what is the required return for this stock?

R = 2.50*1.02/28.5 + .02 = .109 (DIV PMT * 1+g)/Po) + g

5. Consider a bond that is currently priced at $1000. If the face value of the bond is $1000 and the YTM is 4%, what is the coupon rate?

Since the bond is valued at face value, coupon rate = YTM = 4%

1. Consider an unconventional bond with face value $1000. It matures in 25 years, but offers a 7% coupon rate for the first 5 years, a 10% coupon rate for the following 11 years, and no coupon for the remaining lifetime of the bond.

a. If the YTM for the bond is 6.5%, what is bond value today? What is bond value each year? What are current yield and capital gains yield each year? BV0 = (70/.065)*(1-1/1.065^5) + (100/.065)*(1-1/1.065^11)/1.065^5 + 1000/1.065^25 = $1059 CY0 = 70/1059 = .066 CGY0 = -.001 BV1 = 1059*(.999) = 1058

CH 7 Practice problems

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9. Consider a company that most recently paid a dividend of $1.20. They plan to increase the dividend by 24% each year for the next 4 years. After that, they will increase the dividend by12% for 1 year, after which they will level off to a constant growth rate in dividends of 3.5%. The required return for the stock is 15%. What is the value of the stock today? CHEAT SHEET?

What is the value of the stock today? D1 = 1.2*1.24 = 1.49 (Dividend * 1+rate of increase) D2 = 1.49*1.24 = 1.85 D3 = 1.85*1.24 = 2.29 D4 = 2.29*1.24 = 2.84 D5 = 2.84*1.12 = 3.18 (increase by 12% for 1 year) D6 = 3.18*1.035 = 3.29 (Constant growth of 3.5% kicks in) P5 = 3.29/(.15 - .035) = 28.60 (D6/r-g)=Price after year 5 P0 = 1.49/1.15 + 1.85/1.15^2 + 2.29/1.15^3 + 2.84/1.15^4 + 3.18/1.15^5 + 28.60/1.15^5 = $21.62 is the value today 1.15 = 1+r

8. Consider a company that most recently made a dividend payment of $1.25. Dividends are expected to grow at a constant rate of 4% indefinitely. The required return on the company's stock is 9%. Constant Rate = g Required Return = r

What should stock price be today? P0 = 1.25*1.04/.05 = $26 Po=(D1)/(r-g)= Do(1+g)/(r-g) (Div PMT) *(1+r))/(r-g) = Price b. (3 points) What are the dividend yield and capital gains yield? CGY = .04; DY = .05

Call Provision

A provision on a bond or other fixed-income instrument that allows the original issuer to repurchase and retire the bonds. If there is a call provision in place, it will typically come with a time window under which the bond can be called, and a specific price to be paid to bondholders and any accrued interest are defined. Callable bonds will pay a higher yield than comparable non-callable bonds. A bond call will almost always favor the issuer over the investor; if it doesn't, the issuer will simply continue to make the current interest payments and keep the debt active. Typically, call options on bonds will be exercised by the issuer when interest rates have fallen. The reason for this is that the issuer can simply issue new debt at a lower rate of interest, effectively reducing the overall cost of their borrowing, instead of continuing to pay the higher effective rate on the borrowings.

6b. What is bond value one year from today? What is the current yield next year? What is the capital gains yield next year?

BV1 = 2026*(1+(-.0092)) = 2007.39 BVo * (1+(CGYo)) OR BV1 = (120/.05)*(1-1/1.05^17) + 1500/1.05^17 = 2007.39 (Only difference is subtract 1 year) CY1 = 120/2007.39 = .0598 (c/BV1) CGY1 = -.0098 (.05 - .0598)

6c. What is bond value 7 years from now?

BV7 = (120/.05)*(1-1/1.05^11) + 1500/1.05^11 = 1874 (Subtract 6 years) 1/1.05=.9524 .9524^11=.5847 1-.5847=.4153 .4153 x 2400 =996.9609 1.05^11=1.7103 1500/1.7103=877.0391 996.9609 + 877.0391 = 1874

Equations

BVo=(c/r)(1-1/(1+r)^t) + Face Value/(1+r)^t ytmt=Cyt + CGyt Cyt=Ct/BVt CGy=((BVt-1)/(BVt)) -1

Bond P is a premium bond with a 9 percent coupon. Bond D is a 4 percent coupon bond currently selling at a discount. Both bonds make annual payments, have a YTM of 6 percent, and have four years to maturity 1. What is the current yield for bond P and bond D? 2. If interest rates remain unchanged, what is the expected capital gains yield over the next year for bond P and bond D?

Bond P: N=4, I/Y=6, PMT=90, FV=1000, PV=?--->1103.95 1 year later (1 period closer to maturity) N=3, I/Y=6, PMT=90, FV=1000, PV=?--->1080.19 Change in price=$23.76 Current yield=8.15% (90/1103.95) Cap Gain/Loss= - 2.15% (23.76/1103.95) Total Return = 6% Bond D: N=4, I/Y=6, PMT=40, FV=1000, PV=?--->930.70 1 year later: N=3, I/Y=6, PMT=40, FV=1000, PV=?--->946.54 Change in price=$15.8393 Current Yield=4.3% Cap Gain/Loss=1.7% Total Return=2.6%

2. Consider a bond with a coupon rate of 4%, a YTM of 6%, and a face value of $1000. Coupon payments are made annually. a. If this bond matures in 15 years, what are you willing to pay for it today? What are you willing to pay for it in 6 years?

Bond Value (Today) = (40/.06)*(1-1/1.06^15) + 1000/1.06^15 = $805.77 Bond Value (6 years) = (40/.06)*(1-1/1.06^9) + 1000/1.06^9 = $863.97

1. Consider a zero-coupon bond with a yield to maturity (YTM) of 5%, a face value of $1000, and a maturity date 10 years from today. What are you willing to pay for this bond today? What will you be willing to pay for this bond 3 years from today?

Bond Value (Today) = 1000/1.05^10 = $613.91 Bond Value (3 years) = 1000/1.05^7 = $613.91*1.05^3 = $710.68

3. Consider a bond with a face value of $1000, YTM of 5%, and coupon rate of 4%. The bond matures in 5 years. Calculate the value of the bond today, in one year, and in two years. Calculate the percentage change in the price of the bond each year. Calculate the current yield each year. What is the relationship between current yield and percentage price change (capital gains yield) for bonds?

Bond Value (today) = (40/.05)*(1-1/1.05^5) + 1000/1.05^5 = $956.71 Bond Value (1 year from now) = (40/.05)*(1-1/1.05^4) + 1000/1.05^4 = $964.54 Percentage Change (Capital Gains Yield CGY) = (964.54-956.71)/956.71 = .0082 or .82% Current Yield (year 1) = 40/956.71 = .0418 or 4.18% NOTE: CGY + Current Yield = .82 + 4.18 = 5% = YTM Bond Value (2 years from now) = (40/.05)*(1-1/1.05^3) + 1000/1.05^3 = $972.77 CGY = (972.77 - 964.54)/964.54 = .0085 or .85% Current Yield (year 2) = 40/964.54 = .0415 or 4.15% NOTE: CGY + Current Yield = .85 + 4.15 = 5% = YTM

Bond X is a premium bond making semiannual payments. The bond pays a 8 percent coupon, has a YTM of 6 percent, and has 12 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a 6 percent coupon, has a YTM of 8 percent, and also has 12 years to maturity. What is the value of each bond today?

Bond X: FV=1000 PMT=40 N=24 I/Y=3 (YTM) PV=?--->$1,169.36 Bond Y: FV:1000 PMT:30 N:24 I/Y: 4 PV:?--->$847.53

3. Consider a company that most recently paid a dividend of $4 and dividends are expected to grow 20% per year for 2 years, 40% per year for 5 years after that, and 3% per year forever afterward. If the required return for this stock is 15%, what is the value of the stock? CHEAT SHEET

P0 = (4*1.2/1.15) + (4*1.2ˆ2/1.15^2) + (4*1.2^2*1.4/1.15^3) + (4*1.2^2*1.4^2/1.15^4) + (4*1.2^2*1.4^3/1.15^5) + (4*1.2^2*1.4^4/1.15^6) + (4*1.2^2*1.4^5/1.15^7) + (4*1.2^2*1.4^5*1.03/((.15 - .03)*1.15^7) = 149.32 (Divided * 1+g/1+r) + (Dividend * 1 +g ^years for 20% growth/1+r ^ years) + (Dividend * 1 + g^years * 1+g^years/1 + g^years) $4 included every time 20% growth for 1 year, 2 years then locked in at 2 after that 40% growth after 2 years (year 3), t increases until it hits 5 Once t hits 5, 3% forever kicks in, s0 5*1.03. Then divided by 15% required return - 3% *1+r ^ total years

4. Consider a company that is not currently paying dividends. They plan to begin paying dividends in 8 years and will start with a $2 dividend. After that, dividends will increase by 25% each year for 5 years. After that, dividends will increase by 2.5% per year indefinitely. The required return for this stock is 18%.

P0 = 2/1.18^8 + 2*1.25/1.18^9 + 2*1.25^2/1.18^10 + 2*1.25^3/1.18^11 + 2*1.25^4/1.18^12 + 2*1.25^5/1.18^13 + 2*1.25^5*1.025/((.18 - .025)*1.18^13 = 8.39

4. Consider a company that is not currently paying dividends. They plan to begin paying dividends in 8 years and will start with a $2 dividend. After that, dividends will increase by 25% each year for 5 years. After that, dividends will increase by 2.5% per year indefinitely. The required return for this stock is 18%. Trace stock price, dividend yield, and capital gains yield over the years for this stock.

P0 = 2/1.18^8 + 2*1.25/1.18^9 + 2*1.25^2/1.18^10 + 2*1.25^3/1.18^11 + 2*1.25^4/1.18^12 + 2*1.25^5/1.18^13 + 2*1.25^5*1.025/((.18 - .025)*1.18^13 = 8.39 Don't include 1.25 at first. Dividends don't begin until after 8 years. Once you hit 5 years. It's Dividend (2) * 1+g (1.25)^total years paying dividends (5)*1+increase in dividend payments (1.025)

Seniority

Preference in position over other lenders and debts In event of default, subordinated debt holders must give preference to other specified creditors. They will be compensated only after specified creditors have been compensated.

4. Consider a bond with a face value of $1000, YTM of 5%, and coupon rate of 7%. The bond matures in 5 years. Calculate the value of the bond today, in one year, and in two years. Calculate the percentage change in the price of the bond each year. Calculate the current yield each year. What is the relationship between current yield and percentage price change (capital gains yield) for bonds?

Today: (70/.05)*(1-1/1.05^5)+(1000/(1.05)^5)=1086.614 1 year: (70/.05)*(1-1/1.05^4)+(1000/(1.05)^4)=1070.9267 CGY=-1.44% CY=6.44% YTM=5% (6.44-1.44) 2 years: (70/.05)*(1-1/1.05^3)+(1000/(1.05)^3)=1054.53

Martin Software has 11.2 percent coupon bonds on the market with 20 years to maturity. The bonds make semiannual payments and currently sell for 108.4 percent of par? NO SOLVING FOR YTM

YTM: N=40 ---->(20 x 2=40) FV=1000 (par) PV=-1084 ---->(1.084 x 1000=1084) PMT=56 ---->(11.2 x 100=112/2=56) I/Y=?--->5.1035 YTM= 10.21% ------>(5.1035 x 2 = 10.21) Effective Annual Yield=10.47% (1-.051035)^2 = 1.1047 1.1047 -1 = .1047-----> 10.47% Current Yield: 10.33% 11.2 x 100 = 112 112/1084= 10.33%

2. Consider two bonds, each with face value of $1000, YTM of 5%, and mature in 10 years. The only difference between them is that one has a coupon rate of 6% and one has a coupon rate of 8%. a. What happens to the value of each bond if interest rates decline by 1%? b. What happens to the value of each bond if interest rates increase by 1%? c. What is going on here? Interest rate risk is higher for bonds with lower coupon rates. This means that bonds with lower coupon rates experience more dramatic value/price changes when interest rates change. The examples above illustrate this concept.

a) Bond 1 Value (Original) = (60/.05)*(1-1/1.05^10) + 1000/1.05^10 = $1,077.22 Bond 1 Value (new interest rate) = (60/.04)*(1-1/1.04^10) + 1000/1.04^10 = $1,162.22 Change in Bond 1 Value is $85, but the Percentage change in Bond 1 value is $85/$1077.22 = .079 or 7.9% change in value. Bond 2 Value (Original) = (80/.05)*(1-1/1.05^10) + 1000/1.05^10 = $1,231.65 Bond 2 Value (new interest rate) = (80/.04)*(1-1/1.04^10) + 1000/1.04^10 = $1,324.44 Change in Bond 2 Value is $92.78, which looks bigger. BUT, the percentage change in Bond 2 value is $92.78/$1,231.65 = .075 or 7.5% change in value. So, Bond 1 changed in value more than Bond 2. b) Bond 1 Value (Original) = (60/.05)*(1-1/1.05^10) + 1000/1.05^10 = $1,077.22 Bond 1 Value (new interest rate) = $1,000 (c = YTM) = (60/.06)*(1-1/1.06^10) + 1000/1.06^10 = $1,000 (if you want to calculate it). Change in Bond 1 Value is -$77.22, but the Percentage change in Bond 1 value is -$77.22/$1077.22 = .072 or 7.2% change in value. Bond 2 Value (Original) = (80/.05)*(1-1/1.05^10) + 1000/1.05^10 = $1,231.65 Bond 2 Value (new interest rate) = (80/.06)*(1-1/1.06^10) + 1000/1.06^10 = $1,147.20 Change in Bond 2 Value is -$84.45, which looks bigger. BUT, the percentage change in Bond 2 value is -$84.45/$1,231.65 = .069 or 6.9% change in value So again, Bond 1 changed more in value. c) Interest rate risk is higher for bonds with lower coupon rates. This means that bonds with lower coupon rates experience more dramatic value/price changes when interest rates change. The examples above illustrate this concept.

4. Consider a bond with a coupon rate of 5%. It matures in 30 years and has a face value of $1000. Based on current interest rate, the YTM of this bond is 6%. a. What's the value of the bond assuming interest rates do not change? b. What's the value of the bond if you expect the YTM to decline to 4% 10 years from now? CHEAT SHEET

a) Bond Value = (50/.06)*(1-1/1.06^30) + 1000/1.06^30 = $862.35 b) Bond Value = (50/.06)*(1-1/1.06^10) + (50/.04)*(1-1/1.04^20)/1.06^10) + 1000/(1.06^10*1.04^20) = $1002.27

1. Consider two bonds, each with face value of $1000, coupon rate of 5%, and YTM of 5%. The only difference between them is that one matures in 15 years and the other matures in 30 years. a. What happens to the value of each bond if interest rates decline by 1%? b. What happens to the value of each bond if interest rates increase by 1%? c. What is going on here?

a) Both bond values increase. However, the longer-maturity bond sees a more dramatic change in value. Numerically, Bond 1 Value = (50/.04)*(1-1/1.04^15) + 1000/1.04^15 = $1,111.18 and Bond 2 Value = (50/.04)*(1-1/1.04^30) + 1000/1.04^30 = $1,172.92. Before, both bonds were trading at par value. So, we see a bigger price jump for the longer-term bond (Bond 2). b) Both bond value decline. However, the longer-maturity bond again sees a more dramatic change in value. Bond 1 Value = (50/.06)*(1-1/1.06^15) + 1000/1.06^15 = $902.88 and Bond 2 Value = (50/.06)*(1-1/1.06^30) + 1000/1.06^30 = $862.35. Before, both bonds were trading at par value. So, Bond 2 declined in price more. c) Longer-term bonds have more interest rate risk. This means that their values change more dramatically in response to changes in interest rates. The examples above illustrate this concept numerically.

2. Consider a company that most recently paid a dividend of $1.25. For the next 3 years, they have pledged to increase the dividend by 20% each year. After that, they've pledged to level out at a permanent growth rate in dividends of 4%. a. If you require a 16% return, what are you willing to pay for the stock today? b. Trace the dividend and capital gains component of the required return for this stock over time.

a) P0 = (1.25*1.2/1.16) + (1.25*1.2^2/1.16^2) + (1.25*1.2^3/1.16^3) + (1.25*1.2^3*1.04/((.16 - .04)*1.16^3) = 16.01 b) DY0 = 1.25*1.2/16.01 = .094; CGY0 = .16 - .094 = .066 P1 = 16.01*1.066 = 17.07 DY1 = 1.25*1.2^2/17.07 = .1241; CGY1 = .16 - .1241 = .0359

2. Consider a stock that is not currently paying dividends. The first dividend will be paid in 3 years and will be $.50 (i.e. D3 = $.50). Dividends will increase by 35% per year for 4 years after the first dividend, by 25% per year for 4 years after that, by 15% per year for 4 years after that, a nd then by 5% per year in perpetuity.

a. If required return for the stock is 14%, what should the value of the stock be today? What is value of the stock each year for the next 25 years? What are dividend yield and capital gains yield each year for the next 25 years? P0 = (.5/(.14-.35))*(1-(1.35/1.14)^5)/1.14^2 + (.5*1.35^4*1.25/(.14-.25))*(1-(1.25/1.14)^4)/1.14^7 + (.5*1.35^4*1.25^4*1.15/(.14-.15))*(1-(1.15/1.14)^4) /1.14^11+(.5*1.35^4*1.25^4*1.15^4*1.05 /((.14-.05)*1.14^15) = 21.31 DY0 = 0 CGY0 = .14 P1 = 21.31*1.14 = 24.29

2. Consider a company that most recently paid a dividend of $1.25. For the next 3 years, they have pledged to increase the dividend by 20% each year. After that, they've pledged to level out at a permanent growth rate in dividends of 4%.

a. If you require a 16% return, what are you willing to pay for the stock today? P0 = 1.25*1.2/1.16 + 1.25*1.2^2/1.16^2 + 1.25*1.2^3/1.16^3 + 1.25*1.2^3*1.04/((.16 - .04)*1.16^3) = 16.01

9 b-d

b. What is the value of the stock four years from today? P4 = 2.84/1.15 + 28.60/1.15 = 27.34 (Div Value of year 4 from above)/ (1 + r) from above + P5/(1+r) c. What are this year's dividend yield and capital gains yield? DY0 = 1.49/21.62 = .069 (D1/Po) CGY0 = .15 - .069 = .081 (r-DYo) d. What will be the dividend yield and capital gains yield in 10 years? DY10 = .115 CGY10 = .035 Required return = 15 Constant growth rate=3.5