Unformatted text preview: P 79 Common stock value—Constant growth Use the constantgrowth model (Gordon model) to find the value of each firm shown in the following table. Firm Dividend expected next year Dividend growth rate Required return Firm Dividend expected next year Dividend growth rate Required Return A $1.20 8% 13% B $4.00 5 15 C 0.65 10 14 D 6.00 8 9 E 2.25 8 20 P0 = D1 rs  g (Pg: 513 in book) P0= value of common stock D1= pershare dividend expected at the end of year 1 rs= required return on common stock g= constant rate of growth in dividends * I hope this was ok to do I showed the written work for one example and just used the firmulas for the rest as proof of my work For Firm A. d1= 1.20 rs=.13 P0= 1.2 .13  .08 Table: Firm g= .08 P0= 1.2 0.05 P0= 24 Dividend expected next year $1.20 $4.00 $0.65 $6.00 $2.25 Dividend growth rate 8% 5% 10% 8% 8% Required Return 13% 15% 14% 9% 20% A B C D E Value of each firm $24.00 $40.00 $16.25 $600.00 $18.75 P 712. Common stock value—Variable growth Newman Manufacturing is considering a cash purchase of the stock of Grips Tool. During the year just completed, Grips earned $4.25 per share and paid cash dividends of $2.55 per share (D0_$2.55). Grips’ earnings and dividends are expected to grow at 25% per year for the next 3 years, after which they are expected What is the maximum price per share that Newman should pay for Grips if it has a required return of 15% on investments with risk characteristics similar to those of Grips? * Page #/ formulas shown D1 = $2.55 (D0) x 1.25 = $3.1875 D2 = $3.1875 x 1.25 = $3.984 D3= $3.984 x 1.25 = $4.98 ; PV of D1 = 3.1875/(1+.15) = 2.7717 ; PV of D2 = 3.984/(1+.15)2 = 3.0125 ; PV of D3 = 4.98/(1+.15)3 = 3.2744
1 D4 = $4.98 x 1.10 (g2) = $5.478 Sum of PV = 2.7717 + 3.0125 + 3.2744 = 9.0586 Value of stock at the end of initial growth period (P3) = D4/(rg2)= 5.478/(15%  10%)$109.56 Present value (PV) of value of stock at the end the end of year 3 = 109.56/(1+.15)3 = $72.04 Current price/value of the stock, P0 = Sum of PV of dividends in the initial growth period + PV of value of stock at the end of Year 3 $9.0586 + $72.04 = $81.098 Hopefully if I got this right the maximum price per share that Nerman would pay is equal after rounded to $81.10. e of the stock of Grips Tool. (D0_$2.55). re expected Page #/ formulas shown prvioulsy V of value of r rounded to $81.10. P 615. Basic bond valuation Complex Systems has an outstanding issue of $1,000parvalue bonds with a 12% co a. If bonds of similar risk are currently earning a 10% rate of return, how much should the Complex Systems bond sell for today? b. Describe the two possible reasons why the rate on similarrisk bonds is below the coupon interest rate on the Complex Systems bond. c. If the required return were at 12% instead of 10%, what would the current value of Complex Systems’ bond be? Contrast this finding with your findings in part a and discuss.
a.Basic bond valuation Complex Systems has an outstanding issue of $1,000 parvalue bonds with a 12 currently earning a 10% rate of return, how much should the Complex Systems bond sell for today? Coupon rate*par value = coupon payment 12%*$1000= $120 per payment (I am presuming in years) 10% is the yield $1000 is the par value PV is the price you pay today PV = C/(1+y) + C/[(1+y)^2] + C/[(1+y)^3] + ... + C/[(1+y)^t] + par val/[(1+y)^t] PV = 120/1.1 + 120/1.21 + 120/1.331 +... + 120/4.6 + 1000/4.6 PV=$1187 you pay $1187 for the bond today b. Describe the two possible reasons why similarrisk bonds are currently earning a return below the coup Two possibel reason could be 1) The current real interest rate is 10% 2) Credit rating of similar bond is higher (that is they are less risky). c. If the required return were at 12% instead of 10%, what would the current value of Complex Systems' a and discuss. PV = 120/1.12 + 120/1.2544 + ...120/6.1 + 1000/6.1 PV = $1000 FV PMT (Payment Per Period) N Rate PV 1000 120 16 12.00% $1,000.00 Based on the two when done at 12% it is lower than when viewed at 10%. Therefore because the curren 12% I would choose the 10%. current vaule is lower wen at 12% I would choose the 10% parvalue bonds with a 12% coupon interest rate. The issue pays interest annually and has 16 years remaining to its maturity ,000 parvalue bonds with a 12% coupon interest rate. The issue pays interest annually and has 16 years remaining to its ma tems bond sell for today? FV PMT (Payment Per Period) N Rate 1000 120 16 10.00% (pg.344 in book) earning a return below the coupon interest rate on the Complex Systems bond. nt value of Complex Systems' bond be? Contrast this finding with your findings in part . Therefore because the current vaule is lower wen at remaining to its maturity date. years remaining to its maturity date. a. If bonds of similar risk are P55 Risk and probability MicroPub, Inc., is considering the purchase of one of two microfilm cameras, R and S. B should provide benefits over a 10year period, and each requires an initial investment of $4,000. Management has constructed the table (on page 266) of estimates of rates of return and probabilities for pessimistic, most likely, and optimistic results. a. Determine the range for the rate of return for each of the two cameras. b. Determine the expected value of return for each camera. c. Purchase of which camera is riskier? Why Initial investment Annual rate of return pessimistic most likely optomistic Camera R amount probability 4000 1 0.2 0.25 0.3 0.25 0.5 0.25 Camera S amount probability 4000 1 0.15 0.25 0.35 0.2 0.55 0.25 a. Determine the range for the rate of return for each of the two cameras. The range is found by subtracting the return associated with the pessimistic outcome from the return associated with the optimistic outcome. * (277 in book) Camera R Camera S Range 0.1 0.2 b. Determine the expected value of return for each camera. * (279 in book) The value of a return, is the most likely return on an asset. It is calculated as follows r= rj= return for the jth outcome Prj= probability of occurrence of the jth outcome n= number of outcomes considered * couldn’t copy and paste sum of product equation from book, just did it in excel Expected Value 0.25 0.26 c. Purchase of which camera is riskier? Why In general, the higher the standard deviation, the greater the risk. * (280 in book) * couldn’t copy and paste standard deviation equation from book, just did it in excel its on page also that is where I understood the concept of the higher the stdeva. The higher the risk Standard Deviation 0.25 0.26 Camera "S" is more risker as it is not only higher in the stdea, but also in the range. film cameras, R and S. Both 000. Management has imistic, most likely, and imistic outcome (277 in book) (279 in book) 2. Assessing return and risk Swift Manufacturing must choose between two asset purchases. The annual rate of retu (on page 268) summarize the firm’s analysis to this point. a. For each project, compute: (1) The range of possible rates of return. (2) The expected value of return. (3) The standard deviation of the returns. (4) The coefficient of variation of the returns. b. Construct a bar chart of each distribution of rates of return. c. Which project would you consider less risky? Why? Project 257 Rate of return Probability 10% 10 20 30 40 45 50 60 70 80 100 Project 432 Rate of return Probability 10.0% 0.05 15.0% 0.1 20.0% 0.1 35.0% 0.15 30.0% 0.2 35.0% 0.15 40.0% 0.1 45.0% 0.1 50.0% 0.05 0.01 0.04 0.05 0.1 0.15 0.3 0.15 0.1 0.05 0.04 0.01 hases. The annual rate of return and the related probabilities given in the following table a. For each project, compute: (1) The range of possible rates of return. Project 257 Range: 1.00  (.10) = 1.10 Project 432 Range: .50  .10 = .40 (2) The expected value of return. r= Expected return: Project 257 r j= Prj = Rate of Return
rj (Pg. 279 in book) rj= return for the jth outc Prj= probability of occur n= number of outcomes Probability Prj 0.1 0.1 0.2 0.3 0.4 0.45 0.5 0.6 0.7 0.8 1 0.01 0.04 0.05 0.1 0.15 0.3 0.15 0.1 0.05 0.04 0.01 1 0.45 Weighted Value x Prj rj 0 0 0.01 0.03 0.06 0.14 0.08 0.06 0.04 0.03 0.01 0.45 Expected Return formula in book 0.45 Expected return: Project 432 Rate of Return rj 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Probability Prj Weighted Value Expected Return x Prj rj 0.05 0.01 0.1 0.02 0.1 0.02 0.15 0.04 0.2 0.06 0.15 0.05 0.1 0.04 0.1 0.05 0.5 0.05 1 0.03 0.3 0.3 Expected rate of return is 0.300 (3) The standard deviation of the returns. Standard Déviation: (pg. 280) Project 257 rj 0.1 0.1 0.2 0.3 0.4 0.45 0.5 0.6 0.7 0.8 1 r 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 rj  r 0.55 0.35 0.25 0.15 0.05 0 0.05 0.15 0.25 0.35 0.55 (rj  r)2 0.3 0.12 0.06 0.02 0 0 0 0.02 0.06 0.12 0.3 Prj (rj  r)2 x Prj 0.01 0 0.04 0 0.05 0 0.1 0 0.15 0 0.3 0 0.15 0 0.1 0 0.05 0 0.04 0 0.01 .003025. 0.03 Standard Deviation = 0.17 ( I just used the SQRT function) Project 432 rj 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 r 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 rj  r Prj (rj  r)2 0.2 0.04 0.15 0.02 0.1 0.01 0.05 0 0 0 0.05 0 0.1 0.01 0.15 0.02 0.2 0.04 0.05 0.1 0.1 0.15 0.2 0.15 0.1 0.1 0.05 (rj  r)2 x Prj 0 0 0 0 0 0 0 0 0 0.01 Standard Deviation= 0.11 ( I just used the SQRT function) (4) The coefficient of variation of the returns. Project 257 CV = stdev ( pg. 283 in book) cv = Project 432 cv = 0.37 r 0.35 j= return for the jth outcome rj= probability of occurrence of the jth outcome = number of outcomes considered 10% 0.01 r= rj= return for the jth outcome Prj= probability of occurrence of the jth outcome r = expected value of return r j= Prj = r= 10% 0.01 0.45 (formula in book pg. 279) r= rj= return for the jth outcome Prj= probability of occurrence of the jth outcome r = expected value of return r j= Prj = r= 10% 0.05 0.3 (formula in book pg. 279) b. Construct a bar chart of each distribution of rates of return. Project 257 0.45 45% Project 257
0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 10% 10% 20% 30% 40% 45% 50% 60% 70% 80% 100% 0.01 0.04 0.05 0.1 0.15 0.3 0.15 0.1 0.05 0.04 0.01 Project 257 Rate of return Probability 10% 0.01 10% 0.04 20% 0.05 30% 0.1 40% 0.15 45% 0.3 50% 0.15 60% 0.1 70% 0.05 80% 0.04 100% 0.01 Project 432 0.3 30% Project 432
0.25 0.2 0.15 4 0.05 0.1 0.15 0.1 0.05 0.04 0.1 0.05 0 % 100% 10.00% 15.00% 20.00% 35.00% 30.00% 35.00% 40.00% 45 Project 432 Rate of return Probability 10.00% 0.05 15.00% 0.1 20.00% 0.1 35.00% 0.15 30.00% 0.2 35.00% 0.15 40.00% 0.1 45.00% 0.1 50.00% 0.05 t 432 Column O .00% 35.00% 40.00% 45.00% 50.00% c. Which project would you consider less risky? Why? Summary of everything: Project 432 Range Expected Return Standard Deviation Coefficient of Variation 0.4 0.3
0.11 Project 257
1.1 0.45 0.17 0.35 0.37 Projects 257 and 432 differ in expected values, and the book on pg. 283 teaches us that "CV, is a measure of relative dispersion that is useful in comparing the risks of assets with differing expected returns." Since Project 432 has a smaller CV it is the opportunity with lower risk as a smaller CV ...
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This note was uploaded on 04/22/2011 for the course FIN & ACC 504 & 502 taught by Professor Harper&tai during the Spring '11 term at Grand Canyon.
 Spring '11
 Harper&Tai

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