Guermillos_Finance

Week 4 Problems Ch 4: A9: (Rate of Return) After graduation, Adrian moved across the country to Brownsville and bought a small house for $208,000. Bill moved to Columbus a house for $195,000. Four years later they both sold their houses. Adrian netted $256,000 when she sold her house and Bill netted $168,000 on his. A. What annual rate of return did Adrian realize on her house' N=4 R=' PV= -$208000 PMT=0 FV= $256000 PV= C(1/(1+r)⁴ 208000=256000(1/(1+r)⁴ 208000/256000=1/(1+r)⁴ 0.8125=1/(1+r)⁴ (1+r)^4=1/0.8125 ∜(+r)^4=∜1.23077 (1+r)=1.05328 R=1.05328-1 R=0.05328 R=5.33% B. What annual rate of return did Bill realize on his house' N=4 R=' PV= -$195000 PMT=0 FV= $168000 PV= C(1/(1+r)⁴ 195000=168000(1/(1+r)⁴ 195000/168000=1/(1+r)⁴ 1.16071=1/(1+r)⁴ (1+r)⁴=1/1.16071 (1+r)⁴=0.861538 ∜(1+r)=∜0.861538 (1+r)=0.963427 R=0.963427-1 R=-0.036573 R= -3.66% A11: (Calculating the PV and FV of an annuity) Assume an ordinary annuity of $500 at end of each of the next three years. A. What is the present value discounted at 10%' N=3 R=' PV=' R=10% PMT=$500 FV= 0 PV= $500 x [1- 1/(1.10)^3]/.10 PV=$1243.43 B. What is the future value at end of year 3 if cash flows can be invested at 10%' N=3 R=' PV=0 R=10% PMT= $500 FV=' FV=$500x[(1.1)^3-1]/0.1 FV=$1655 Ch 5: A1: (Bond valuation) A $1,000 face value bond has a remaining maturity of 10 years and a required return of 9%. The bonds rate is 7.4%. What is the fair value of this bond' Formula: Present value of maturity + Present value of coupon payment Present value of maturity= 1000(1+9%)^-10 Present value of maturity= 422.41 Present value of coupon payments= 75(1-(1+9%)^-10)/9% Present value of coupon payments= 481.32 Fair value of bond= 422.41 and 481.32= $903.73 A10: (Dividend discount model) Assume RHM is expected to pay a total cash dividend of $5.60 next year and its dividends are expected to grow at a rate of 6% per year forever. Assuming annual dividend payments, what is the current market value of a share of RHM stock if the required return on RHM common stock is 10%' Formula: Current market value of the share= Expected dividend/(required return-growth rate) Current market value of the share= 5.60/(.10-.06)= $140 A12: (Required return for a preferred stock) James River $3.38 preferred is selling for $45.25. The preferred dividend is nongrowing. What is the required return on James River preferred stock' Formula: PV perpetuity= Dividend/Value of the Stock Required return= Dividend/PV Required return= $3.38/$45.25= .0746= 7.46% or rounded up 7.5% A14: (Stock valuation) Let’s say the Mill Due Corporation is expected to pay a dividend of $5.00 per year on its common stock forever into the future. It has no growth prospects whatsoever. If the required return on Mill Due’s common stock is 14%, what is a share worth' Formula: P₀= D1/(r-g) P₀= $5.00/(0.14-0.00)= $35.71 B16: (Interest-rate risk) Philadelphia Electric has many bonds trading on the New York Stock Exchange. Suppose PhilEl’s bonds have identical coupon rate of 9.125% but that one issue matures in 1 year, one in 7 years, and the third in 15 years. Assume that a coupon payment was made yesterday. A. If the yield to maturity for all three bonds is 8%, what is the fair price of each bond' a. N=1*2=2 R=8%/2= 4% PV=' PMT=9.125%(1000/2)=$45.625 FV= $1000 PV= -$1010.61 b. N=7*2=14 R=8%/2=4% PV=' PMT= 9.125%(1000/2)=$45.625 FV=$1000 PV= -$1059.42 c. N=15*2=30 R=8%/2=4% PV=' PMT=9.125%(1000/2)=$45.625 FV=$1000 PV= -$1097.27 B. Suppose that the yield to maturity for all of these bonds changed instantaneously to 7%. What is the fair price of each bond now' a. N=1*2=2 R= 7%/2=3.5% PV=' PMT=9.125%(1000/2)=$45.625 FV=$1000 PV= -$1020.18 b. N= 7*2=14 R= 7%/2=3.5% PV=' PMT=9.125%(1000/2)=$45.625 FV=$1000 PV= -$1116.0 c. N= 15*2=30 R=7%/2=3.5% PV=' PMT= 9.125%(1000/2)=$45.625 FV=$1000 PV= -$1195.42 C. Suppose that the yield to maturity for all of these bonds changed instantaneously again, this time to 9%. Now what is the fair price of each bond' a. N=1*2=2 R=9%/2=4.5% PV=' PMT= 9.125%(1000/2)=$45.625 FV=$1000 PV= -$1.001.17 b. N=7*2=14 R=9%/2=4.5% PV=' PMT=9.125%(1000/2)=$45.625 FV= $1000 PV= -$1006.39 c. N= 15*2=30 R= 9%/2=4.5% PV= ' PMT= 9.125%(1000/2)=$45.625 FV= $1000 PV= -$1010.18 D. Based on the fair prices at the various yields to maturity, is interest-rate risk the same, higher, or lower for longer-versus shorter-maturity bonds. B18: (Default risk) You buy a very risky bond that promises a 9.5% coupon and return of the $1,000 principal in 10 years. You pay only $500 for the bond. A. You receive the coupon payments for three years and the bond defaults. After liquidating the firm, the bondholders receive a distribution of $150 per bond at the end 3.5 years. What is the realized return on your investment' N= 2.5 x3=7.5 R=' PV= -$500 PMT= 9.5%(1000)/2=$47.50 Fv= $150-47.50=$102.50 R= -2.87% APY= (1+r)m-1 APY= (1-0.0287)2-1 APY= -5.66% B. The firm does far better than expected and bondholders receive all of the promised interest and principal payments. What is the realized return on your investment' N= 10(2)=20 R=' PV=-$500 PMT= 9.5%(1000)/2=$47.50 R= 11.05% APY= (1+r)m-1 APY= (1+0.1105)2-1 APY= 23.32% B20: (Constant growth model) Medtrans is profitable firm that is not paying a dividend on its common stock. James Weber, an analyst for A.G. Edwards, believes that Medtrans will begin paying a $1.00 per share dividend in two years and that the dividend will increase 6% annually thereafter. Bret Kimes, one of James’ colleagues at the same firm, is less optimistic. Bret thinks that Medtrans will begin paying a dividend in four years, that the dividend will be $1.00, and that it will grow at 4% annually. James and Bret agree that the required return for Medtrans is 13%. A. What value would James estimate for this firm' P₁=D₂/(r-g)= $1.00/(.13-.06)=14.285 or $14.29 P₀=$14.29/(1+.13)^1= $12.64 B. What value would Bret assign to the Medtrans stock' P₃= D₄/(r-g)= $1.00/(.13-.04)= $11.11 P₀= $11.11/(1+.13)^3= $7.70 Ch 7: C1: (Beta and required return) The riskless return is currently 6%, and Chicago Gear has estimated the contingent returns given here. A. Calculate the expected returns on the stock market and on Chicago Gear stock. Expected return Stock Market= 0.20(-.10%) + 0.35(10%) + 0.30(15%) + 0.15(25%)= 9.75% Expected return Chicago Gear= 0.20(-.15%) + 0.35(15%) + 0.30(25%) + 0.15(35%)= 15.00% B. What is Chicago Gear’s beta' Beta= 0.20(-.10-0.0975)^2 + 0.35(0.10-0.0975)^2 + 0.30(0.15-0.0975)^2 + 0.15(0.25-0.0975)^2= 0.0121 Cov(Chicago, Stock Market)= 0.20(-0.15-0.15)(-0.10-0.0975) + 0.35(0.15-0.15)(0.10-09.0975) + 0.30(0.25-0.15)(0.15-0.0975) + 0.15(0.35-0.15)(0.25-0.0975)= 0.018 Beta= 0.018/0.0121= 1.49 C. What is Chicago Gear’s required return according to CAPM' Required return= 0.06+1.49(0.0975-0.06)=0.1159 or 11.59% | | |Realized Return | |State of the Market |Probability that State Occurs |Stock Market |Chicago Gear | |Stagnant |0.20 |(10%) |(15%) | |Slow Growth |0.35 |10 |15 | |Average Growth |0.30 |15 |25 | |Rapid Growth |0.15 |25 |35 |