Question # 1
Current investigation has gathered the following financial data from ABC Company. You are required to calculate the following:
Bond: Calculate the value of a Rs. 5,000 (par value) bond paying interest at an
annual coupon interest rate of 10% with 10 years maturity and the required return on similar-risk bonds is currently a 12% annual rate paid annually.
Common stock: Company has recently paid annual dividend of Rs.1.50 per common share this year. The Company expects earnings and dividends to grow at a rate of 7% per year for the anticipated future. What required rate of return for this stock would result in a price per share of Rs. 32?
Question # 2
Using the basic equation of capital asset pricing model (CAPM), solve followings for the unknown.
1. Find the risk free rate of return with a required rate of return of 18% and a beta of 1.50 when the market return is 16%.
2. Find the beta for a stock with a required rate of return of 15% when the risk free rate of return and market risk premium are 10% and 2.5% respectively.
(Show complete calculations and provide all formulas as they carry marks)
Last Date of this assignment is June 13, 2011.
Solution:
Question # 1
1. Value of Bond
PV = Rs. 4,434.9776
2. Required rate of return.
rCE = 11.69 %
Question # 2
1. Risk free rate of return.
Rf = 12 %
2. Beta for stock.
βi = - 0.667
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Calculate the value of a Rs. 5,000 (par value) bond paying interest at anannual coupon interest rate of 10% with 10 years maturity and the requiredreturn on similar?risk bonds is currently a 12% annual rate paid annually.
Value of Bond Vb = INT(PVIFA Kd,N) + M(PVIF Kd,N)
We have M=Maturity value of bond = 5000,
Coupon =10% annual. So INT = 10%*5000 = $500 & Kd=12% = Current Int rate
Period N=10yrs
Putting values we get
Vb=500*(PVIFA 12%,10) + 5000(PVIF 12%,10)
ie Vb = 500*[1/Kd - 1/{Kd(1+Kd)^N}] + 5000*(1/(1+Kd)^N
ie Vb = 500*[1/12% - 1/{12%*(1+12%)^10}] + 5000*(1/(1+12%)^10)
ie Vb = 500*(1/12% - 2.6831) + 5000*0.32197
ie Vb = 2825.11 + 1609.85
ie Vb= $4434.96
So Current Market value of Bond is $4434.96
Using the basic equation of capital asset pricing model (CAPM), solve followingsfor the unknown.
1. Find the risk free rate of return with a required rate of return of 18% anda beta of 1.50 when the market return is 16%.
2. Find the beta for a stock with a required rate of return of 15% when therisk free rate of return and market risk premium are 10% and 2.5%respectively.
1. Find the risk free rate of return with a required rate of return of 18% anda beta of 1.50 when the market return is 16%.
Required return Ks =Risk-free rate + Market riskpremium* beta
So Ks = kRF + Beta (Market Return-kRF) = kRF - kRF*Beta + Beta*Market Return
ie kRF = (Ks - Beta*Mkt Return)/(1-Beta)
we have Ks = 18%, Beta = 1.50, Mkt Return = 16%
SO kRF = (18% -1.5*16%)/(1-1.5) = 6%/0.5 = 12%
SO kRF = 12%...................Ans (1)
2. Find the beta for a stock with a required rate of return of 15% when therisk free rate of return and market risk premium are 10% and 2.5%respectively.
Required return Ks =Risk-free rate + Market riskpremium* beta
So Beta = (Ks - kRF)/MRP
We have Ks = 15%, kRF = 10% & MRP = 2.5%
So Beta = (15%-10%)/2.5% = 2.0.......Ans (2)
Company has recently paid annual dividend of Rs.1.50 per common share this year. The Company expects earnings and dividends to grow at a rate of 7% per year for the anticipated future. What required rate of return for this stock would result in a price per share of Rs. 32?
Do=1.50
groeth rate g =7%
Price expected P1=32
We require Rate of Return Ks
Now we know that Stoock Price P1 = D1/(Ks-g) = Do*(1+g)/(Ks-g)
Solving for Ks, we get
Ks-g = D0(1+g)/P1
ie Ks = g + D0*(1+g)/P1 = 7% + 1.50*(1+7%)/32 = 0.12 = 12%
So required rate of return for this stock is Ks = 12%
