MGT201 ASSIGNMENT # 2 SOLUTION
Wednesday, June 30, 2010 Posted In FM , MGT Edit This
Here is the proposed solution.
Solution Q # 1 (Stock Beta)
Given:
Current price per share of common (Po*) = 80
Expected dividend per share next year (DIV1) = 5
Constant annual dividend growth rate (g) = 7%
Risk free rate of return (rRF) = 6%
Return on market portfolio (rM) = 10%
Beta (βA) =?
We know that:
Po* = DIV1 / {rRF + (rM - rRF) * βA – g}
80 = 5/ {6% + (10% - 6%)* βA – 7%}
80 = 5/ {6% + (4%)* βA – 7%}
80 = 5/ {(4%)* βA – 1%}
{(4%)* βA – 1%}*80 = 5
{(4%)* βA – 1%} = 5/80 = 0.0625
(4%)* βA = 0.0625 + 1% = 0.0625 + 0.01 = 0.0725
βA = 0.0725/4% = 0.0725/ 0.04 = 1.8125 Ans
Solution Q # 2 (Bond Valuation)
a) Given Data (Bond A):
Coupon payment per annum © = 2000*10%= 2000* 0.1 = 200
Required rate of return (rD) = 14% = 0.14
Par value or face value (PAR) = 2000
Maturity Period or Term = 3 Years
Bond Price (PV) =?
We know that:
PV = C1/ (1+rD) + C2 /(1+rD) 2 + C3 / (1+rD)3 + PAR / (1+rD)3
PV = 200/ (1 + 0.14) + 200/ (1 + 0.14)2 + 200/ (1+ 0.14)3 + 2000/ (1 + 0.14)3
PV = (200/1.14) + (200/ 1.2996) + (200/1.4815) + (2000/ 1.4815)
PV = 175.4386 + 153.8935 + 134.9983 + 1349.9831
PV = 1814.3135 (Bond A)
b) Given Data (Bond B):
Coupon payment per annum © = 2000*10%= 2000* 0.1 = 200
Required rate of return (rD) = 14% = 0.14
Par value or face value (PAR) = 2000
Maturity Period or Term = 5 Years
Bond Price (PV) =?
We know that:
PV = C1/ (1+rD) + C2 /(1+rD) 2 + C3 / (1+rD)3 + C4/(1+rD)4 + C5/(1+rD)5+ PAR / (1+rD)5
PV = 200/ (1+ 0.14) + 200/(1+0.14)2 + 200/(1+0.14)3 + 200/ (1+0.14)4 + 200/(1+0.14)5
+2000/(1+0.14)5
PV = (200/1.14) + (200/ 1.2996) + (200/1.4815) + (200/1.6889) + (200/1.9254) + 2000/1.9254
PV = 175.4386 + 153.8935 + 134.9983 + 118.4203 + 103.8745 + 1038.7452
PV = 1725.3704 (Bond B)
c) If ABC wants to minimize the Interest Rate Risk, which bond should be purchased? Why?
Answer:
When interest rate rises, bond price falls. Inversely, when interest rate falls, bond price rises. The longer the maturity period, the greater is the interest rate risk.
According to LAWARENCE J. GITMAN FINANCIAL MANAGEMENT (12th EDITION) interest rate risk is the market interest rate fluctuation that directly affects the bond’s value that have constant coupon payment, to reduce the fear of market interest risk diversify the portfolio as it can be spread and chose the bond with shorter duration.
So, ABC should purchase bond A having the shorter maturity period than bond B.
Here price of bond A is 1814.3135 is greater than the price of bond B, which is 1725.3704
Solution Q # 1 (Stock Beta)
Given:
Current price per share of common (Po*) = 80
Expected dividend per share next year (DIV1) = 5
Constant annual dividend growth rate (g) = 7%
Risk free rate of return (rRF) = 6%
Return on market portfolio (rM) = 10%
Beta (βA) =?
We know that:
Po* = DIV1 / {rRF + (rM - rRF) * βA – g}
80 = 5/ {6% + (10% - 6%)* βA – 7%}
80 = 5/ {6% + (4%)* βA – 7%}
80 = 5/ {(4%)* βA – 1%}
{(4%)* βA – 1%}*80 = 5
{(4%)* βA – 1%} = 5/80 = 0.0625
(4%)* βA = 0.0625 + 1% = 0.0625 + 0.01 = 0.0725
βA = 0.0725/4% = 0.0725/ 0.04 = 1.8125 Ans
Solution Q # 2 (Bond Valuation)
a) Given Data (Bond A):
Coupon payment per annum © = 2000*10%= 2000* 0.1 = 200
Required rate of return (rD) = 14% = 0.14
Par value or face value (PAR) = 2000
Maturity Period or Term = 3 Years
Bond Price (PV) =?
We know that:
PV = C1/ (1+rD) + C2 /(1+rD) 2 + C3 / (1+rD)3 + PAR / (1+rD)3
PV = 200/ (1 + 0.14) + 200/ (1 + 0.14)2 + 200/ (1+ 0.14)3 + 2000/ (1 + 0.14)3
PV = (200/1.14) + (200/ 1.2996) + (200/1.4815) + (2000/ 1.4815)
PV = 175.4386 + 153.8935 + 134.9983 + 1349.9831
PV = 1814.3135 (Bond A)
b) Given Data (Bond B):
Coupon payment per annum © = 2000*10%= 2000* 0.1 = 200
Required rate of return (rD) = 14% = 0.14
Par value or face value (PAR) = 2000
Maturity Period or Term = 5 Years
Bond Price (PV) =?
We know that:
PV = C1/ (1+rD) + C2 /(1+rD) 2 + C3 / (1+rD)3 + C4/(1+rD)4 + C5/(1+rD)5+ PAR / (1+rD)5
PV = 200/ (1+ 0.14) + 200/(1+0.14)2 + 200/(1+0.14)3 + 200/ (1+0.14)4 + 200/(1+0.14)5
+2000/(1+0.14)5
PV = (200/1.14) + (200/ 1.2996) + (200/1.4815) + (200/1.6889) + (200/1.9254) + 2000/1.9254
PV = 175.4386 + 153.8935 + 134.9983 + 118.4203 + 103.8745 + 1038.7452
PV = 1725.3704 (Bond B)
c) If ABC wants to minimize the Interest Rate Risk, which bond should be purchased? Why?
Answer:
When interest rate rises, bond price falls. Inversely, when interest rate falls, bond price rises. The longer the maturity period, the greater is the interest rate risk.
According to LAWARENCE J. GITMAN FINANCIAL MANAGEMENT (12th EDITION) interest rate risk is the market interest rate fluctuation that directly affects the bond’s value that have constant coupon payment, to reduce the fear of market interest risk diversify the portfolio as it can be spread and chose the bond with shorter duration.
So, ABC should purchase bond A having the shorter maturity period than bond B.
Here price of bond A is 1814.3135 is greater than the price of bond B, which is 1725.3704
