Question

You are considering three investments. The first is a bond that is selling in the market at $1,200. The bond has a $1,000 par value, pays interest semi-annually at 10%, and is scheduled to mature in 10 years. For bonds of this risk class you believe that a 12% rate of return should be required. The second investment that you are analysing is a preference share ($100 par value) that sells for $95 and pays an annual dividend of $10. Your required rate of return for this share is 10%. The last investment is an ordinary share ($35 par value) that recently paid

a $5 dividend. The firm's earnings per share have increased from $4 to $8 in 10 years, which also reflects the expected growth in dividends per share for the indefinite future. The share is selling for $40, and you think a reasonable required rate of return for the share is 20%.

Required:

1. Calculate the value of each security based on your required rate of return.
2. Calculate the expected return of each security.

Answer 1

a

Bond

face value =1000

annual coupon rate = 10%

semiannual coupon amount = 1000*10%/2 = 50

years to maturity =10

semiannual years to maturity (n) =10*2 = 20

required return = 12%

semiannual rate of return (i) =12%/2 = 6%

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

50*(1-(1/(1+6%)^20))/6%) + (1000/(1+6%)^20)

=885.3007878

So bond price on basis of required rate of return is $885.30

Preferred stock

Annual dividend paid = 10

required rate of return (i) =10%

Price of preferred stock = D/i

=10/10%

=100

So Price of preferred stock is $100 based on required rate of return

Common stock

Last paid dividend (D0)=5

Required rate of return (ke) =20% or 0.20

EPS last value = 4

EPS increased value = 8

number of years gap (n) =10

Growth rate formula (g) = ((future dividend/last dividend)^(1/n))-1

=((8/4)^(1/10))-1

=0.07177346254

Price of stock (p0) = D0*(1+g)/(ke-g)

=5*(1+0.07177346254)/(0.20-0.07177346254)

=41.79218607

So price of common stock is $41.79 based on required return

b

Bond

Selling price or bond price = 1200

face value =1000

annual coupon rate = 10%

semiannual coupon amount = 1000*10%/2 = 50

years to maturity =10

semiannual years to maturity (n) =10*2 = 20

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

1200 =(50*(1-(1/(1+i)^20))/i) + (1000/(1+i)^20)

i is the semiannual expected rate of return at which bond price is equal to $1200

Assume i is 3.5%

bond price =(50*(1-(1/(1+3.5%)^20))/3.5%) + (1000/(1+3.5%)^20)

=1213.18605

Assume i is 3.60%

bond price =(50*(1-(1/(1+3.6%)^20))/3.6%) + (1000/(1+3.6%)^20)

=1197.185219

interpolation formula = lower rate +((uper rate - lower rate)*(Uper price - bond actual price)/(uper price - lower price))

3.5% +((3.6%-3.5%)*(1213.18605-1200)/(1213.18605-1197.185219))

=0.03582408532

Annual expected rate of return =0.03582408532*2

=0.07164817064 or 7.16%

So Expected rate of return on bonds is 7.16%

Preferred stock

Annual dividend =10

market price =95

Expected rate of return of preferred stock = dividend/market price

=10/95

=0.1052631579 or 10.53%

So expected return on preferred stock is 10.53%

Common stock or equity

last dividend paid (D0)= 5

Market price of share (P0)= 40

EPS last value = 4

EPS increased value = 8

number of years gap (n) =10

Growth rate formula (g) = ((future dividend/last dividend)^(1/n))-1

=((8/4)^(1/10))-1

=0.07177346254

Expected rate of return of stock (ke) formula =( D0*(1+g)/Po) + g

=(5*(1+0.07177346254)/40)+0.07177346254

=0.2057451454

or 20.57%

So expected rate of return of ordinary stock is 20.57%

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