Question

marry told you that she has $10,000 and wants to make an investment. However, she does not know which security to purchase. You have decided to give her three alternatives: corporate bond, preferred stock and common stock:

• Corporate Bond of Trusted Bank (par value $1000, interest payments 6.35%, maturity 5 years, market price $1020, required rate of return 5%);
• Preferred Stock of Best Equipment, Inc. (dividend $2.63, market price $26.25, required rate of return 8%);
• Common Stock of Great Resorts, Inc. (par value $5, the most recent dividend $1.60, EPS (earnings per share) grew from $2.23 to $3.30 in past 5 years (growth 8.15%), market price $52, required rate of return 12%).

You have also explained your aunt that required rate of return is strictly linked to the risk of each security.

Question 3. Answer the following questions:

1. Calculate the value of each security.
2. Which investment should your aunt select? Why?
3. Assume that earnings of Great Resorts, Inc. would grow at 1 percent above the historical growth rate. How does this affect your answers to parts (a) and (b)?  
4. What required rates of return would make your aunt indifferent to all three options?

Answer 1

a) Value of Bond =63.5/1.05+63.5/1.05^2+....+63.5/1.05^5+1000/1.05^5

=63.5/0.05*(1-1/1.05^5)+1000/1.05^5 = $1058.45

As compared to market price of $1020, it gives an excess value of $38.45 on investment of $1020

So, on investment of $10000, excess value =38.45/1020*10000 =  $376.96

Value of Preferred Stock = Dividend/required rate = $2.63/0.08 =$32.875

As compared to market price of $26.25, it gives an excess value of $6.625 on investment of $26.25

So, on investment of $10000, excess value = 6.625/26.25*10000 = $2523.81

Value of Stock = D0*(1+g)/(r-g) = 1.6*1.0815/(0.12-0.0815) =$44.95

As the market price is higher , this option cant be considered

b) Aunt would probably select the Bond as it is the safest of all although the return on it is the least. If she is more risk taking, she would select the Preferred stock which generates higher excess value whereas the Stock is overvalued.

c) If earnings of Great Resorts, Inc. would grow at 1 percent above the historical growth rate,

Value of Stock = D0*(1+g)/(r-g) = 1.6*1.0915/(0.12-0.0915) =$61.28

As compared to market price of $52, it gives an excess value of $9.28 on investment of $52

So, on investment of $10000, excess value = 6.625/26.25*10000 = $1784.076

The Stock is now undervalued, however, Aunt will still likely select the Bond or if she is more risk taking, the Preferred stock. So, choice does not change.

d) When the required rates are exactly as per the market expectations resulting in market prices, she will be indifferent

When the required rate from bond is such that Bond price = 1020

i..e when the required rate is 5.8768% (Use hit and trial method or Solver)

For the preferred stock, when required rate = 2.63/26.25 =10.02%

and for the stock , when required rate = D1/P0+g = 1.7304/52+0.0815 = 0.033277+0.0815 =11.48%