Assume an all equity firm has been growing at a 15 percent annual rate and is ex
ID: 2818215 • Letter: A
Question
Assume an all equity firm has been growing at a 15 percent annual rate and is expected to continue to do so for 3 more years. At that time, growth is expected to slow to a constant 4 percent rate. The firm maintains a 30 percent payout ratio, and this year's retained earnings net of dividends were $1.4 million. The firm's beta is 1.25, the risk-free rate is 8 percent, and the market risk premium is 4 percent. If the market is in equilibrium, what is the market value of the firm's common equity (1 million shares outstand¬ing)?
Explanation / Answer
Step 1:
Using CAPM equation:
Cost of equity = Risk free rate + Beta x Market risk premium
Cost of equity = 8% + 1.25 x 4%
Cost of equity = r = 13%
.
Step 2:
Dividend = Retained earnings / (1-Payout ratio) x Payout ratio
Dividend = 1.4 / (1-30%) x 30%
Dividend = $0.60 million
Step 3:
Answer is > ~ $9.18 million
Year
Growth
Dividend Cash flow
Price of stock*
Net cash inflow
Discounting = Df
Present value
n
G
Dn = D0*(1+g)^n
P
NF = Dn + P
Df = 1/(1+13%)^Year
=NF*Df
1
15.00%
0.6900
0.690
0.884956
0.611
2
15.00%
0.7935
0.794
0.783147
0.621
3
15.00%
0.9125
10.54
11.469
0.693050
7.949
Total = Value of stock today =
9.18
Working:
Price of stock* at 3rd year = Dividend at 3rd year x (1+Revised growth rate)/(Cost of equity or Df – Revised growth rate)
Price of stock* at 3rd year = 0.9125 x (1+4%)/(13% - 4%) = $10.5444444 million
Year
Growth
Dividend Cash flow
Price of stock*
Net cash inflow
Discounting = Df
Present value
n
G
Dn = D0*(1+g)^n
P
NF = Dn + P
Df = 1/(1+13%)^Year
=NF*Df
1
15.00%
0.6900
0.690
0.884956
0.611
2
15.00%
0.7935
0.794
0.783147
0.621
3
15.00%
0.9125
10.54
11.469
0.693050
7.949
Total = Value of stock today =
9.18
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