Question

Ryan’s Electronics is doing well recently. Ryan’s annual earnings (expected to continue indefinitely) average $5 million. The company has a market beta of 1.5. The market risk premium is 6%, and the rate for government T-bills is 5%. The combined federal-state tax rate is 40%. Ryan’s has $10 million of debt outstanding with a cost of 10%.

It is now the end of 2020, and Ryan would like to retrieve part of his investment from Ryan’s Electronics to start a new business. He decides to issue 1 million shares, 60% of which he will retain, and 40% of which he will offer for sale to the public in an IPO. He is pleased to discover that underwriting fees are waived for his firm. Ryan decides to set the issue price at $15 per share.

1. What cost of capital (cost of equity) should Ryan’s assign?

2. To what level does the stock price rise after the IPO?

3. How much cash is generated by the IPO for Ryan?

Answer 1

Ke: Cost of Equity Kd: Cost of debt

Rf: Risk free rate / Government t bill rate = 5% t: tax rate= 40%

MRP: Market risk Premium= 6% I: effective interest rate =10%

b: beta = 1.5 D: Total debt = $10million

E: Total equity

n: Total no. of shares = 1million

1) As per CAPM model:

Ke = Rf+b(MRP)

= 5%+ 1.5*(6%)

= 14%

Kd = 10%(1-40%)

= 6%

D= $10 million

E= $15 million

Kc:Cost of capital = Ke*[E/(D+E)] + Kd*[D/(D+E)]

=14%* (15/25) + 6%*(10/25)

= 10.8%

2)Since income is expected to continue till perpetuity : using perpetuity formula

Value of the firm = Income/Kc

= $5million/10.8%

= $46.3 million

Also,

Value of the firm = Market value of debt + Market value of debt

therefore,

46.3= Post Ipo price of share * no of shares + 10

x: post ipo price of share = $(46.3-10)million/ 1 million= $36.3 ( this is the level to which price will grow post ipo)

3) Cash generated = 60 % * Total cash generated

= 0.60*$(36.3-15)milion

=$12.78 million