Question

EGI is a firm in the gaming sector with 350 million of equity and $175 million of debt in its capital structure (market values). It has 10 million shares outstanding with a 12% unlevered cost of capital and 4% risk free interest rate on its debt. The corporate tax rate is 30%. The firm is planning to come up with a new handheld video game that is expected to have an initial investment of $25 million with project having the same business risk as that of EGI’s existing assets. The new investment is expected to generate annual EBIT of $8 million which is expected to grow at 2% per annum until perpetuity?

a.  EGI initially proposes to fund the new project by issuing equity. If investors were not expecting this investment, and if they share EGI’s view of the project’s profitability, what will the share price be once the firm announces the project plan?

b.  Suppose investors think that the EBIT from EGI’s new project will be only $3 million per year without any growth (i.e. $3 million every year to perpetuity). What will the share price be in this case? How many shares will the firm need to issue?

c.  Suppose EGI issues equity as in part (b). Shortly after the issue, new information emerges that convinces investors that management was, in fact, correct regarding the cash flows from the new project. What will the share price be now? Why does it differ from that found in part (a)? How much will the old and new shareholders gain after the new information arrives?

d.  Suppose EGI instead finances the expansion with a $25 million issue of permanent risk-free debt. If EGI undertakes the expansion using debt, what is its new share price once the new information comes out?

Answer 1

Unlevered cost of capital = Unlevered cost of equity = 12 %

MM Proposition 2 with taxes :

Levered cost of equity = Unlevered cost of equity + D/E * (Unlevered cost of equity - cost of debt)*(1-tax rate)

12 %+( (175 / 350)*(12% -4%)*(1-30%))

14.80%

Therefore , Cost of Capital ( WACC )

(175/(175+350)) * ( 1- 0.3) * ( 4%) + (350/(175+350)) * ( 14.8%)=

10.80%

a.If the firm wishes to raise 25 million wholely by issuing equity :

New value of equity = 375 million

Therefore, applying the WACC formula for this new proportion of debt and equity , the new cost of capital is 10.98 %

(175/(175+375)) * ( 1- 0.3) * ( 4%) + (375/(175+375)) * ( 14.8%)=

10.98%

NPV of the project at the above WACC,

-25+(8/(10.98%-2%))=

64.08686

mlns.

So, value added by the project = 64.08686 million

New value of equity = 350 + 64.08686

414.08686

Mlns.

The firm sells equity worth 25 million at the initial price ( of 350/10 = 35 )

Therefore , the number of shares sold = 25million / 35

714285.71

The number of outstanding shares now = 10million + 714285.71

10714286

Therefore the price of each share = value of equity/ total number of outstanding shares

= 414.08686 / 10714286

38.65

b ) In case of EBIT being $ 3 mln. Without any growth,

NPV=-25+(3/10.98%)=

2.322404

mlns.

Therefore , new value of the firm would be 350 + 2.322404 million

352.322404

mlns.

The investors would expect the shares to be diluted in the process of raising money

The total number of shares once 25 million is raised will be same as above ( in the investors' minds ) = 10714286

Therefore , the investors would expect the price to be = firm value / number of outstanding shares

New price =352322404/10714286=

32.88

Now once the firm wants to raise money , they would have to raise 25 million by selling shares at this new price

Therefore they would have to sell $ 25 million / 32.8832 shares

760267

shares

c..Now after raising money at this new price, the number of outstanding shares=10760267

Once the investors realise that the management's predictions were right ,

The firm value = same as in case a. ie. $ 414 0866 mlns

Therefore , value of each share = firm value / total number of shares

414.08686*1000000/10760267=

39.45

This will be the new price of each share

Each old investor would make 39.45 - the original price of each share

39.45 - 38.65=

0.8

per share

Each new investor would make 39.45 - price of share in b

39.45-32.88=

6.57

per share

d.If the firm raises 25 million solely by borrowing ,

New Debt level =175+25=200 million

Applying WACC formula to get the cost of capital , the new cost of capital is

(200/(200+350))*( 1- 0.3)*( 4%)+ (350/(200+350))*(14.8%)=

10.44%

NPV of the Investment=-25+(8/(10.44%-2%))=

69.786730

So,the new equity value = 350+69.79=$ 419.79 mlns

Number of shares outstanding is the same as original = 10 million

Therefore , the new price of each share = 419.79 mlns./10 mlns .=

$41.97