Question 1

OldBooks, a book selling company with market assets of $100M, equity beta of 1.2 and D/E=1, is considering expanding into the internet business.

They have the following estimations regarding their potential on-line operations:

a) Next period cash flows of $2M growing in perpetuity at 4%

b) Required investment $15M

c) Equity beta of a comparable internet business with a D/E ratio of 1/3 is 2.

Risk-free rate rf = 4%, and the market premium is 8%. Both OldBooks' and the comparison firm's debt are risk free.

Assume that the tax rate is zero.

 

1) According to these projections, should OldBooks expand into the internet business?

 

2) Suppose that OldBooks decides to enter in the internet business. To do so, it issues securities to obtain the necessary capital for the investment (i.e., it does not use internally generated funds to invest). Find the value of the assets of the combined company after entering in the internet business. (Hint: Given that we are ignoring taxes, you can ignore the financing sources that OldBooks will use to make the required investment)

3) Find the cost of capital (i.e., WACC) of OldBooks before entering in the internet business and after doing so. Does it change? Explain briefly.

1) NPV = $1.67 million 

Since the NPV is greater than 0 , the Oldbook should expand business.

 

2) Value of Assets = $116.67M

 

3) WACC before expansion = 8.8%

WACC after expansion = 16%

Yes WACC will change and it will be higher than before .

 

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Step-by-step explanation

Working Note 1 Calculation of Equity beta for Internet business, 

 

Step 1 

Deleveraging the equity (levered) beta of comparable firm in Internet business to remove effect of leverage 

Unlevered Beta (β_^U,) = β_L/ 1 + [(D/E)*(1-tax)]

β_U = 2 / 1 + (1/3)

β_U = 2/ (4/3) or 2/(1.3333)

β_U = 1.5

 

Step 2 

Releveraging the beta ie adjusting unlevered beta for the leverage level of Oldbook firm

D/E of Oldbook ltd = 1

β_U of comparable pure play (in Internet business) firm = 1.5

 

Levered Beta (β_L) = (β_U^,) * 1 + [(D/E)*(1-tax)]

β_L = 1.5 * (1+1)

β_L = 3

 

So the equity or levered beta of Oldbook's Internet business is 3 which will be used to calculate Cost of equity in Internet business as per CAPM. 

 

Working note 2

Calculation of WACC for Internet business as it will be used as discount rate for calculating NPV 

WACC = (Weight of Debt  * Cost of Debt) + (Weight of equity * Cost of equity)

 

step 1 

Calculation of cost of equity  for Internet business as per CAPM 

 

Cost of Equity or r_e  = Risk free rate + ( Market Risk Premium * Beta )

r_e= 4% + (8*3) = 28%

 

Cost of Debt (rd) = 4%

 

Step 2

Calculation of Weights 

D/E = 1 

As 

V = D + E 

V = 1 + 1 

V = 2

*V is total value of firm 

 

So, 

Weight of Equity = E/V = 1/2 

Weight of Debt = D/V = 1/2 

 

WACC or Cost of capital or r = [(1/2*28%) + (1/2*4%)]

WACC = 14% + 2%

WACC = 16%

 

 

Answer of 1)

To make a decision about expanding the business we will calculate NPV OF it

 

• NPV =- INITIAL INVESTMENT + PRESENT VALUE OF FUTURE CASH FLOWS 
• Initial Investment = $15 million 
• PV of Cash flows 

As it is a perpetuity the PV = Cashflow/ (r - g)

Where

r = Cost of Capital = 16%

g = Growth rate = 4%

PV =  $2 M /(16%-4%)

PV = $2M /12%

PV of future Cashinflows = $16.67 million 

So, 

NPV = - $15 M + $16.67 M 

NPV = $1.67 million 

 

Since the NPV is greater than 0 , the Oldbook should expand business.

 

Answer to 2)

 

Before investing, OldBooks is worth $100M. For the project, it issues new securities worth $15M. Also, the NPV of the project increases the wealth of old shareholders by $1.67M. 

Therefore, the company is worth $100M + $15M + $1.67M = $116.67M after investing in the project. 

 

Answer to 3)

OldBooks has an equity beta of 1.2, and a D/E of 1

 

So weight of both debt and equity in capital structure are 1/2. 

Given that there are no taxes, 

WACC = (Weight of Debt  * Cost of Debt) + (Weight of equity * Cost of equity)

 

For WACC before expansion 

W_E  = 1/2 

W_D = 1/2

Cost of Debt = 4%

COST OF EQUITY = 4% + 1.2 * 8% = 13.6% 

 

WACC before expansion

 =  [(1/2)* 13.6%]) + [(1/2) *4%] = 8.8%

For WACC After expansion 

W_E  = 1/2 

W_D = 1/2

Cost of Debt = 4%

COST OF EQUITY = 4% + ( 3 * 8%) = 28% 

 

WACC after expansion

 =  [(1/2)* 28%]) + [(1/2)*4%] = 16%

 

 

Yes WACC will change and it will be higher than before because Internet business has its own specific risk.  This expansion will result in increase in overall risk of Oldbook. This can be verify with Beta which is the measure of risk., Before expansion Equity beta was 1.2 and after expansion it is 3. Thus increase in risk was reason for increased cost of equity and overall WACC .