Class 14: APV, Terminal Value

Question 1

WACC Valuation Example (part 1):

• Cashflow before interest and tax in year 1= $100
• Growth rate= 10% per year forever
• β_E=2, r_i=10%, r_m-r_f=5%
• The firm pays tax at 30%
• Firm will keep debt/(debt+equity) ratio at 15% forever
• Debt is risk-free

What’s the formula for the value of the firm?

Answer 1

The value of a levered firm is the present value of the expected discounted cashflows at the WACC.

Question 2

WACC Valuation Example (part 2):

• Cashflow before interest and tax in year 1= $100
• Growth rate= 10% per year forever
• β_E=2, r_i=10%, r_m-r_f=5%
• The firm pays tax at 30%
• Firm will keep debt/(debt+equity) ratio at 15% forever
• Debt is risk-free

Calculate the WACC:

Answer 2

Step 1: calculate the WACC

1. Calculate the WACC= W_D*(1-T_c)*r_D+W_E*r_E
2. Calculate the CAPM, you are going to need it to get the r_E that you need to plug in the formula for the WACC. You can calculate using the Beta of equity.
3. Plug in all the numbers in the WACC formula

Question 3

WACC Valuation Example (part 3):

• Cashflow before interest and tax in year 1= $100
• Growth rate= 10% per year forever
• β_E=2, r_i=10%, r_m-r_f=5%
• The firm pays tax at 30%
• Firm will keep debt/(debt+equity) ratio at 15% forever
• Debt is risk-free

Calculate the value of the company:

Answer 3

This example is a growing perpetuity so plug in all the numbers in the formula for growing perpetuities.

Question 4

Two instances when we cannot use the Equity Beta measured from stock returns:

Answer 4

Reason 1) Firm’s current leverage is different from target leverage

Reason 2) Private firm’s leverage is different from comparable public firms’ leverage

Question 5

Why can’t we use the Equity Beta if firm’s current leverage is different from target leverage?

Answer 5

If the firm is going to have a different target leverage in the future, you cannot use historical data, you can’t use the same Beta of Equity.

This is because if the leverage changes, if the leverage goes up the beta of the company goes up. If the firm has more leverage, risk is higher.

What you do in this case is unlever and relever.

Question 6

Given that measuring β_D ⇒ [r_D= r_f + β_D (r_M-r_f)] is extremally difficult to calculate what are the two alternatives to go around this?

Answer 6

1. Use the YTM (coupon) of the treasury bonds
2. Use the yield on a bond index of equal credit rating (a credit spread over Treasuries) And the credit spread is going to be a credit spread of the credit rating equivalent to the firm. So if the firm is BB rated, you go and find a credit spread for BB. A credit spread is the difference in yield between a U.S. Treasury bond and another debt security of the same maturity but different credit quality.

Question 7

What valuation method is used in venture capital?

Answer 7

The APV (Adjusted Present Value)

The APV, the value of the leveraged firm, is the present value of the same free cashflows that we have learned from the beginning at discounted at (being the weighted average of But without the tax, and then you are going to calculate the present value of the tax shield separately.