Please give a solution with fomula not excel, thank you. Consider a firm F with

Question

Please give a solution with fomula not excel, thank you.

Consider a firm F with the following features Firm F will close its business at time 20 Earnings before interest and taxes (EBIT) is 200 at time 1, 400 at time 2, and then it grows every year at a rate of 5% until time 20. Amortization is worth 100 at time 1, 150 at time 2, and then it decreases every year at a rate of 6% until time 20. Capital expenditure (CAPEX) is 40 at time 1, 2, . 20. . Net working capital (NWC) is 100 today, 150 at time 1, and 280 at time 2. From time 3 to time 20, change in NWC is worth 80. Bankruptcy costs are expected to be 500 at time 20. ·The cost of unlevered equity is 7%. . Debt consists of a bond with face value 1000. Coupon payments are made at time 2, , 20. Today's value of the bond is 1000, Cost of debt is 1%. ·The corporate tax rate is 20% Remark: The notation t+ stands for time t right after cash-flows have been paid. 1) What is the coupon rate of the bond (cB)? 2) What is the value, at time 2+, of firm F's tax shields (TS2+)? 3) What is the value, at time 2+, of a security that pays the EBIT ( BIT)? Hint: Discount cash-flows using the cost of unlevered equity. 4) What is the value, at time 2+, of a security that pays the amortization (V ")? Hint: Discount cash-flows using the cost of unlevered equity. 5) What is the value, at time 2+, of a security that pays the CAEXVPEX)? Hint: Discount cash-flous using the cost of unlevered equity.

Explanation / Answer

1. Face Value of the Debt =$1000

Market Value of the Debt = $1000

Cost of Debt = 1%

Time to Maturity = 20 years

So, Market Value of the Debt = Coupon Interest* pvifa (cost of debt%, n years) + Face Value of Debt * (cost of debt%, n years)

Or, 1000 = coupon interest * pvifa (1%, 20yrs) + 1000* pvif (1%, 20yrs)

Or, 1000 = coupon interest* (18.05) + 1000*0.8195

Or, 1000-819.50 = coupon interest * (18.05)

Or, 180.50/18.05= coupon interest

Or, coupon interest = $10

Again Coupon Interest = Face Value * Coupon Rate

Or, $10 = $1000* Coupon Rate

Or, Coupon rate = 1%

2. At (time 2+) value of Tax shields would be; Tax Shields on Amortization + Tax Shields on Interest on Debt

Interest on Debt => Face Value of Debt* Interest cost of Debt = $1000*1% = $10

Since corporate Tax rate is 20%, so Tax shields on Interest rate would be $10*20% = $2

(Tax shields only looks at those values which reduces the income taxes)

Amortization for the (time 2+) is $150 so tax shields on amortization would be $150*20% = $30

So the total value of Firm’s Tax Shields on (time 2+) is ($30+$2= $32)

3. At (time 2+) value of EBIT at cost of unlevered equity would be;

In the second Year EBIT was $400

Cost of unlevered Equity is 7%

So, EBIT value at (time 2+) = EBIT/ (1+cost of unlevered equity) ^2

Or, EBIT value at (time 2+) = $400/ (1.07) ^2 = $349.38

4. At (time 2+) value of Amortization at cost of unlevered equity would be;

In the second Year Amortization was $150

Cost of unlevered Equity is 7%

So, Amortization value at (time 2+) = Amortization/ (1+cost of unlevered equity) ^2

Or, Amortization value at (time 2+) = $150/ (1.07) ^2 = $131.02

5. At (time 2+) value of CAPEX at cost of unlevered equity would be;

CAPEX is the initial Expenditure the company makes at 0th Year but in this case it is remaining $40 from (1 to 20 years)

So, CAPEX value at (time 2+) = CAPEX/ (1+cost of unlevered equity) ^2

Cost of unlevered Equity is 7%

Or, CAPEX value at (time 2+) = $40/ (1.07) ^2 = $34.94.

In General CAPEX value is made at the 0th Year so it's value would remain the same since ; CAPEX/ (1+cost of unlevered equity)^0 is the formula and anything divided by something whose power is "0" would inculcate a value of 1 so CAPEX would yield the same value of $40.

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