The firm just restructured its debt at no additional cost so that all the liabil

Question

The firm just restructured its debt at no additional cost so that all the liabilities are in the form of a single bond maturing in exactly 5 years. This was done in such a manner that the new debt was just enough to retire all current liabilities and the former long term debt. That is, your Balance Sheet contains only Owner’s Equity and Long Term Debt. The current estimate is that the Market Value of the firm is $29.75MM and that its standard deviation is roughly 23%.

(a) What are the Market Values of Equity and Debt? Use the same risk free rate of 10%

In light of the debt restructuring, one of the largest shareholders in the company asked to speak to you and the CEO to discuss a few opportunities she sees in the market that could benefit all the company stakeholders. The investor asked for your help regarding two mutually exclusive investments of $5MM that would be financed exclusively with a bond with similar terms to the outstanding long term debt. The cost of issuing such bond is estimated at 5% of the notional value and it is expected to raise exactly the $5MM needed. The cash flows generated by both investments have present values of $7.5MM.

(b) The first investment proposed is such that it will consolidate operations and make the company less risky. The new estimated standard deviation of assets is around 18%. What are the new Market Values of Equity and Debt under this investment?

(c) The second investment opportunity makes the company substantially riskier; the new estimated standard deviation of assets is 75%. What are the new Market Values of Equity and Debt under this investment?

(d) Comment on the results obtained in (b) and (c). Namely, is it the case that all stakeholders will benefit if the firm engages in one of the investments above?

Income Statement 2016 Sales $43,000,000 Taxes: 40% COGS $30,000,000 Other expenses $5,000,000 Shares Outstanding 1,000,000 Depreciation $2,000,000 Market-to-Book Ratio 1.25 EBIT $6,000,000 Interest $2,000,000 Taxable income $4,000,000 Taxes (40%) $1,600,000 Net income $2,400,000 Dividends $600,000 Add to RE $1,800,000 Balance Sheet, Dec 31, 2016 Assets Liabilities & Owners’ Equity Current Assets Current Liabilities Cash $500,000 Accounts Payable $1,000,000 Accounts Receivable $1,000,000 Notes Payable $3,000,000 Inventory $2,000,000 Total CL $4,000,000 Total CA $3,500,000 Long Term Debt $10,000,000 Fixed Assets Owners’ Equity Net PP&E $25,000,000 Common Stock $6,500,000 Retained Earnings $8,000,000 Total Equity $14,500,000 Total Assets $28,500,000 Total L & OE $28,500,000

Explanation / Answer

a)

Rate of Debt = Interest / Principal x 100 = $2,000,000 / $10,000,000 x 100 = 20%. Here, we have considered the Interest amount prior to tax, taken from the Income Statement.  

However, it is more accurate to consider the after tax cost of debt for financial analysis since a firm gains on tax savings on debt. Hence, the after tax cost of debt (Kd) = Rate of Debt (1-Tax Rate) = 20 (1-0.40) = 12%.

At no additional cost, i.e. Cost of Debt remaining the same, new Debt = Value of Current Liabilities + Long Term Debt = $4,000,000 + $10,000,000 = $14,000,000

Market Value of Debt = C[(1 – (1/((1 + Kd)^t)))/Kd] + [FV/((1 + Kd)^t)]

Where C is the interest expense = 12% x $14,000,000 = $1,680,000

Kd is the current cost of Debt = 12%

t is the weighted average maturity = 5 years

FV represents the total debt = $14,000,000

Market Value of Debt = $1,680,000[(1 – (1/((1 + 0.12)^5)))/0.12] + [$14,000,000/((1 + 0.12)^5)] = $14,000,000

Market Value of the Firm (given) = $29,750,000

Therefore, Market Value of Equity = $15,750,000

b,c,d)

Evaluating the two Investment Opportunities:

Option 1-

PV of future cash inflows = $7.5MM

Standard Deviation (risk) = 18%

Option 2 -

PV of future cash inflows = $7.5MM

Standard Deviation (risk) = 75%

The question states that the two mutually exclusive investments of $5MM would be financed exclusively with a bond with similar terms to the outstanding long term debt (5 yrs, 12%). The cost of issuing such bond is estimated at 5% of the notional value and it is expected to raise exactly the $5MM needed.

Therefore, all variables except risk being similar, we should pick the less risky option 1.  

Market value of Debt = $2,280,000[(1 – (1/((1 + 0.12)^5)))/0.12] + [$19,000,000/((1 + 0.12)^5)] = $16,837,134

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