HOMEWORK SET IV

I XYZ Company had the following income statement last year:

Revenue 1,000,000Variable costs 600,000Rent 50,000Depreciation 40,000

It was capitalized with 1,250,000 owners’ equity, 600,000 bank loans, for which it pays 6%. It has 800,000 in equipment and 50,000 in cash. Assume a 35% corporate profits tax rate.

A] Calculate XYZ’s (AT)ROE and coverage ratio.

EBITDA=Revenue-Variable costs-Rent=1,000-600-50=350 (thousands)EBIT=EBITDA-Depreciation=350-40=310 (thousands)EBT=EBIT-Interest=310-600*6%=274 (thousands)Net Income=EBT-Tax=274*(1-0.35)=178.1 (thousands)ROE=Net Income/Equity=178.1/1250=14.248%Coverage ratio=EBITDA/Interest=350/(600*6%)=9.72

B] For this year XYZ borrows an additional $400,000 from its bank at the same interest rate in order to purchase that amount more in equipment and expand operations. As a result, revenue and variable costs both increase 20%. And depreciation rises accordingly. Calculate the new ROE and coverage ratio.Depreciation was 5% because 40k/800k, and so it’s still 5% of the new number. Equity didn’t increase even though we bought new equipment, b/c we didn’t gain or lose equity, but gained debt and equipment. Revenue=1,000*1.2=1200 (thousands)Variable cost=600*1.2=720 (thousands)Rent=50 (thousands)EBITDA= Revenue-Variable costs-Rent=1200-720-50=430 (thousands)Depreciation=((800+400)/800)*40=60 (thousands)EBIT= EBITDA-Depreciation=430-60=370 (thousands)EBT=EBIT-Interest=370-(600+400)*6%=310 (thousands)Net Income=EBT-Tax=310*(1-0.35)=201.5 (thousands)ROE=Net Income/Equity=201.5/1250=16.12%Coverage ratio=EBITDA/Interest=430/((600+400)*6%)=7.17

C] Instead of funding the new equipment as in B], the company borrows 200,000 and raises 200,000 in new equity. Redo the calculations.Revenue=1,000*1.2=1200 (thousands)

Variable cost=600*1.2=720 (thousands)Rent=50 (thousands)EBITDA= Revenue-Variable costs-Rent=1200-720-50=430 (thousands)Depreciation=((800+400)/800)*40=60 (thousands)EBIT= EBITDA-Depreciation=430-60=370 (thousands)EBT=EBIT-Interest=370-(600+200)*6%=322 (thousands)Net Income=EBT-Tax=322*(1-0.35)=209.3 (thousands)ROE=Net Income/Equity=209.3/(1250+200)=14.43%Coverage ratio=EBITDA/Interest=430/((600+200)*6%)=8.96

D] XYZ does not expand operations, so does not need to borrow more funds. Instead, to increase ROE, it borrows 200,000 and returns that amount to the equity holders. Redo the ROE and coverage calculations.EBITDA=Revenue-Variable costs-Rent=1,000-600-50=350 (thousands)EBIT=EBITDA-Depreciation=350-40=310 (thousands)Debt=600+200=800 (thousands)EBT=EBIT-Interest=310-800*6%=262 (thousands)Net Income=EBT-Tax=262*(1-0.35)=170.3 (thousands)Equity=1250-200=1050 (thousands)ROE=Net Income/Equity=170.3/1050=16.22%Coverage ratio=EBITDA/Interest=350/(800*6%)=7.29

II Under the original assumptions for XYZ Company in question I, the stock market has given it a market capitalization of 1,500,000 (100,000 shares outstanding). A hedge fund is formed to purchase 1,000 shares of XYZ. The fund’s leverage ratio is 4:1. What is its book value?

Book Value per share=1250/100=12.5

Market Value per share=1500/100=15

Payment of hedge fund=15*1,000=15,000

The book value of the fund=15,000*1/4=3750

XYZ now decides to employ strategy B above. As a result, its stock price appreciates 10%. The hedge fund marks-to-market. What is the hedge fund’s book value under B compared to its original? What is XYZ’s book value under B compared to its original?

Market Value per share=15*1.1=16.5

Payment of hedge fund=16.5*1,000=16,500

The book value of the fund=16,500*1/4=4125

So the hedge fund’s book value under B increase by (12,375-11,250)=1,125 compared to its original

The XYZ’s book value = (100,000-1000)*12.5+1000*16.5=1,237,500+16,500=1,254,000

The change of XYZ’s book value = 1,254,000-1,250,000=4,000

Another way to calculate the book value of XYZ is:

The change of XYZ’s book value = (15*1.1-12.5)*1000=4,000

III

A] Rutgers Rotisserie (RR) had $50 million in owners’ equity at the start of 2015. A million shares were outstanding, with a price at 20% premium to book value. What were its market value and book value; market value-per-share and book value-per-share?

Book value = 50 millionBook value per share = 50 million /1 million= 50Market value per share = 50 * 1.2 = 60Market value = 60*1million = 60 million

B] RR retained $5 million of its after-tax profits in 2015. What were its market value and book value; market value-per-share and book value-per-share as of Jan 2 2016, assuming same relationship between market and book value-per-share?Book value = 50 + 5 = 55 millionBook value per share = 55 million /1 million= 55Market value per share = 55 * 1.2 = 66Market value = 66 * 1 million = 66 million

C] Given the situation in B], RR issues an additional 100,000 shares on Jan 3 at a 2% discount to its Jan 2 price. What are its market value and book value; market value-per-share and book value-per-share?Market value per share = 66 * (1-2%) = 64.68Book value = 55 million + 64.68 * 100,000 = 61.468 millionBook value per share = 61.468 million / 1.1 million = 55.88