Question

1. Suppose that the Matrix Corporation has $120 million of assets, all equity financed, and that the firm has 6 million shares of stock outstanding valued at $20 per share. Now that management has identified investment opportunities requiring $60 million of NEW funds and it can be raised in one of the following 3 ways:

• Strategy 1: Issue $60 million equity.

• Strategy 2: Issue $30 million of equity and borrow $30 million with r = 8%.

• Strategy 3: Borrow $60 million with r = 8%.

a) Suppose the firm’s rate of return is r ∗ = 15%, compute the earnings per share for the 3 financing strategies listed above.

b) Suppose the firm’s rate of return is r ∗ = 10%, compute the earnings per share for the 3 financing strategies.

c) Suppose the firm’s rate of return is r ∗ = 5%, compute the earnings per share for the 3 financing strategies.

Answer 1

As per the given problem,

Requirement of new funds = $60 million.

Share value per share = $20

No.of new shares issued under 3 strategies:

Particulars	Strategy 1	Strategy 2	Strategy 3
New funds raised	$60 million	$60 million	$60 million
New funds raised through equity (a)	$60 million	$30 million	-
Share price(b)	$20	$20	$20
No.of shares issued (c)= a/b	3 million shares	1.5 million shares	0
Existing shares (d)	6 million shares	6 million shares	6 million shares
Total equity shares (e)= c+d	9 million shares	7.5 million shares	6 million shares

Rate of interest for borrowings = 8%

Case 1: Firms rate of return (r) = 15%

Particulars	strategy 1-100% Equity	strategy 2- 50%Equity,50%debt	Strategy 3-100% debt
New funds	$60 million	$60 million	$60 million
Old funds	$120 million	$120 million	$120 million
Total funds(a)	$180 million	$180 million	$180 million
Rate of return (b)	15%	15%	15%
Earnings before interest & taxes(EBIT) c=(a*b)	$27,000,000	$27,000,000	$27,000,000
(-) Interest (Debt * 8%) (d)	-	($2,400,000) ($60 million * 8%)	($4,800,000) ($60 million * 8%)
Earnings before taxes (e=c-d)	$27,000,000	$24,600,000	$22,200,000
(-) Taxes (f)	-	-	-
Earnings after taxes (g)=(e-f)	$27,000,000	$24,600,000	$22,200,000
No.of equity shares (h)	9,000,000 shares	7,500,000 shares	6,000,000 shares
Earnings per share (i)=(g) /( h)	$3 per share	$3.28 per share	$3.7 per share

Case 2: Firms rate of return (r) = 10%

Particulars	strategy 1-100% Equity	strategy 2- 50%Equity,50%debt	Strategy 3-100% debt
New funds	$60 million	$60 million	$60 million
Old funds	$120 million	$120 million	$120 million
Total funds(a)	$180 million	$180 million	$180 million
Rate of return (b)	10%	10%	10%
Earnings before interest & taxes(EBIT) c=(a*b)	$18,000,000	$18,000,000	$18,000,000
(-) Interest (Debt * 8%) (d)	-	($2,400,000) ($60 million * 8%)	($4,800,000) ($60 million * 8%)
Earnings before taxes (e=c-d)	$18,000,000	$15,600,000	$13,200,000
(-) Taxes (f)	-	-	-
Earnings after taxes (g)=(e-f)	$18,000,000	$15,600,000	$13,200,000
No.of equity shares (h)	9,000,000 shares	7,500,000 shares	6,000,000 shares
Earnings per share (i)=(g) /( h)	$2 per share	$2.08 per share	$2.2 per share

Case 3: Firms rate of return (r) = 5%

Particulars	strategy 1-100% Equity	strategy 2- 50%Equity,50%debt	Strategy 3-100% debt
New funds	$60 million	$60 million	$60 million
Old funds	$120 million	$120 million	$120 million
Total funds(a)	$180 million	$180 million	$180 million
Rate of return (b)	5%	5%	5%
Earnings before interest & taxes(EBIT) c=(a*b)	$9,000,000	$9,000,000	$9,000,000
(-) Interest (Debt * 8%) (d)	-	($2,400,000) ($60 million * 8%)	($4,800,000) ($60 million * 8%)
Earnings before taxes (e=c-d)	$9,000,000	$6,600,000	$4,200,000
(-) Taxes (f)	-	-	-
Earnings after taxes (g)=(e-f)	$9,000,000	$6,600,000	$4,200,000
No.of equity shares (h)	9,000,000 shares	7,500,000 shares	6,000,000 shares
Earnings per share (i)=(g) /( h)	$1 per share	$0.88 per share	$0.7 per share