Question

Marcus owns a laundromat and Nancy owns a nearby video arcade. Marcus thinks that there are many potential synergies between his business and Nancy’s business. If he buys her out and moves her video arcade into the spare room in the back of his laundromat, he will be able to sell some of the surplus change machines for $10,000 after taxes, and not having to pay rent on two spaces will increase the video arcade EBIT by $24,000 per year for the foreseeable future. Finally, he will be able to partially finance this purchase using a small business loan on very favorable terms. While he normally pays an interest rate of 5.5% when borrowing for his business, the city government is willing to loan him $100,000 for 5 years at 4% to help him make the purchase. Nancy’s cost of equity is 18%, and the tax rate is 40%.

What is the NPV of the subsidized business loan to Marcus?

What is the NPV of all the synergies of this merger?

If Nancy’s video arcade has a market value of $400,000, what is the highest price Marcus could justify offering her for her business?

Answer 1

Calculation of NPV of Business Loan to Marcus
Year	Loan	Interest @ 4%	Tax Savings	Disc @ 5.5%	PV
1		$4,000	$1,600	0.94787	$2,275
2		$4,000	$1,600	0.89845	$2,156
3		$4,000	$1,600	0.85161	$2,044
4		$4,000	$1,600	0.80722	$1,937
5	$1,00,000	$4,000	$1,600	0.76513	$78,350
NPV					$86,762
Calculation of NPV of Synergy
Year	EBIT	Interest	Tax	EAT	Disc @ 18%	Surplus	PV
0					1	$10,000	$10,000
1	$24,000	$4,000	$8,000	$12,000	0.8474576		$10,169
2	$24,000	$4,000	$8,000	$12,000	0.7181844		$8,618
3	$24,000	$4,000	$8,000	$12,000	0.6086309		$7,304
4	$24,000	$4,000	$8,000	$12,000	0.5157889		$6,189
5	$24,000	$4,000	$8,000	$12,000	0.4371092		$5,245
5 Year Onwards	$24,000		$9,600	$80,000	0.4371092		$34,969
				(14400/18%)
NPV							$82,495