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# PROBLEM 1 Given Cost of capital Initial growth forecast Revised growth forecast Capital Raised Initially Shares issued to D&amp;amp;B Follow-up

Problem – 1 (25%)
Start-up company VacationHoliday went through the first round of financing in January 2009. At
that time, the after-tax cash flow forecast looked as follows:
Jan 2009 Jan 2010 Jan 2011 Jan 2012 Jan 2013 and onwards
(\$ 10,000,000) (\$ 2,000,000) \$ 3,000,000 \$ 5,000,000 \$5,500,000 (10%
annual growth)
The company raised \$ 10,000,000 by selling 500,000 common shares to a private equity investor
D&B (the agreement did not have any anti-dilution clause). The after-tax cost of capital
(expected long-term annual return) was 25%. All remaining shares were retained by
entrepreneurs.
In January 2010, the revised after-tax cash flow forecast looked as follows
Jan 2010 Jan 2011 Jan 2012 Jan 2013 Jan 2014 and onwards
(\$ 4,000,000) \$ 1,000,000 \$ 3,000,000 \$ 5,000,000 \$5,300,000 (6% annual
growth)
New private equity investor H&I has agreed to invest \$ 4,000,000 in the company by buying
newly issued common shares (no additional shares were issued between rounds). The after-tax
cost of capital (expected long-term annual return) remains at 25%. The company has no debt.
a. Last year, in January 2009, what were the VacationHoliday post-money valuation and the
ownership structure (total number of shares, number of shares belonging to entrepreneurs
and D&B)?
b. In January 2010 what were the VacationHoliday post-money valuation and the ownership
structure (total number of shares, number of shares belonging to entrepreneurs, D&B, and
H&I)?
c. What is D&B’s one year return (no dividends were paid, so the return is equal to capital
gains/losses)?
d. What kind of a problem does D&B have? What is the typical form of private equity
investment and how does it help to avoid this problem?
Hint: you might find my PowerPoint slides and Excel example provided in Session 8
If you forgot the formula for growing perpetuity, you can find its explanation on page 222:
(1 ) t
t
CF g
PV
k g
+
=

,
where k is the discount rate and g is the cost of capital.
PROBLEM 1 Given Solution Legend Cost of capital 25% = Value given in problem Initial growth forecast 10% = Formula/Calculation/Analysis required Revised growth forecast 6% = Qualitative analysis or Short answer required Capital Raised Initially \$10,000,000 = Goal Seek or Solver cell Shares issued to D&B 500,000 = Crystal Ball Input Follow-up Investment \$4,000,000 = Crystal Ball Output Initial Cash Flow Projections Jan-09 Jan-10 Jan-11 Jan-12 Jan-13 Jan-14 CF (\$10,000,000) (\$2,000,000) \$3,000,000 \$5,000,000 \$5,500,000 \$6,050,000 10% 1. Pre-money valuation = Share outstanding before financing x Price per share Revised Projections 2. Post-money valuation = Shares outstanding after financing x Price per share Jan-10 Jan-11 Jan-12 Jan-13 Jan-14 3. Post-money valuation = Pre-Money Valuation + Amount Invested CF (\$4,000,000) \$1,000,000 \$3,000,000 \$5,000,000 \$5,300,000 4. Ownership % = number of shares owned/total shares outstanding 6% a. 21200000 Initial Valuation - 1 2 3 4 Jan-09 Jan-10 Jan-11 Jan-12 Jan-13 Jan-14 CF (\$10,000,000) (\$2,000,000) \$3,000,000 \$5,000,000 \$5,500,000 \$6,050,000 Value Share Price Ownership # of Shares Percentage Entrepreneur's D&B's shares 500,000 Total number of shares b. Next Year Valuation 0 1 2 3 4 Jan-10 Jan-11 Jan-12 Jan-13 Jan-14 CF (\$4,000,000) \$1,000,000 \$3,000,000 \$5,000,000 \$5,300,000 Value Share Price Ownership # of Shares Percentage Entrepreneur's D&B's shares 500,000 H&I shares Total number of shares c. D&B's return d.
PROBLEM 2 Given Solution Legend EBITDA 2009 \$2,000,000 = Value given in problem Added EBITDA \$500,000 = Formula/Calculation/Analysis required Funding need \$3,000,000 = Qualitative analysis or Short answer required VC's required rate of return 25% = Goal Seek or Solver cell Rate on convertible debt 8% = Crystal Ball Input Term 5 years = Crystal Ball Output EBITDA multiple 5 EBITDA growth rate 15% Revised EBITDA growth rate 12% Solution Estimated EBITDA EBITDA 2009 \$2,500,000 Estimated EBITDA 2011 \$5,028,393 Multiple 5 Enterprise Value \$25,141,965 Less: Debt \$(3,000,000) Equity Value in 2011 \$22,141,965 VC's Cash Flows 8-3 Year Cash Flows 0 \$(3,000,000) 1 240,000 2 240,000 3 240,000 4 240,000 5 240,000 Year 5 Conversion Value VC Rate of Return -24.4% VC's Share 0.0% c. What share of the firm's equity will the VC require? Revised growth rate 12% Estimated EBITDA EBITDA 2009 3,000,000 Estimated EBITDA 2011 3,120,418 Multiple 5 Enterprise Value \$15,602,091 Less: Debt \$3,000,000 Equity Value in 2011 \$18,602,091 VC's share 0.00% a. What is the value of the combined firm in five years? b. What share of the firm's equity will the VC require? Solved for using Goal Seek
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