Question

Happy Times, Inc., wants to expand its party stores into the Southeast. In order to establish an immediate presence in the area, the company is considering the purchase of the privately held Joe’s Party Supply. Happy Times currently has debt outstanding with a market value of $210 million and a YTM of 8 percent. The company’s market capitalization is $310 million and the required return on equity is 13 percent. Joe’s currently has debt outstanding with a market value of $28 million. The EBIT for Joe’s next year is projected to be $15 million. EBIT is expected to grow at 7 percent per year for the next five years before slowing to 5 percent in perpetuity. Net working capital, capital spending, and depreciation as a percentage of EBIT are expected to be 6 percent, 12 percent, and 5 percent, respectively. Joe’s has 1.95 million shares outstanding and the tax rate for both companies is 35 percent.

a. What is the maximum share price that Happy Times should be willing to pay for Joe’s? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

b. After examining your analysis, the CFO of Happy Times is uncomfortable using the perpetual growth rate in cash flows. Instead, she feels that the terminal value should be estimated using the EV/EBITDA multiple. The appropriate EV/EBITDA multiple is 7. What is your new estimate of the maximum share price for the purchase?

Answer 1

Part a)

Step 1: Calculate Weighted Average Cost of Capital for Happy Times

The WACC is calculated as below:

WACC = Weight of Debt*After-Tax Cost of Debt + Weight of Equity*Cost of Equity

where Weight of Debt = 210,000,000/(210,000,000+310,000,000), After-Tax Cost of Debt = 8*(1-35%) = 5.2%, Weight of Equity = 310,000,000/(210,000,000+310,000,000) and Cost of Equity = 13%

Using these values in the above formula, we get,

WACC = 210,000,000/(210,000,000+310,000,000)*5.2% + 310,000,000/(210,000,000+310,000,000)*13% = 9.85%

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Step 2: Calculate Annual Cash Flow

The value of annual cash flow is arrived as follows:

	Year 1	Year 2	Year 3	Year 4	Year 5
EBIT	15,000,000	16,050,000	17,173,500	18,375,645	19,661,940
Less Taxes	5,250,000	5,617,500	6,010,725	6,431,476	6,881,679
Net Income	9,750,000	10,432,500	11,162,775	11,944,169	12,780,261
Add Depreciation	750,000	802,500	858,675	918,782	983,097
Operating Cash Flow	10,500,000	11,235,000	12,021,450	12,862,952	13,763,358
Less Capital Spending	1,800,000	1,926,000	2,060,820	2,205,077	2,359,433
Change in NWC	900,000	963,000	1,030,410	1,102,539	1,179,716
Cash Flow from Assets	7,800,000	8,346,000	8,930,220	9,555,335	10,224,209
Terminal Value [10,224,209*(1+5%)/(9.85%-5%)]	0	0	0	0	221,348,852
Annual Cash Flow	$7,800,000	$8,346,000	$8,930,220	$9,555,335	$231,573,061

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Step 3: Calculate Value of the Firm (Joe) Today

The value of the firm today is determined as below:

Value of the Firm Today = Cash Flow Year 1/(1+WACC)^1 + Cash Flow Year 2/(1+WACC)^2 + Cash Flow Year 3/(1+WACC)^3 + Cash Flow Year 4/(1+WACC)^4 + Cash Flow Year 5/(1+WACC)^5

Substituting values in the above formula, we get,

Value of the Firm Today (Joe) = 7,800,000/(1+9.85%)^1 + 8,346,000/(1+9.85%)^2 + 8,930,220/(1+9.85%)^3 + 9,555,335/(1+9.85%)^4 + 231,573,061/(1+9.85%)^5 = $172,089,086

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Step 4: Calculate Maximum Offer Price for Joe’s

The maximum offer price is arrived as follows:

Maximum Offer Price = (Value of the Firm Today (Joe) - Market Value of Debt (Joe))/Number of Shares Outstanding = (172,089,086 - 28,000,000)/1,950,000 = $73.89 (answer for Part a)

The maximum share price that Happy Times should be willing to pay for Joe’s is $73.89.

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Part b)

Step 1: Calculate Terminal Value using EV/EBITDA Multiple

The terminal value using EV/EBITDA multiple is calculated as follows:

EBITDA = EBIT for Year 5 + Depreciation for Year 5 = 19,661,940 + 983,097 = $20,645,037

Terminal Value = EBITDA*EV = 20,645,037*7 = $144,515,259

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Step 2: Calculate Revised Value of the Firm (Joe) Today

The revised value of the firm today is arrived as below:

Revised Value of the Firm Today (Joe) = 7,800,000/(1+9.85%)^1 + 8,346,000/(1+9.85%)^2 + 8,930,220/(1+9.85%)^3 + 9,555,335/(1+9.85%)^4 + 144,515,259/(1+9.85%)^5 = $117,662,965 [terminal value will include the Year 5 cash flow, therefore it will not be separately included in the cash flow for Year 5]

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Step 3: Calculate New Estimate of Maximum Share Price

The new estimate of maximum offer price is calculated as below:

New Estimate of Maximum Share Price = (Revised Value of the Firm Today (Joe) - Market Value of Debt (Joe))/Number of Shares Outstanding = (117,662,965 - 28,000,000)/1,950,000 = $45.98 (answer for Part b)

The new estimate of the maximum share price for the purchase would be $45.98.