Question

Palooka is a new cosmetics firm which is about to make an initial public offering. It has no physical assets and no debt. Palooka is coming out with an equity issue to raise $100 million from the markets. The funds raised will be invested in the commercial production of Stumblebum (a new fragrance for men). There is a 0.8 probability that Stumblebum will catch on with the 'young and beautiful' set. In that case, earnings will be $1 million immediately (at date 0) and will grow at 50% a year for 15 years and then stabilize at that same value forever. There is a 0.2 probability that Stumblebum will not make a noticeable impact, in which case all the investment will then be wasted (the company will have no earnings ever). Assume the market discounts cash flows at 10%. For simplicity, you can assume that the IPO happens on January 1, the investment occurs on January 2, and the earnings (if any) happen on January 3 of that year. In other words, we’re assuming that the IPO, the investment, and the initial earnings (if any) will all occur at date 0. a.) What is the value of the equity before the issue? Assume that no one knows whether Stumblebum will succeed. [HINT: Use the following formula: Value of Equity = Present value of cash flows from existing assets + Net Present Value of cash flows from future investments - Present Value of debt (if any)]. b.) If there are 1 million Palooka shares before the issue, what is the value of each share? c.) What is the price investors will pay for shares in the new issue? (Hint: What happens if it differs from the price of shares before the issue?)

Answer 1

Future Cashflow if investment is successful

Year	Earnings
0	1,000,000.00
1	1,500,000.00
2	2,250,000.00
3	3,375,000.00
4	5,062,500.00
5	7,593,750.00
6	11,390,625.00
7	17,085,937.50
8	25,628,906.25
9	38,443,359.38
10	57,665,039.06
11	86,497,558.59
12	129,746,337.89
13	194,619,506.84
14	291,929,260.25
15	437,893,890.38

After year 15 earnings will be constant forever

PV for future cash flows after year 15 at year 15 = Perpetual cashflow / discount rate = 437,893,890 / 0.1 = 4,378,938,900

PV formula with growth in cashflow = [P/ (r-g)] * [1- {(1+g)/(1+r)}^n]

P is first payment at year 1 = 1,500,000

r is discount rate = 10%

g is growth rate = 50%

n is period = 15

So putting all vales in above formula , PV at year 1 = 389,356,184

Now NPV of all the future cash flow from year 0 to year 15 at year 0 = 1,000,000 + 389,356,184 = 390,356,184

NPV of all the cashflow = 390,356,184 + 4,378,938,900 = 4,769,295,084.34

There is 0.8 probability that this cashflow will come, SO NPV = 4,769,295,084.34 * 0.8 = 3,815,436,067

Investment at year 0 = 100,000,000

NPV = 3,815,436,067 - 100,000,000 = 3,715,436,067

Value of Equity = Present value of cash flows from existing assets + Net Present Value of cash flows from future investments - Present Value of debt

Present value of cash flows from existing assets = 0

Present Value of debt = 0

Net Present Value of cash flows from future investments = 3,715,436,067

So, Value of Equity =  3,715,436,067