I have a question about a study guide question my professor posted. In the part
ID: 2647411 • Letter: I
Question
I have a question about a study guide question my professor posted. In the part of the question marked by asterisks she is saying the value of the firm will be 200 when she says "s(200/1.05)", but shouldn't that number be 440/1.05 instead of 200 because the project generates 340, and the firm already has 100? I can't seem to figure out how she got the value of 200 when calculating new share holder value.
5. Velcro currently has no debt in its financial structure. It has assets in place that will be worth $100 million next year with certainty. Velcro is currently considering a real investment which will cost $100 million today. If the investment is successful, it will pay a single cash flow of $340 million next year. If it is a failure, the investment will produce zero cash flows. The probability of success is 50%, with the outcome uncorrelated with the return on market. The risk-free rate is 5%. Velcro has just secured a one year loan from a bank to help finance investment (not necessarily fairly priced). The loan amount is $60 million and carries a single payment of $70 million next year. Assuming Velcro has currently 1 million shares outstanding, what is the MINIMUM number of new shares of equity that must be issued in order to finance the rest of investment?
If new equity will be issued and project undertaken, the cash flows to shareholders are
CFGood = 100+340-70=370 CFBad = 100-70=30
or the equity value will be
Equity= [(.5)370 + (.5)30]/(1.05) = 190.4
***The new shareholders will own stake s(200/1.05) . Since the project costs $100 and $60 is financed by debt, the new shareholders will only need to contribute 40. Thus,
40 = s (190:4)
s = 0:21
If n new shares will be issued, and N were outstanding, the stake of new shareholders is
s= n/(n+N)
0:21 = n/(n+N)
= 0.266 mil
Explanation / Answer
The total value will be $200 because we need to raise finance worth $100 extra. The project income is not being considered here but only the initial outflow of $100 million plus the existing value of $100 million. So a total of $200 million is required.
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