1. Which investment should Sammy choose? Sammy is endowed with $10,000,000 and i
ID: 2626702 • Letter: 1
Question
1. Which investment should Sammy choose?
Sammy is endowed with $10,000,000 and is considering whether to invest in a business venture. Perfect capital markets, interest rate of 6%.
Investment A-1 million, End of year cash flow-1.8 million
Investment B-2 million, End of year cash flow-3.3 million
Investment C-3 million, End of year CF-4.4 million
Investment D-4 million, End of year CF-5.4 million
2. Sammy is also considering a ticket scalping business venture. Sammy estimates that for a $2,000,000 investment in inventory she can sell the tickets for $6,000,000 in the next year (CFs realixed in precisely one year). Also has 6% interest rate. What's the NPV of the ticket scalping venture?
3. What's the new value of Sammy's corporation?
4. Suppose that instead of using her own $2 million to start the new business venture Sammy wants to issue 100,000 new shares in order to raise equity. What price should new investors be willing to pay? How many shares need to be sold to new investors?
5. How would the answer differ if Sammy isn't guaranteed to sell the tickets for $6,000,000?
6. CFs from ticket sales are estimated to have this distribution: Prob 0.2-$5M, Prob 0.5-$3M, Prob 0.3-$2M. What's the new value of Sammy's Corp?
7. What price should outside investors be willing to pay for Sammy's shares?
Explanation / Answer
Since Sammy has $10mn to invest let us assume that she is willing to select multiple investments out of the given ones.
1. Let us calcualte the NPV of each investment at the rate of 6%. (All figures are in million USD)
As we can see that all the investment have a positive NPV, she can invest in all of them. which would lead to the total value of Sammy's organisation as $4.06mn.
2. Now Sammy also wants to enter into the ticket scalping business. Lets calcualte the NPV of thid business. For an investment of $2 mn she gets $6mn as cash flows next year again at 6%. This would give you an NPV of 6/(1.06)-2 = $3.66mn. This NPV is higher than all the above investment and it is wiser to invest the 2mn in this instead of investment B. (As the amount of capital she has is only 10mn)
3. Assuming Sammy decides to not invest in investment B and instead decides to go with the ticket scalping business. The total value of Sammy's corp would be 0.7+1.15+1.09+3.66 = $6.6mn
4. Now if she wants to save her 2mn and want to raise equivalent equity. The price investors would be willing to pay 6600000/100000 = $66 per share and at this share price Sammy will have to issue 2000000/66 = 30303 shares to get an amount of $2mn
5. If she is not guarenteed to sell tickets for $6mn then the investors would be willing to pay less for her company as they need to be compesated for the risk that they are assuming in case Sammy fails to deliver. So the share price would fall.
6. With the given distribution the end of the year cash flow would be estimated as 0.2*5 + 0.5*3+ 0.3*2 = $3.1mn. So the new value of Sammy's corp would be 0.7+1.15+1.09+3.1 = $6.04mn
7. The investors now would be willing to pay $60.4 per share instead of $66
Investment A B C D CF0 -1 -2 -3 -4 CF1 1.8 3.3 4.4 5.4 NPV@6% 0.70 1.11 1.15 1.09Related Questions
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