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##### FINE 342 Finance 2 Assignment 3 Fall 2014

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Question;FINE 342: Finance 2Assignment 3: Fall 2014The assignment is due by 6pm on Friday December 5th.You may slide the assignment under my officedoor (220) any time before then. You may work alone or in groups of up to 5 students. You can workwith students from other sections. Only one copy needs to be handed in per group. You must show yourwork to receive credit. Typed or handwritten are both OK.Risk Shifting1) All investors are risk neutral and the risk free rate is 10%. Assume the tax rate is 0%.Today is t = 0. Project A requires a cash outflow of $100 at t = 0, and will produce a single risk free cashinflow of $165 at t = 1. Your corporation only has $50, (and no other assets), and is considering whetherto issue debt or equity to raise the remaining $50 needed to undertake the project.a) If you issue equity, what fraction of your company would you have to sell in order to raise $50?b) What is the NPV, for existing equity holders, of issuing equity and undertaking Project A?c) If you issue debt, you will issue a 1?year, zero coupon bond. What would the promised facevalue of the 1?year, zero coupon bond have to be in order to raise $50 today? d) What is the NPV, for equity holders, of issuing debt and undertaking Project A?e) Should you issue equity or debt?Suppose that you raised $50 by issuing debt with the face value you obtained in part c). However, afterreceiving the funds from debtholders you have the opportunity of investing in Project B rather thanProject A. Project B also requires a $100 investment at t = 0, but Project B is not risk free: at t = 1, ProjectB either produces a cash inflow of $11, with probability 0.5, or a cash inflow of $297 with probability 0.5.f) What is the NPV, for equity holders, of issuing debt with the promised face value obtained inpart c), and investing in Project B?g) What promised face value of debt would debtholders have required in order to lend you $50 ifthey had anticipated that you would invest in Project B, rather than Project A? h) Assuming the face value of debt obtained in part g), what is the NPV, for equity holders, ofissuing debt and undertaking Project B?i) If instead of issuing debt, you had issued equity, would you invest in Project A or Project B? j) Assume that debtholders anticipate that you will do what is optimal for shareholders after debtis issued. Based on this assumption, should you issue debt, or equity, and should you invest inProject A, or Project B?Real Options2) Company X is an all equity oil producer with 1M shares outstanding. They own a plot of land with 1Mbarrels of oil reserves and no other assets. The firm has to decide on when to produce and sell oil.Given the nature of their land, they have two methods of production: ?fast? and ?in advance?. In eachcase the full 1M barrels of oil are produced and there is no remaining oil.Fast: when using the fast approach the oil is sold in the same period as the production decision is made.Production costs are $70 per barrel and is spent when the production decision is made. The fastapproach can be used at t = 0, t = 1, or t = 2. Production costs are paid from the simultaneous oil salerevenues so no external financing is needed.In advance: When using the in advance approach the oil is available one period after the productiondecision is made. Production costs are $60 per barrel and is spent when the production decision ismade. The advance approach can only be used at t = 0 or t = 1. Production costs are paid from theproceeds of an equity issuance.Assume investors are risk neutral and the risk free rate is 0%. Ignore taxes. For simplicity assume that att = 2 the land is worth 0, regardless of whether you have produced oil or not.The spot price of oil at t = 0 is $80 per barrel. The evolution of oil prices at t = 1 and t = 2 is shown in thetree below. Each branch from t = 0 to t = 1 has a 1/3 probability and each branch from t = 1 to t = 2 has a1/2 probability.**Note: Even though investors are risk neutral and the risk free rate is 0, the price of oil does not have toequal its expected price one period later because of things like storage costs and convenience yield thatmake commodities slightly different than financial assets. You don?t need to worry about this, but I justthought I would mention it in case you were concerned there was a logical inconsistency in the problem.t = 0 t = 1 t = 2E: 120B: 90F: 55G: 78A: 80 C: 75H: 50I:100D: 60J: 40a) Assuming that at t = 1 you decided to wait until t = 2 to make a production decision, what is theoptimal action at t = 2 for each node E, F, G, H, I, J. Your possible actions for each node at t = 2are:i) Fast production and sell oil at t = 2ii) No productionb) Assuming that at t = 0 you decided to wait, what is the optimal action at t = 1 for each node B, C,D? Your possible actions for each node at t = 1 are:i) Fast production and sell oil at t = 1ii) In advance production at t = 1 and sell oil at t = 2iii) Wait until t = 2 to make a production decisionc) What is the optimal strategy at t = 0 for node A? Your possible actions are:i) Fast production and sell oil at t = 0ii) In advance production at = 0 and sell oil at t = 1iii) Wait until t = 1 to make a production decisiond) Based on the information above and the optimal production strategy, what would the stockprice be at each node A, B, C, D, E, F, G, H, I, J? Show your results in a tree like the one above.Also indicate how many shares would be outstanding at each node (if an equity issuance occursat a node indicate the number of shares before and after the equity issuance).e) Same question as part d, but now assume that any external financing is done by issuing a 1?yearzero coupon bond with price of $60M and face value of F. Note: the bond may not be risk free,so you have to find F such that bondholders are willing to pay $60M. There are no bankruptcycosts.Commitment problems, reputation, and randomized strategiesThe question below shows that not being able to commit to an action can lead to suboptimal outcomes.It also shows that randomized strategies can be more efficient than fixed strategies. Finally, it showshow reputation can play an important role in determining optimal actions.3) Today is t = 0. All investors are risk neutral and the risk free rate is 0%. You are an entrepreneur andhave an investment opportunity that costs 100 at t = 0. The opportunity can have a good outcome(payout = 160) and a bad outcome (payout = 80) at t = 1. If you exert full effort (work), then theprobability of each outcome is 50%. If you don?t work (shirk), then the outcome will be bad (80) withcertainty, but you will derive a private benefit of 18.You are trying to finance the project by issuing a 1?year zero coupon bond with price = 100 and facevalue = F. In case of default the assets are liquidated and the proceeds are turned over to thedebtholders. There are no bankruptcy costs. Note that if you shirk you still derive the $18 privatebenefit, even if there is a default.a) Would it be possible to issue debt if debtholders thought you would shirk?b) Would it be possible to issue debt if debtholders though you would work? If so, what face valuewould they require? (Hint: You must also confirm that given this face value, it is in fact optimalfor you to work.)Now assume that in case of default, you can propose to the bondholders a renegotiation instead ofliquidation. Under renegotiation the debt would be worth 85 (instead of 80 under the liquidationscenario), and equity would be worth 10 (instead of 0 under the liquidation scenario).Comment: The above scenario could happen if, for example, a business is worth more as a going concernthan in liquidation. Another example could be a homeowner who has defaulted on their mortgage. Thebank could foreclose on the property (liquidate), or they could renegotiate the loan. It could be thatrenegotiating the mortgage has a higher NPV than foreclosure for the bank, and is also beneficial to thehomeowner relative to foreclosure.c) Given these new assumptions, what is the optimal strategy for the bondholders if ever the badoutcome occurs? (The options are liquidate or accept renegotiation.)d) Suppose you anticipate that the bank will take their optimal action in case of default. What isyour optimal action (work or shirk) given the face value you found in part b?e) Suppose that bondholders anticipate your answer to part d. Would they still be willing to buy for100 the bond with the face value you found in part b? Is there any face value that would enableyou to raise the required 100?f) Suppose bondholders could commit in advance to always liquidating in case of default. Wouldyou be able to issue the bond with the face value you found in part b?Comment: Would this commitment be credible? Perhaps it could be if the lender has reputationalconcerns and wants to show other borrowers that this is the type of action they take when there is adefault.While committing to liquidate allows the project to be financed with debt, it is not an efficient solutionsince there is a 50% chance that the firm will be liquidated (you work, but 50% of the time the outcomeends up being bad anyways). From a total welfare point of view, we would say that the most efficientoutcome (?first best?) would be for you to work and for the bondholders to always accept renegotiationin case of default. Unfortunately, this does not work in this example since if that were the lender?s policy,it would actually be optimal for you to shirk, not work. So the ?first best? solution cannot beimplemented.What is the ?second best? solution? It turns out that always liquidating is not the second?best solution.The second best solution involves a randomized strategy by the lender: in case of default, liquidate withprobability x and renegotiate with probability (1?x), for the lowest value of x that ensures that it isoptimal for you to work. The face value of the bond also has to satisfy the condition that the value of thebond is in fact equal to 100. The lower the probability of liquidation, the more efficient, since the firm isworth more under renegotiation than under liquidation.g) Find x and the face value F that implements the ?second best? solution described above. (Hint:you will have two equations and 2 unknowns. First equation: given x and F you will beindifferent between work and shirk. Second equation: given that you work and given x and F,the bond is in fact worth 100.)Comment: The above model can explain why lenders will sometimes renegotiate and sometimesliquidate. For reputational purposes lenders need to show that they are tough (liquidate sometimes).They need to show that they are just tough enough to make it worthwhile for borrowers to try theirhardest to pay back their loans. Indeed, this is supported by some empirical findings and explains howreputational concerns can explain some seemingly counterintuitive liquidations.The above model is based on an influential paper by Bolten and Scharfstein (they derive many otherresults as well). The paper is very academic and I don?t recommend you read it, but I provide the link incase you are curious: http://www.people.hbs.edu/dscharfstein/THEORY_OF_P_90.pdf.Randomized strategies appear elsewhere as well. For example, random audits, sports, and even rockpaper scissors.

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