Fascinating geometric mean return calculation for Da Vinci’s ‘Salvator Mundi’; at its recent $450 million sales price, the annual rate of return for this artwork over the course of five centuries comes out to around 1.35%.

For what it’s worth, our discussion last Thursday concerning how corporate risk management “fixes” the underinvestment problem is based upon the following journal article:

Garven, James R. and Richard D. MacMinn, 1993, “The Underinvestment Problem, Bond Covenants and Insurance,” *Journal of Risk and Insurance*, Vol. 60, No. 4 (December), pp. 635-646. (cited 84 times according to Google Scholar)

I have decided to cancel class on Tuesday, November 21. On Tuesday, November 28, we will complete our coverage of the Why is Risk Costly to Firms? lecture note (specifically, the asset substitution and managerial incentives topics which appear on pp. 26-43).

The final problem set for the semester (Problem Set 11) is now due on Tuesday, November 28 (instead of Tuesday, November 21). The final scheduled class meeting for Finance 4335 is Thursday, November 30; class on that day will be devoted primarily to a review session for the final exam, which is scheduled for Tuesday, December 12, 2:00 p.m. – 4:00 p.m. in Foster 402.

Happy Thanksgiving!

]]>The classic capital budgeting model (such as you learned in Finance 3310) implicitly assumes that the firm has unlimited liability and faces linear taxes. When these assumptions hold, then the net present value (NPV) of a project is calculated by estimating expected values of future incremental after-tax cash flows and discounting them at an appropriate risk-adjusted discount rate. However, we showed during yesterday’s class meeting how limited liability and nonlinear taxes imply that the net present value of a project depends upon the manner in which incremental after-tax cash flows interact with cash flows from existing assets. Consequently, the after-tax value of equity is equal to the difference between the pre-tax value of equity and the value of the government’s tax claim (both of which we model as call options on the firm’s assets). Furthermore, project NPV corresponds to the difference in after-tax value of equity (assuming the project is undertaken), minus the after-tax value of equity (assuming the project is not undertaken).

Problem Set 10 provides an opportunity to apply these concepts. Here are some hints for parts A through E of Problem Set 10 :

- In part A, apply the option pricing framework to determine the pre-tax value of equity (
*V*(*E*), where*V*(*E*) =*V*(Max(0,*F-B*)), the value of debt (*V*(*D*), where*V*(*D*) =*V*(*B*– Max(0,*B-F*)), and the value of taxes (*V*(*T*), where*V*(*T*) =*V*(Max(0,*F-TS*)), assuming that this investment is not undertaken. Helpful hint: we performed these same calculations in class yesterday for the problem described on pp. 17-18 of the http://fin4335.garven.com/fall2017/risk_costly_chapter7.pdf teaching note. - In order to determine whether the project should be undertaken, in part B you need to after-tax equity value (i.e.,
*V*(*E*) –*V*(*T*)) which obtains under the assumption that the investment is undertaken. Once you obtain that result, the net present value (NPV) of the project is the difference between the after-tax value of equity (*V*(*E*) –*V*(*T*)) in part A (which you have already calculated) and the after-tax value of equity which obtains if the investment is undertaken. The decision to invest or not to invest depends upon whether the NPV of the investment is positive (in which case you undertake the project) or negative (in which case you do not undertake the project). - An investment tax credit (ITC) is quite literally a check sent by the U.S. Department of the Treasury to the company; thus, the NPV when there is an ITC is equal to the NPV that you calculated in part B plus the value of the ITC. At that point, whether you invest or don’t invest depends upon whether NPV is positive or negative (as in part B). The ITC in this case increases project NPV by $1 million.
- In order to answer part D, you need to redo the calculation described in the first paragraph above using a 20% tax rate rather than a 35% tax rate.
- In order to answer part E, you can figure out the tax rate at which the firm is indifferent about making the investment by trial-and-error, or better yet, adapt the Tax Options spreadsheet located on the lectures notes page to the parameters upon problem set 10 is based and use Solver.

As per our discussion in class today, I just modified Problem Set 10 so that it considers the effect of the corporate tax policy change that is currently under consideration; i.e., the lowering of the corporate tax rate from 35% to 20%. This is addressed in part D of the new version of Problem Set 10. If you have previously downloaded Problem Set 10, throw that copy away and replace it with the version that I just uploaded to the course website at http://fin4335.garven.com/fall2017/ps10.pdf.

]]>… are available at http://fin4335.garven.com/fall2017/ps9solutions.pdf…

]]>As a follow-up to my “Clarification of expectations for and hints concerning Problem Set 9” posting from earlier today, here I show all of the code that appears throughout the Credit Risk Spreadsheet and explain its logical foundations:

]]>A student asked me whether it’s okay to use an Excel spreadsheet to solve problem set 9. While I generally encourage students to use Excel for the purpose of *validating* their work (especially for computationally challenging problem sets such as the present one), I also expect students to demonstrate understanding and knowledge of the logical framework upon which any given problem is based. In other words, I expect you to show and explain your work on this problem set just as you would have to show and explain your work if this was an exam question.

As I am sure you are already well aware, you can obtain most of the “correct” answers for problem set 9 by simply downloading and opening up the Credit Risk Spreadsheet in Excel and performing the following steps:

- For part A, open the Firm 1 worksheet, replace the “.4” in cell B3 with “.3”. Then the answers for the three questions are in cells F4, F3, and F5 respectively.
- For part B, open the Firm 2 worksheet, replace the “.4” in cell B3 with “.5”. Then the answers for the three questions are in cells F4, F3, and F5 respectively.
- For part C, assuming that you are able to follow the logic presented in my On the economics of financial guarantees blog post from yesterday afternoon, the fair insurance premiums appear on both of the worksheets, and presumably you also understand from our study of financial derivatives that the expected return on a default-free bond is the riskless rate of interest.

The problem with simply plugging and chugging the spreadsheet template is that one can mechanically follow the steps outlined above without necessarily understanding the credit risk problem. The key takeaway from our study of credit risk is that limited liability causes prices of bonds issued by risky (poor credit quality) firms to be lower than prices of bonds issued by safe (good credit quality) firms. In the case of this problem set, firms 1 and 2 are identical in all respects expect for asset risk, and because of limited liability, this implies that in the absence of a financial guarantee, firm 2’s bonds are riskier than firm 1’s bonds. Thus, firm 2’s bonds have a lower market value (and a correspondingly higher yield, or expected return) than firm 1’s bonds, and firm 2 can expect to have to pay more than firm 1 for a financial guarantee which transfers the default risk from investors over to a financial guarantor. In a competitive market, the fair premium for such a guarantee is given by the value of the limited liability put option.

By all means, make use of the Credit Risk Spreadsheet to validate your answers for the problem set. But start out by devising you own coherent computation strategy using a piece of paper, pen or pencil, and calculator. Since you know that the value of risky debt is equal to the value of safe debt minus the value of the limited liability put option, one approach to solving this problem set would be to start out by calculating the value of a riskless bond, and the value of the limited liability put option. The value of a riskless bond is , where *B* corresponds to the promised payment to creditors. The value of the option to default (*V*(*put*)) can be calculated by applying the BSM put equation (see the second bullet point on page 8 of http://fin4335.garven.com/fall2017/lecture16.pdf); this requires 1) calculating and , 2) using the Standard Normal Distribution Function (“z”) Table to find and , and 3) inputting your and values into the BSM put equation, where the exercise price corresponds to the promised payment to creditors of $500,000, and the value of the underlying asset corresponds to the value of the firm, which is $1,000,000. Once you obtain the value of the safe bond (*V*(*B*)) and the value of the option to default (*V*(*put*)) for each firm, then the fair value for each firm’s debt is simply the difference between these two values; i.e., *V*(*D*) = *V*(*B*) – *V*(*put*). Upon finding *V*(*D*) for firm 1 and firm 2, then you can obtain these bonds’ yields to maturity *(YTM* ) by solving for *YTM *in the following equation: .

Since the value of equity corresponds to a call option written on the firm’s assets with exercise price equal to the promised payment to creditors, you could also solve this problem by first calculating the value of each firm’s equity (*V*(*E*)) using BSM call equation (see the second bullet point on page 7 of http://fin4335.garven.com/fall2017/lecture16.pdf and substitute the value of assets ($1,000,000) in place of *S* and the promised payment of $500,000 in place of *K *in that equation). Once you know *V*(*E*) for each firm, then the value of risky debt (*V*(*D*)) is equal to the difference between the value of assets (*V*(*F*) = $1,000,000) and *V*(*E*)*. *Upon calculating *V*(*D*) in this manner, then obtain these these bonds’ yields to maturity *(YTM* ) by solving for *YTM *in the following equation: .

See the (November 2014) *Wall Street Journal *article entitled “A Federal Guarantee Is Sure to Go Broke” and related article from November 2015 entitled “Moody’s Predicts PBGC Premiums Will Become Unaffordable“.

Think of PBGC as essentially the FDIC of private pensions. Thus, the analysis the flowchart shown at the bottom of my “On the economics of financial guarantees” blog post concerning how FDIC guarantees bank deposits applies here; in the diagram from that posting, simply replace “FDIC” in the diagram with “PBGC”, and in place of “Bank” and “Depositors”, substitute “Company offering private pension to Workers” and “Workers”.

Quoting from the above referenced *WSJ *article:

]]>How is the PBGC insurance program doing on its 40th anniversary? Well, it is dead broke. Its net worth is negative $62 billion as of the end of September. That is even more broke than it was a year ago, when its net worth was negative $36 billion… The PBGC has total assets of $90 billion but total liabilities of $152 billion. So its assets are a mere 59% of its liabilities. Put another way, its capital-to-asset ratio is negative 69%.

Why does the government have such a pathetic record at guaranteeing other people’s debts? It isn’t that Washington wasn’t warned. “My son, if you have become surety for your neighbor, have given your pledge for a stranger, you are snared in the utterance of your lips,” reads Proverbs 6: 1-2.