Category Archives: Announcements

Original source for our coverage of the underinvestment problem

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)

No class on Tuesday, November 21

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!

Some hints for Problem Set 10

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 :

  1. 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) = \tauV(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 teaching note.
  2. 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).
  3. 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.
  4. 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.
  5. 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.

Clarification of expectations for and hints concerning Problem Set 9

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:

  1. 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.
  2. 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.
  3. 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 V(B) = B{e^{ - rT}}, 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; this requires 1) calculating {d_1} and {d_2}, 2) using the Standard Normal Distribution Function (“z”) Table to find N({d_1}) and N({d_2}), and 3) inputting your N({d_1}) and N({d_2}) 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: V(D) = B{e^{ - YTM(T)}}.

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 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: V(D) = B{e^{ - YTM(T)}}.

Merton: Applications of Option-Pricing Theory (shameless self-promotion alert)…

Now that we have begun our study of the famous Black-Scholes-Merton option pricing formula, it’s time for me to shamelessly plug a journal article that I published early in my academic career which Robert C. Merton cites in his Nobel Prize lecture (Merton shared the Nobel Prize in economics in 1997 with Myron Scholes “for a new method to determine the value of derivatives”).

Here’s the citation (and link) to Merton’s lecture:

Merton, Robert C., 1998, Applications of Option-Pricing Theory: Twenty-Five Years Later, The American Economic Review, Vol. 88, No. 3 (Jun. 1998), pp. 323-349.

See page 337, footnote 11 of Merton’s paper for the reference to Neil A. Doherty and James R. Garven (1986)… (Doherty and I “pioneered” the application of a somewhat modified version of the Black-Scholes-Merton model to the pricing of insurance; thus Merton’s reference to our Journal of Finance paper in his Nobel Prize lecture)…

Midterm 2 grade statistics for Finance 4335

I have posted midterm 2 exam grades to Canvas, and I will return your exam booklets to you during next Tuesday’s Finance 4335 class meeting. In the meantime, if you haven’t already done so, I highly recommend reviewing the exam solutions.

For the second midterm exam, here are the descriptive statistics:

Average 77.80
Standard Deviation 18.41
Minimum 18
25th percentile 70
50th percentile 79.50
75th percentile 92
Maximum 100

Midterm exam 2 information…

Midterm 2 will be given during class on Thursday, November 2. This test consists of 4 problems. You are only required to complete 3 problems. At your option, you may complete all 4 problems, in which case I will throw out the problem on which you receive the lowest score.

The questions involve topics which we have covered since the first midterm exam. Topics covered include 1) demand for insurance, 2) moral hazard/adverse selection, 3) portfolio theory/capital market theory, and 4) financial derivatives (calls and puts specifically).

By the way, I have posted the formula sheet that I plan to use on the exam at the following location:

As I noted in my “Plans for next week in Finance 4335” blog posting, tomorrow’s class meeting will be devoted to a review session for midterm exam. If you haven’t already done so, I highly recommend that you review Problem Sets 5-8 and also try working the Sample Midterm 2 Exam (solutions are also provided) prior to coming to class tomorrow.