Monday, November 11, 2013

Weighted Average Cost Of Capital for an uncharacteristic project

Honestly here is the sort of calculation that you want to circle, then come back to if you have enough time.

Refried Bean Company (RBC) is considering a project in the high-end hotdog business. Its debt currently has a yield of 10%. Degen has a leverage ratio of 2.5 and a marginal tax rate of 40%. Luxury Hotdogs Inc. (LHI), a publicly traded firm that operates only in the high-end hotdog business, has a marginal tax rate of 30%, a debt-to-equity ratio of 2.5, and an equity beta of 1.2. The risk-free rate is 4% and the expected return on the market portfolio is 10%. Calculate the appropriate WACC to use in evaluating the Refried Bean Company's boutique schnitzel project.

This is just a WACC problem with a twist. Instead of calculating the WACC with the cost of equity, we need to calculate a "project cost of equity" and add it to RBC's cost of debt. We get the project cost of equity from the risk free rate, plus the Project Beta times the difference between the return on the market portfolio, and the risk free rate: The Project Beta is derived from LHI's Asset Beta, which we can find using figures given.

Step one, find LHI's asset beta: Basset = company beta[1 / (1 + (1 - LHI's tax rate)( LHI's debt to equity ratio))]  = 1.2[1 / (1 + (1 - 0.30)(2.5))] = 0.28

Step two, find RBC's equity beta for this project: Bequity = Basset[1 + (1 - RBC's tax rate)(LHI's equity beta)] = 0.28[1 + (1 - 0.4)(1.2)] = 0.48

Step three, find the project cost of equity: 4% + 0.48(10% - 4%) = 6.9%

Step four, find RBC's cost of debt: 10%(1 - 0.4) = 6%

Step five, find the weight of RBC's debt and equity: Wdebt = 0.6 and Wequity = 0.4

Step six, solve for the project's WACC: 0.6(6%) + 0.4(6.9%) = 3.6 + 2.76 = 6.36%

Like most problems, the hardest part is getting started. I always get mixed up with step one and two, but with some practice it isn't as impossible as it seems.

Now a word of caution, yesterday I didn't really know how to do this. There is a good chance I've made mistakes, if you see one, please comment.

Sunday, November 10, 2013

Variance and standard deviation of perfectly correlated two-stock protfolios

Here's another quick tip, if you're faced with a question regarding a two stock portfolio, if the stocks are perfectly positively correlated. If this is the case, you can save yourself a heap of time by avoiding the long calculation: σ portfolio = [W12σ12 + W22σ22 + 2W1W2σ1σ2r1,2]1/2
If the two stocks, or whatever type of assets, have a correlation of 1.0, then you can simply find a weighted average.

Here's an example: If 30% of an investor's portfolio consists of an asset with a standard deviation of 0.4 and 70% consists of an asset with a standard deviation of 0.2, you can solve for the overall standard deviation of the portfolio like this:
(0.3)(0.4) + (0.7)(0.2) = 0.12 + 0.14 = 0.26
Now isn't that a lot faster than dragging out the long calculation with all those 0's and chances to miss a button. Lets hope there's a question like this on December 7th!

Friday, November 8, 2013

How to use your calculator's NPV functions to complete a two-stage dividend discount model

I got my but kicked on the CFA Institute mock exam yesterday, mainly because I ran out of time. I've been going through the calculations and trying to find ways to speed them up a bit. Here's one that anyone with a TI BA 2 plus calculator, or just about any calculator with net present value (NPV) functions.

Valuing a company with a period of accelerated dividend increases to be followed by a a slower more stable rate requires you to find the DDM value at the point in time where the accelerated dividend growth stops, then add that to previous dividends

Borrowing from Mock Exam - morning session, question 82 (available free to registered candidates):
The accelerated dividend distributions are: D1=$2.00, D2=$2.50, and D3=$3.13
The first slow/stable distribution is: D4=$3.28
Here's the crux of using the two stage model: use the DDM to find a value for the company's shares at time 3 using the given investor required rate of return, $3.28/(0.12-0.05)=$46.86

Add that to the last accelerated distribution for the cash flow at time 3: $46.86+$3.13=$49.99 ~ $50.00

Now, here's how to use your calculator's NPV functions to find a current value per share:
CF0=0, CF1=2, CF2=2.5, CF3=50, I=12

This gives you a NPV=39.37, which is a penny off from the answer.

Sorry about the lack of subscripts, but I think you can get the picture from here. Go ahead and hit me up with any questions.