Valuing Real Assets: The Risk free case.

Tracking portfolios

Tracking Portfolios become very important in determining the value of many assets. One application of this is to determine the value of real assets through the use of tracking portfolios.

Definition: A tracking portfolio is a portfolio of financial securities whose return minimizes the variance of the difference between the tracking portfolio and the portfolio that is being tracked.

THE INVESTMENT DECISION

TAKE ON ALL PROJECTS WITH A POSITIVE NPV

REJECT ALL PROJECTS WITH A NEGATIVE NPV

WHY?

The Definition of Efficient Markets:

What does that say about the NPV of investing in a financial asset?

Tracking portfolio example:

Suppose that the firm has a risk free investment opportunity with the following cash flows:

INCREMENTAL CASH FLOWS ($millions)

time         0         1         2         3         4         5

              -10       2          3         3         3        3

Is this a good investment?

By the NPV Rule:

Ask the investor whether he could recreate these cash flows at a lower cost?

Consider the market for Treasuries since that is as close as we can get to a "riskless security.

Government Principal Strips Maturing in February:

                Ask Price     YTM

1998         99.84375     5.84

1999         94.6875       5.38

2000         89.875         5.33

2001         85.21875     5.36

2002         80.96698     5.42 Extrapolated
                                            from Nov. & May
2003         76.375         5.44

Estimated price of the Feb 2002 strip:

                P_o = 100/(1+.0542)⁴
                     = 80.967

 
We can now find the Value of the Tracking Portfolio.

The portfolio consists of

$2 million principle amount of Feb 1999 principal strips

$3 million "     "     " Feb '00 to '03 "     strips.
 

What would it cost to create this portfolio?
 

.946875 X 2million   = $1,893,750

.89875 X 3million     =  2,696,250

.8528175 X 3million =  2,558,452.50

.8096698 X 3million =  2,429,009.40

.76375 X 3million     =  2,291,250

Total                             11,868,711.90

Example 2:

You are considering investing in a new procedure for producing widgets. The incremental cash flow from this procedure looks as follows:

time             0             1             2             3             4

CF             -9             -2             3             4             5

Present Values:

.946875 X -2million = -$1,893,750

.89875 X 3million    =    2,696,250

.8528175 X 4million =   3,411,270

.8096698 X 5million =   4,048,349

Total                               8,262,119

REJECT PROJECT

The Basic question is can you achieve the same cash flow with the tracking (replicating) portfolio at lower cost.

Internal Rate of Return (IRR)

The internal rate of return, conceptually, is not a variable you want to look at. Nevertheless it is important because there are a number of important corporations that use for project analysis.

Def: The IRR is that interest rate which makes the NPV of a project equal to zero.

Thus in the example we used above:

INCREMENTAL CASH FLOWS ($millions)

time             0             1             2             3             4             5

                  -10            2             3             3             3             3

We can calculate the IRR as that "y" which makes the equation:

If you calculate the IRR you get: 11.7%

In the second example

 time             0             1             2             3             4

CF             -9             -2             3             4             5
 

IRR is: 2.96%

What is the hurdle rate? It is the "yield to maturity" of the portfolio of the tracking portfolio. Or that interest rate that makes the present value of the cash flows equal the price of the replicating portfolio.

Thus for Example 1: The cost was: $11,868,711.90. What is the yield to maturity of this portfolio? Thus the hurdle rate is: 5.48%. IRR > Hurdle Rate

In the second example, the hurdle rate was 5.43%

IRR < Hurdle Rate

Economic Value Added (EVA) Stern Stewart Assoc.

Suppose we have an investment which costs $1,000 and returns 25% per year forever. At an opportunity Cost of Capital of 10%, what is the NPV of this project?

EVA Approach

EVA = {Forecast of NOPAT - Required NOPAT}

{ Expected rate of return - Cost of Capital} X BVCapital

Example:

Capital invested: $1,000

Forecasted Net Operating Profit After Taxes E(NOPAT)

$250

Target Net Operating Profit After Taxes

$100

EVA is: $150 per year.

MVA is the Present Value of EVA or:

                $150 per year discounted at 10%
                $1500 the same as NPV
 

                            Coke and the mysterious containers