Valuing Assets: Warren Buffett Style
In the Berkshire Hathaway Annual Report from 2000, Warren Buffett detailed the formula for valuing all assets: “a bird in the hand is worth two in the bush.” This little adage was first developed in 600 B.C. by a man named Aesop. Warren Buffett goes on to tell us that to fully complete the formula, three questions must be answered:
 How certain are you that there are indeed birds in the bush?
 When will they emerge and how many will there be?
 What is the riskfree interest rate?
He goes on to tell us that if these three questions can be answered then the maximum value of the bush and the number of birds in the hand to pay for it will be known. "And of course, don’t literally think birds. Think dollars,” says Buffett.
This law, according to Buffett, is immutable, and it applies to the purchase of farms, bonds, stocks and lottery tickets. Buffett states, “Just insert the correct numbers, and you can rank the attractiveness of all possible uses of capital throughout the universe.”
We will use this model to rank the attractiveness of attending an Ivy League University compared to its public and private contemporaries and answer the question, is an Ivy League degree worth it?
Your Future Cash Flows and Your Degree
Ultimately, Aesop’s fable leads us to a discounted cash flow model that requires four key inputs:
 The price tag or the cost of the investment, which in this case is the cost of a fouryear degree;
 Current earnings, or the starting salary after receiving a fouryear degree;
 A discount rate; and
 Growth rates.
Four Years of Tuition and Fees
Let’s first determine the fouryear total cost for public, private, and Ivy League institutions. It is necessary to use a starting point of 2016 tuition and fees and inflate them each year for four years by an average tuition inflation rate to reach a total fouryear cost. Collegedata.com reported that 2016 tuition and fees for public and private universities were $24,061 and $47,831 respectively while Bloomberg indicated that one year of Ivy League education in 2016 cost the equivalent of a highend SUV ($63,000). The average annual tuition rate increase from 1958 to 2001 was 8%, according to FinAid.org. Using this information, we can inflate 2016 tuition and fees for four years to arrive at a total cost for each of our collegiate buckets:
Table 1: 2016 to 2019 Tuition and Fees Based on an 8% Tuition Inflation Rate

Public 
Private 
Ivy League 
2016 
$ 24,061 
$ 47,831 
$ 63,000 
2017 est. 
$ 25,986 
$ 51,657 
$ 68,040 
2018 est. 
$ 28,065 
$ 55,790 
$ 73,483 
2019 est. 
$ 30,310 
$ 60,253 
$ 79,362 
FourYear Total Cost 
$ 108,422 
$ 215,532 
$ 283,885 
Expected Starting Salaries
Next, it is necessary to determine the expected starting salaries upon graduation for each of our tiers, as our cash flow model is dependent on an earnings stream that can be grown over time at a realistic rate. (In the realm of stocks, earnings are used for this figure. In this model, starting salaries are used.) Keep in mind, our hypothetical scholar will not graduate until 2019, so it is necessary to inflate the starting salary to 2019 expectations.
Using data mining and statistical modeling, Payscale.com provides starting salaries for each of our collegiate buckets. The top eight reported school salaries for each college category were averaged together to find the 2015 starting salaries. The results are as follows:
2015 Starting Salaries
 Public: $62,527
 Private: $43,075
 Ivy League: $67,025
Next, it is necessary to inflate these salaries to a 2019 figure. As reported by the U.S. Bureau of Economic Analysis, the average annual wage growth rate from 1960 to 2015 was 6.33%. Since we are equating our college returns to longterm investment, this is an ideal growth rate. In the following table, the 2015 starting salaries were increased by 6.33% a year for four years to arrive at a 2019 hypothetical starting salary.
Table 2: Starting Salaries Increased at 6% a Year 2015 to 2019

Public 
Private 
Ivy League 
2015 
$ 62,527 
$ 43,075 
$ 67,025 
2016 
$ 66,485 
$ 45,802 
$ 71,268 
2017 
$ 70,693 
$ 48,701 
$ 75,779 
2018 
$ 75,168 
$ 51,784 
$ 80,576 
2019 
$ 79,927 
$ 55,062 
$ 85,676 
Thus, the scholar graduating in 2019 can expect to earn an average starting salary of $79,927, $55,062, or $85,676 for a public, private, or Ivy League education respectively.
Quick Valuation Ratios
The information we have gathered so far can be used to determine the future value of the starting salaries and to calculate quick valuation ratios to calculate initial value indicators. These ratios are not necessary for our discounted cash flow model, but they can provide corroborating evidence to our eventual cash flow model.
First, let’s estimate what each collegiate tier resulting salaries will be paid in ten years. In the following table, the starting salaries for each tier is projected forward ten years, using the time value of money (TVM) calculation for future value and the 6.33% annual growth rate.
Table 3: Expected 2029 Salary Based on 2019 Starting Salary and 6.33% Annual Wage Growth

Public 
Private 
Ivy League 
2019 Starting Salary 
$ 79,927 
$ 55,062 
$ 85,676 
2029 Projected Salary 
$ 147,655 
$ 101,720 
$ 158,277 
P/Y 
1 
1 
1 
PV 
$ (79,927) 
$ (55,062) 
$ (85,676) 
N 
10 
10 
10 
I/Y 
6.33% 
6.33% 
6.33% 
CPT FV (2029 Projected Salary) 
$ 147,655 
$ 101,720 
$ 158,27 
According to these projections, a college grad from a public university can expect to be making $147,655 by 2029, while a private and Ivy League grad can expect to make $101,720 and $158,277 respectively.
These salary calculations put into place some quick valuation ratios:
Table 4: Starting Salary to Cost Ratios

Public 
Private 
Ivy League 
Fouryear Cost 
$ 108,422 
$ 215,532 
$ 283,885 
2019 Starting Salary 
$ 79,927 
$ 55,062 
$ 85,676 
2029 Projected Salary 
$ 147,655 
$ 101,720 
$ 158,277 
Cost to 2019 Starting Salary 
1.36 
3.91 
3.31 
Cost to 2029 Projected Salary 
0.73 
2.12 
1.79 
These ratios can be thought of as the equivalent to P/E ratios used for stocks that provide quick, valueataglance insight – and remember, the lower, the better.
It is easy to see that the public collegiate tier comes out as a clear winner with a costto2019startingsalary ratio of 1.36 compared to 3.91 and 3.31 for the private and Ivy League tiers. The public tier furthermore drops to a paltry .73 for the costto2029projectedsalary ratio compared to 2.12 and 1.79 for private and Ivy League institutions and remember, the lower, the better. At a fiftythousandfoot level, the public school education offers greater value than its rivals. If this were a stock, public schools would be trading at a P/E of 10 versus their peers that would be trading at a P/E of 30.
The Discounted Cash Flow Model
Now let’s move on to our discounted cash flow (DCF) model, which is truly the point of this exercise. Remember, the following inputs are necessary to build the model:
Inputs
 The price tag, or the cost of the investment, which, in this case, is the cost of a fouryear degree;
 Current earnings, or the starting salary after receiving a fouryear degree;
 A discount rate; and
 Growth rates.
We have already determined the total 2016 to 2019 tuition and fees (cost) for attending each of the collegiate tiers, and we have found the 2019 starting salaries for each. Now, let’s decide on a discount rate and growth rates.
The Discount Rate
The discount rate is the rate used to discount future earnings back to a presentday dollar figure and will be a combination of the riskfree rate that is the 30year TBill rate and an equity risk premium. The reasoning behind this is that the 30year TBill rate is what an individual investor can expect to gain in return (riskfree) if the money to attend college was invested instead. The equity risk premium reflects the uncertainty over what the future salary will be. The 30year TBill according to Treasury.gov is 3.34% as of Oct. 15, 2018, and the equity risk premium according to Aswath Damodaran is 5.08% as of January 2018. (He publishes this rate monthly.) The total discount rate will, therefore, be 5.08%.
First and Second Stage Growth Rates
The growth rates will be the rates used to grow the starting salaries to a future value. As noted previously, 1960 to 2015 average annual wage growth rate as reported by the U.S. Bureau of Economic Analysis was 6.33%. This figure will be used for both the first and second stage growth rates. Certainly, a more shortterm scientific analysis could be used to determine what the growth rate will be in the nearterm, but when it comes to forecasting, I will take the weight of a 55year average over a shortterm guess.
Summary of Inputs
The inputs for our discounted cash flow model are as follows:
Table 6: Summary of Discounted Cash Flow Model Inputs

Public 
Private 
Ivy League 
FourYear Cost (Tuition and Fees) 
$ 108,422 
$ 215,532 
$ 283,885 
Discount Rate 
9.16% 
9.16% 
9.16% 
2019 Starting Salaries 
$ 79,927 
$ 55,062 
$ 85,676 
First and Second Stage Growth Rates 
6.33% 
6.33% 
6.33% 
The Results
This is where the magic of the spreadsheet comes into play. I pluggedin our previouslynoted inputs into an Excel sheet that has the discounted cash flow, time, and value of money formulas built in and arrived at the following results:
Table 7: Present Value of Discounted Future Earnings and Rate of Return Based on FourYear Cost

Public 
Private 
Ivy League 
PV 
$ 3,003,075 
$ 2,068,811 
$ 3,219,095 
FourYear Cost 
$ 108,422 
$ 215,532 
$ 283,885 
Rate of Return 
84.7% 
33.5% 
38.4% 
The ultimate goal of the discounted cash flow model is to arrive at a singular present value dollar figure (the figurative bird in the bush) that can be compared to other present value figures for other collegiate tiers, and used to determine a rate of return based on the initial investment or, in our case, the fouryear tuition and fees for a degree. Underneath the hood, the model is taking the starting salaries, projecting them forward to a future value based on the growth rate, and then discounting these future earnings back to a present day dollar value using the discount rate.
From the results, a clear winner emerges: public schools have a net present value of approximately $3 million compared to $2.07 million and $3.22 million for private and Ivy League schools respectively. In relation to costs, public schools deliver an 84.7% return compared to 33.5% and 38.4% for private and Ivy League schools. (Note: the rate of return, in this case, is the discount rate that would be necessary to equate the present value to the fouryear cost of the degree. For example, a discount rate of 84.7% for the public tier results in a PV of $108,422, which is the same as the cost.) Corroborating value evidence was also previously supported by our costtosalary ratio analysis, which showed that public schools delivered a 1.36 cost to 2019 starting salary as opposed to 3.91 and 3.31 for private and Ivy League universities respectively. As an interesting aside, Ivy League schools deliver a return that is fairly close to the return delivered by private colleges: 38.4% versus 33.5%.
The Bottom Line
Is an Ivy League education worth it? Our discounted cash flow model delivers a resounding no. According to this model, an individual is much better off valuewise to attend a public school as they can expect to receive a much higher return based on their invested tuition and fees. Of course, this analysis is based on many assumptions: tuition rates, wage growth rates, and discount rates.
Further, it can vary dramatically with the slightest of variances. Think of it as the Hubble Space Telescope; adjust a knob in the slightest, and you are looking at a completely different universe. Still, the assumptions are grounded in rationality, and the evidence is fairly damning for the Ivy League. No, it is not worth it.
Back to Warren Buffett’s Aesop fable. We now know how many birds are in the bush, when they will emerge and the discount rate. Based on this, a soontobescholar will be much better served valuewise by picking the shrub labeled “public.” It may not appear as illustrious as other elite topiaries, but it certainly will be filled with many birds. And of course, don’t literally think birds. Think of dollars.