Cost-Benefit Analysis of Attending University

The decision of whether to attend university requires the consideration of a multitude of factors which must be considered before making a choice. This includes weighing up the opportunity costs of all university expenses and the wage that could have been earned whilst working, versus the benefits of a wage premium that graduates achieve and the potentially large difference in future earnings.

The earning profiles of graduates and non-graduates differ almost immediately at university entrance age, as most non-graduates are likely to enter the labour market in entry-level jobs or apprenticeships. On the other hand, graduates are not likely to be in full time employment during their studies, but tend to enter the labour market at a later stage, although perhaps in a higher paying job, as shown in Figure 1. At the age of 21, the average wage stream of a graduate quickly crosses and overtakes that of a non-graduate, the opportunity cost of not being in work outweighed by the benefit of the higher average earning stream. The act of attending university may also signal to an employer a higher aptitude for the skills required in a job, potentially making them more employable.

A female graduate can be expected to earn about £250,000 more if they have a degree over the course of a lifetime, and men are expected to earn about £170,000 more¹. Nevertheless, subject choice plays a large role in future earnings, with medicine and dentistry students earning up to £46,700 on average, more than double the earnings of art and design students, earning £20,100 on average, although these degree choices also depend on ability. Graduates from different universities also have different earnings, with those from Russell Group universities earning 40% more on average than those from other institutions.

However, the costs accumulated by the end of a degree must also be taken into account; the £9,250 per year tuition fee loan is hefty and the maintenance loans caps at £11,354 per annum³, which is dependent on whether the university is in London and on the income of the parents. On average students graduate with debts of more than £50,000¹. Once a graduate earns in excess of £25,000, 9% of their income over the threshold is payed towards reimbursing their loan at a real interest rate of 3% p.a., and any remaining debt is cancelled after 30 years¹, although complete repayment is unlikely for most.

Cost-benefit analysis can be applied in order to determine whether the future benefits of investing in university are worthwhile, using the net present value of the earnings of graduates versus non-graduates. To simplify the model, the present value of the cash flow (the annual profit) each year is examined. The assumptions that must be taken into account are that the average starting salary of a non-graduate is £16,000⁸, the average starting salary of a graduate is £26,000⁵ , both with a long-run real earnings growth rate of 1.1%⁶, and that the individuals will be in employment for 50 years, although the non-graduate starts employment 3 years earlier than the graduate. This would also mean that repayment of the tuition loan would begin immediately, at 9% of however much above the threshold they earn yearly. The NPV is calculated as the growth adjusted wages that graduates earn over non-graduates minus the cost of the loan with a 3% real interest rate p.a..The discount rate is taken as 5%, which reflects the personal relative value placed on future versus current consumption. Using the formula:

NPV = $\left(–16,000\right)+\frac{–16176–0}{(1+5\%{)}^1}+\frac{–16353–0}{(1+5\%{)}^2}+\frac{10000–92.7}{(1+5\%{)}^3}+\dots +\frac{17092–1802.1}{(1+5\%{)}^{50}}$

= £174,122 > 0

The NPV is clearly indicates that the investment to education is justified as the return to higher education will be positive and large.

Despite positive returns, the rate of interest can affect individual’s decisions. Currently the maximum interest on a tuition loan is the Retail Price Index (RPI), presently at 3.3% plus up to 3%. RPI is a measure of inflation, but is more volatile than the Consumer Price Index. This could over time increase the value of the loan, which could negatively impact a particularly high earning graduate, who without an increase in interest rates would have been able to repay the loan completely. This does not apply to those who can privately finance their education, as they have no loan to accumulate interest on.

The choice of degree subject could vary greatly between individuals. Some are driven only by the eventual rate of return of going to university, and some are driven by a passion for a subject. The ability of a student often has the greatest impact on choice, as students are more likely to choose a degree in which they are capable in, but this could also depend on the risk aversion of the individual. If a student is risk preferring they may be more inclined to attempt to study a more difficult degree with a higher payoff, but they could fail or attain a lower class degree, than had they studied an easier subject. The degree class can impact future lifetime earnings of an individual, with a higher class degree leading to higher earnings. Figure 2. shows that the range of median earnings is over a spread of £26,600 annually, indicating that degree choice has a significant impact on earnings and should be carefully deliberated.

Prospective students may have incomplete information about degree choice, and may lack information about their ability to succeed at university, leading to a risky investment with an uncertain payoff. The individual should choose to maximise their utility, taking into consideration their ability and interest in a subject. In order to reduce dropout rates and improve scores the universities should have full information about the pupil so as to make sure that the degree is suitable for their ability.

Now to consider that the individual has chosen to study economics, but there is a probability of a half that half-way through their working life the subject matter of a degree becomes irrelevant. As the degree quality still affects the university premium, the expected value should be calculated in order to conclude whether the individuals decision will be affected or not. The student then has the first outcome of the economics degree remaining relevant, or the economics degree becoming obsolete. The second outcome is the degree class, a first class honours, second class honours or a third class honours. When attaining a good degree, in this case first class, the wage premium is on average 8%¹¹. Assuming that graduating with a first class degree will entail the individual to an 8% premium on top of an average economics graduate wage, a third class degree will reduce the premium by 8% also. The second W_B’ variable is included to show the premiums on an average graduate degree, also using 8%. These outcomes are laid out in Figure 3.

There are six possible outcomes for the expected pay-off, using the formula E(W) =  p_A* W_A + (1- p_A )* W_B.

1. E(W) = 0.5 * 40,000 + 0.5 * 43,200 = 41,600

2. E(W) = 0.5 * 40,000 + 0.5 * 40,000 = 40,000

3. E(W) = 0.5 * 40,000 + 0.5 * 36,800 = 38,400

4. E(W) = 0.5 * 30,000 + 0.5 * 32,400 = 31,200

5. E(W) = 0.5 * 30,000 + 0.5 * 30,000 = 30,000

6. E(W) = 0.5 * 30,000 + 0.5 * 27,600 = 28,800

These findings that graduating with a first class honours whether or not the subject matter of economics becomes irrelevant is not surprising. The expected wage of non-graduates averages around £23,000⁵, which is still 25.22% lower than if the degree subject did not matter and the student graduated with a third class honours. Risk can be included in the model if it is extended to the expected utility theory, whereby risk is also considered with regard to the expected value. The expected utility of the degree staying relevant and achieving a second class degree would be : EU = 0.5*U(40,000) + 0.5*U(40,000). With the assumption that this individual is risk-averse and therefore has a concave utility function of U( $W$

) = $\sqrt{W}$

, the individual has a decreasing marginal utility to wealth as for every additional increase in utility, the returns to utility are diminishing. Their expected utility would be 200, moreover for equation six the expected utility is 170 but for a non-graduate the expected utility is 152. This shows an increase in the expected utility by attending university at every level.

Although the individual has chosen to commit their opportunity costs to maximising their welfare by choosing to study, it is surprising that governments make use of public funds to subsidise this investment in human capital, as the returns to the investment are largely a private gain⁷. Taxpayer money is used to make up the difference of what the individual does not repay, signifying the strong interest the government has for maximising individual’s welfare. Beyond that, the government has the ability to redistribute wealth and resources to members of society less endowed¹⁰, in order to reduce inequality and improve efficiency and equity within a society. Inequality is still prevalent in the wage gap between men and women, in which the degree subject and university has no influence. Five years after graduation, the wage gap has increased up to 14%¹, which continues with age. In addition, market mechanisms do not always allow for a fair allocation of income, for which government subsidies in the form of tuition loans as an in-kind transaction can allow prospective graduates from a poorer background to attend university. Although the government has improved access to university for poorer students, the issue of social mobility has not been eradicated, with richer students earning around 10%¹ more than their poorer colleagues even doing the same subject at the same university.

A change that benefits some people without harming any others, called the Pareto principle, should be the ideal when making welfare decisions. If a reallocation of goods to subsidise for university tuition benefits multiple people, then it may be valued as favourable by some people, but a judgement of equity has many different interpretations and the efficient allocation of resources does not necessarily mean the most equal amongst a society.

It could be argued that education and training are the most valuable investments in human capital. Assuming that humans are rational beings, they ultimately seek to maximise their own utility, which could be achieved through completing a degree at university, although not without careful consideration of factors such as the individual’s own ability, the degree to pursue and which institution to pursue it in. The benefits of increased labour market earnings must be weighed against the costs of student debt, but overall the benefits of attaining a degree still greatly overshadow the costs.

Bibliography

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Figure 1. Dearden, L. (2004). An analysis of higher education reforms. [online] Available at: https://www.researchgate.net/ [Accessed 14 Nov. 2018].

Figure 2 . BBC News. (2017). The degrees that make you rich… and the ones that don’t. [online] Available at: https://www.bbc.co.uk/news/education [Accessed 10 Nov. 2018].