Question

Linda is considering studying towards a Bachelor of Agribusiness degree, which takes three years to complete. The degree would cost her $9,500 per year in fees, payable at the beginning of each year. Instead of studying towards the BAgB degree, Linda could get a job immediately, earning $35,000 per year (assume this amount is paid at the end of each year). She estimates that he would receive an additional $20,000 per year (i.e. $55,000 per year) in income for 40 years after graduation, if she completes the BAgB degree. At a discount rate of 10%, this additional income has a present value equal to 7.347 times the annual amount. Considering only the private costs and benefits of this decision, and assuming a discount rate of 10%, should Linda study towards a BAgB degree? Show all your workings.

Answer 1

Present value of BAgB degree's costs = present value of annuity due of $9500 for k = 10% and n = 3 years. Note that is an annuity due because fees are payable at the beginning of each year. Now present value of annuity due = P + P*[1-(1+r)^-(n-1)/r]

= 9500 + 9500*[1-1.1^-(2)/0.10]

= $25,987.60

Opportunity cost of job not taken if degree is pursued will be = present value of $35,000 per year. This is a normal annuity as payments are made at the end of each year. Hence its present value = P* [ 1- (1+i)^(-n)/i]

= 35,000 * [ 1- 1.1^-3/0.1]

= $87,039.82

Thus total costs of degree (including the opportunity cost) = 25987.60 + 87039.82 = $113,027.42

Benefits of graduation = additional income of $20,000 for 40 years at 10%. Now present value of this benefit = 20,000 * 7.347 (as given in the question) = $146,940

Thus we can see that benefits of $146,940 > costs of $113,027.42. Hence Linda should study towards a BAgB degree.