Zhengxi, aged 21, is considering whether or not to go to university for four yea
ID: 1198745 • Letter: Z
Question
Zhengxi, aged 21, is considering whether or not to go to university for four years. For simplicity assume that he is paid, and pays tuition, at the beginning of each year, and that his alternative income streams are both in real terms. If he attends university he will earn $40000 per year after graduation. If he does not attend he will earn $35000 per year. Zhengxi expects that the probability of unemployment will be constant each year of his working life at 10% if he attends university, and 20% if he does not. He expects to retire at age 65 (e.g. he expects to work for 40 years if he attends university). The direct costs of attending university are $5000 per year. The real rate of interest is 4%.
a)Identify the direct and opportunity costs of attending university.
b)Based on Zhengxi’s expectations, show whether he should go to university
Explanation / Answer
a) the direct costs are cost of attending university and opportunity cost is the earning Zhengxi (Z) will be missing if he joins the university
b) We will use Present Worth (PW) method to analyse the decision
Actual earning per year with 10% probability of unemployment after attending university = 40000*(100-10)/100 = 36000
Actual earning per year with 20% probability of unemployment when not attending university = 35000*(100-20)/100 = 28000
MARR = 4% = 0.04
PW of not attending university = 28000/(1+0.04)^0 + 28000/(1+0.04)^1 +28000/(1+0.04)^2 + ................................+ 28000/(1+0.04)^43 +28000/(1+0.04)^44 = 28000((1-(1/1.04)^45)/(1-1/1.04) (Sum of geometric progression) = 28000*0.829/0.038 = $610842
PW of attending university =PW of Earning - PW of cost of education
PW of cost of education = 5000/(1.04)^0 + 5000/(1.04)^1 + 5000/(1.04)^2 + 5000/(1.04)^3 = $18875
PW of earning = 36000/(1.04)^4 + 36000/(1.04)^5 + 36000/(1.04)^6 + ..................................+ 36000/(1.04)^43 + 36000/(1.04)^44 = 639855
PW of Attending university = 639855-18875 =$620980
So he should go to univeraity as PW of going to university is more.
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