Question

Consider an eighteen-year-old high school student that is about to graduate. She lives for two periods. If she decides to attend university, she has zero earnings in Period 1 and she earns $1,400,000 in Period 2. However, if she decides NOT to attend university, she earns $600,0000 in Period 1 and $650,000 in Period 2. Suppose university is free (i.e. no tuition) and the discount rate is 0.1 to discount the earnings in Period 2.

a) Should she attend university? Show your work.

b) Based on the information above, what is the internal rate of return?

Answer 1

PV of earnings with university education at year 0 = 1,400,000 x P/F(0.1, 2) = 1,400,000 x 0.8264

= 1,156,960

PV of earnings without university education at year 0 = 600,000 x P/F(0.1, 1) + 650,000 x P/F(0.1, 2)

= 600,000 x 0.9091 + 650,000 x 0.8264 = 545,460 + 537,160

= 1,082,620

Since PV of earnings with university education is higher, she should attend university.

(b)

If IRR be r%, then PV of earnings of both options discounted at IRR is equal.

1,400,000 x P/F(r%, 2) = 600,000 x P/F(r%, 1) + 650,000 x P/F(r%, 2)

(1,400,000 - 650,000) x [1 / (1 + r)²] = 600,000 / (1 + r)

750,000 / (1 + r) = 600,000 [multiplying both sides by (1 + r)]

1 + r = 1.25

r = 0.25

r = 25%