Question

First part of the question: Eighteen-year-old Linus is thinking about taking a five-year university degree. The degree will cost him $25,000 each year. After he's finished, he expects to make $50,000 per year for 10 years, $75,000 per year for another 10 years, and $100,000 per year for the final 10 years of his working career. All these values are stated in real dollars. Assume that Linus lives to be 100 and that real interest rates will stay at 5% per year throughout his life.

Linus is also considering another option. If he takes a job at the local grocery store, his starting wage will be $40,000 per year, and he will get a 3% raise each year, in real terms, until he retires at the age of 53. Assume that Linus lives to be 100.

i.    Calculate the present value of Linus’s lifetime earnings, using a spreadsheet or using the growing annuity formula. You can find the formula in the lesson notes, at the end of Note 7 in Lesson 4.    (1 mark)

ii. Use that value to determine Linus’s permanent income, i.e., how much can Linus spend each year equally over the rest of his life?                                                          (1 mark)

c.       Do you think Linus is better off choosing option a. or option b.? Consider both financial and non-financial measures.

Answer 1

i) The present value of the lifetime earning

Let us consider 18th year of Mr. Linus as the base year or Zeroth year or the present year

Option A: Earning after a five-year university degree.

Present value = 50000(P/A,5,10)(P/F,5,5) + 75000(P/A,5,10)(P/F,5,15) + 100000(P/A,5,10)(P/F,5,25)

Using DCIF Tables

Present value = 50000(7.7217)(0.7835) + 75000(7.7217)(0.4810) + 100000(7.7217)(0.2953)

Present value = $809080

Option B: Taking a job at a local grocery store (The number of years of work = 53 - 18 = 35 years)

Present value = [40000 + 0.03*40000(A/G,5,35)](P/A,5,35)

Using DCIF Tables

Present value = [40000 + 0.03*40000(12.2498)](16.3742)

Present value = $ 895665

ii) How much can Linus spend each year equally over the rest of his life ie (100-18 = 82 years) using:

a) Option A with PV = $809080

Annual worth = PV(A/P,5,82)

(A/P,5,82) =  i(1+i)^n / (1+i)^n – 1 =  0.05(1+0.05)^82 / (1+0.05)^82 – 1 = 0.050932

Annual worth = 809080(0.050932)

Annual worth = $41208

b) Option B with PV = $895665

Annual worth = PV(A/P,5,82)

(A/P,5,82) =  i(1+i)^n / (1+i)^n – 1 =  0.05(1+0.05)^82 / (1+0.05)^82 – 1 = 0.050932

Annual worth = 895665(0.050932)

Annual worth = $45618

iii) In order to choose a better option let us use net present worth comprisn for both the options

​​​​​Net Present worth = Present worth of benefits(Already calculated) -  Present worth of costs

Option A

​​​​​Net Present worth = 809080 - 25000(P/A,5,5)

Using DCIF Tables

​​​​​Net Present worth = 809080 - 25000(4.3295)

​​​​​Net Present worth = $700842.5

Option B

Net Present worth = 895665 - 0

Net Present worth = $895665

Based on the financial aspect (Present worth analysis) Option B is better. However, Non financial consideration will also influence taking option A into consideration as it would give advantage to getting better prospects on the job.

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