Question

Problem #2: Schooling Bill lives for four periods. He is currently considering the following alternative education work options.

A) He starts working immediately, earning $200,000 in period 1 (today), $250,000 in period 2, $280,000 in period 3, and $300,000 in period 4. 1

B) He spends $100,000 to attend college in period 1 (and does not work), earns $300,000 in periods 2, $450,000 in period 3, and $550,000 in period 4.

C) After completing college in period 1 (which costs $100,000), he attends graduate school in period 2 (and does not work), which costs another $100,000. After receiving his graduate degree, he will earn $600,000 in period 3, and $800,000 in period 4.

Assume Bill’s discount rate is 10% per period and answer the following questions.

1. Calculate the present value of Bill’s earnings associated with each of these alternatives (using a calculator). What education path maximizes Bill’s net present value of his lifetime earnings?

2. Now assume that the graduate program offers a research assistantship which covers his graduate school expenses in period 2 for alternative c. What education path maximizes Bill’s net present value of his lifetime earnings now?

3. Suppose Ann has the same alternatives as Bill but her discount rate is 30%. What education path maximizes Ann’s net present value of his lifetime earnings? (assume that she also receives an assistantship for grad school so that her direct schooling cost in period 2 is zero for alternative c)

Answer 1

ANSWER :-

1)

Present value for Bill for each of the alternatives are:

Option 1 :

PV = {200000/(1+.10)^1} + {$250000/(1+.10)^2} + {$280000/(1+.10)^3} + {$300,000/(1+.10)^4}

=181818.181+206611.57+210368.14+204904.03

PV = 803,701.927

Option 2 :

PV = {-100000/(1+.10)^1} + {$300000/(1+.10)^2} + {$450000/(1+.10)^3} + {$550,000/(1+.10)^4}

=-90,909.09+247,933.884+338,091.66+375,657.400

PV = 870,773.854

Option 3

PV = {-100000/(1+.10)^1} + {$0/(1+.10)^2} + {$600000/(1+.10)^3} + {$800,000/(1+.10)^4}

=-90,909.090+0+450,788.880+601,051.84

PV = 960,931.630

The third option maximizes the NPV for Bill.

2)

Dividing the expense of education in two parts – 100000/2 = 50000

PV = {-50000/(1+.10)^1} + {$50000/(1+.10)^2} + {$600000/(1+.10)^3} + {$800,000/(1+.10)^4}

=-45,454.54+41,322.314+450,788.88+546,410.76

PV = 993067.418

The third part maximizes his path of earning.

3)

Option 1 :

PV = {200000/(1+.30)^1} + {$250000/(1+.30)^2} + {$280000/(1+.30)^3} + {$300,000/(1+.30)^4}

=153,846.153+147,928.994+127,447.517+105,038.338

PV = 534,261.002

Option 2 :

PV = {-100000/(1+.30)^1} + {$300000/(1+.30)^2} + {$450000/(1+.30)^3} + {$550,000/(1+.30)^4}

=-76,923.076+177,514.792+204,824.761+192,570.288

PV = 497,986.765

Option 3

PV = {-100000/(1+.30)^1} + {$0/(1+.30)^2} + {$600000/(1+.30)^3} + {$800,000/(1+.30)^4}

= -76,923.076+0+273,099.681+280102.237

PV = 476,278.842

For Ann option 1 is the best option.

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