Adam Smith is considering an MBA degree. He estimates that he will forgo after t
ID: 2619185 • Letter: A
Question
Adam Smith is considering an MBA degree. He estimates that he will forgo after tax income of $8,000 a year (he will have a part time job), during the three years it will take him to complete the degree, but his expenses will be $5,000 a year less than if he were working. Tuition will be $9,000 at the beginning of the first year, $10,000 at the beginning of second year, and $11,000 at the beginning of third year. He estimates that his income will be $14,000 a year higher, after tax, for his 25-year working life after he receives the MBA. He can borrow money needed at an interest rate cost of 10%, after tax.
a. What is the present value today (t=0) of additional income earned after MBA degree ? (example of answer format: $1000.00 or 1000)
b. What is the NPV of getting an MBA degree? (example of answer format: $1000.00 or 1000)
Explanation / Answer
a. What is the present value today (t=0) of additional income earned after MBA degree?
We can use following Present Value of an Annuity formula to calculate the present value of additional income earned after MBA degree after 3 years
PV of additional income = PMT * [1-(1+i) ^-n)]/i
Where
Present value of additional income (PV) =?
Annuity payments (additional income) PMT =$14,000
Annual interest rate I =10%
Number of periods n = 25 years
Therefore,
PV of additional income = $14,000 * [1- (1+10%) ^-25]/10%
= $127,078.56
Therefore the present value of additional income earned after MBA degree after 3 years (at t=3) will be $127,078.56.
And present value of this annuity today is (at t=0)
= $127,078.56/ (1+10%) ^3
= $95,476
Therefore present value of additional income earned after MBA degree is $95,476.
b. What is the NPV of getting an MBA degree?
Net present value (NPV) of getting an MBA degree = present value of additional income earned after MBA degree – Present value of cost incurred for MBA degree
Present value of cost incurred for MBA degree = present value of forgone after tax income of $8,000 a year for three years - expenses of $5,000 a year (as it will be less than if he were working) + present value of tuition fees
Where,
Present value of forgone after tax income of $8,000 a year for three years - expenses of $5,000 a year
= $3,000/ (1+10%) ^1 + $3,000/ (1+10%) ^2 + $3,000/ (1+10%) ^3
=$2,727.27 + $2,479.34 + $2,253.94
= $7,460.56
Tuition will be $9,000 at the beginning of the first year, $10,000 at the beginning of second year, and $11,000 at the beginning of third year
Therefore Present value of tuition fees = $9,000 / (1+10%) ^0 + $10,000 / (1+10%) ^1 + $11,000 / (1+10%) ^2
= $9,000 + $9,090.91 + $9,090.91
= $27,181.82
Present value of cost incurred for MBA degree = $7,460.56 +$27,181.82 = $34,642.38
The Net present value (NPV) of getting an MBA degree = $95,476- $34,642.38
=$60,833.62
Therefore Net present value (NPV) of getting an MBA degree is $60,833.62.
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