Question

What is the Net Present Value (NPV) and Internal Rate of Return (IRR) of spending $120,000 today on law school assuming you made $50,000/year before going to law school and $55,000/year for the next 35 years after law school? Assume you could invest this money elsewhere and earn 13%? with financial calculator

answer NPV = ($82,072.14); IRR = 2.26%

Answer 1

Formula for Net Present Value (NPV) calculation

Net present value (NPV) of Project = Present value of future cash flows - initial cash outflow

Where,

Initial Outflow of Cash for project = -$120,000

Present value (PV) of future cash flows can be calculated in following manner

Cash inflows or additional earning (PMT) = $55,000 - $50,000 = $5,000 per year for 35 years

Discount rate i =13%

And time period n = 35 years

Therefore using PV of annuity formula as cash flows are even

PV = PMT * [1-(1+i) ^-n)]/i

PV = $5000 * [1- (1+13%) ^-35]/13%

= $37,927.86

Therefore,

NPV = $37,927.86 - $120,000

=-$82,072.14

Internal rate of return (IRR) is the interest rate at which the net present value of all the cash flows from an investment equal zero.

As the cash inflow is even internal rate of return (IRR) can be calculated as

PV = PMT * [1-(1+i) ^-n)]/i

Where,

Present value (PV) = $120,000

Cash inflows or additional earning (PMT) = $5,000 per year

Internal rate of return (IRR) i =?

And time period n = 35 years

Therefore,

$120,000 = $5,000 * [1- (1+i) ^-35]/i

Use financial calculator to calculate interest rate (I/Y); I = 2.26%