Question

You have just won ​$20,000 in the state​ lottery, which promises to pay you ​$1,000​ (tax free) every year for the next twenty years. The interest rate is​ 5%. ​Note: all payments made at the beginning of each year. Part 2 In​ reality, you receive the first payment of ​$1,000​ today, which is worth ​$    enter your response here today. ​(Round your response to the nearest penny.​)

Answer 1

The value of the second​ $1,000 payment is worth $ 952.38

The net present value is given by the expression as shown below:

         $NPV = \frac{future value }{(1 + r)^{n} }$

Plugging the values in the above expression,          

Future value =$1,000

                    r=0.05

                    n=1

            $NPV = \frac{1000}{(1 + 0.5)^{1} }$

           $NPV = 952.38$

The value of the second​ $1,000 payment is worth $ 952.38

What Is Net Present Value (NPV)?

Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. NPV is used in capital budgeting and investment planning to analyze the profitability of a projected investment or project. NPV is the result of calculations used to find today’s value of a future stream of payments.

Net Present Value (NPV) Formula:

$NPV = \frac{R_{t} }{(1 + r)^{t} }$

where:

$R_{t}$ =Net cash inflow-outflows during a single period

i =Discount rate or return that could be earned in alternative investments.

t=Number of timer periods

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