## ASSIGNMENT 6

**Used Symbols**

PV = Present Value

FV = Future Value

n = The discounting period

r = the discount rate/interest rate

- To what present value would $20,000 received in five years, assuming an annual discount rate of 5%?

PV = FV/(1+r)^{n}

= 20,000/(1 + 5%)^{5}

**Present Value = $15,670.52**

- Benefits received in the future are adjusted to their present value (discounted) because:
- they are uncertain.
- the future may never come, or may come under unforeseen circumstances.
- markets indicate that people need to be compensated for postponing the enjoyment of benefits
**None of the above is true.**- You won a $1,000,000 in the Hoosier Lottery. You can tell your instructors what you really think of them, quit school, quit your job and never have to work another day in your life. You are a free person. Are you really?

Your decision with your lottery winnings has 2 options.

- Take $50,000 per year for the next 20 years
- Take the Cash Option. You know that cash today is worth more than cash tomorrow because you learned the time value of money in V186. You believe that you can invest and get a better return than the Lottery’s discount rate or that you can enjoy the benefits of winning now instead of later.

You decide to take the Cash Option (2) so….

You remember from V186 the discounting formula in the Mikesell textbook. It is PV=FVn/(1+r)n

The Hoosier Lottery has a discount rate of 6%. How much money will you receive by taking the cash option?

PV = FV/(1+r)^{n}

PV= 1 million /(1 + 6%)^20

PV=1,000,000/3.207

**PV= $311,817.90**

- To what present value would $50,000 received in five years, assuming an annual discount rate of 4%

PV = FV/(1+r)^{n}

= 50,000/(1.04)^{5}

**PV = $41096.36**

- To what present value would $250,000 received in ten years, assuming an annual discount rate of 15%?

PV = FV /(1 + r)^{n})

PV = 250,000/(1+ 15%)^{10}

**PV =$61,796.18**

- To what present value would $500,000 received in six years, assuming an annual discount rate of 5%?

PV = FV/(1 + r)^{n})

PV = $500,000/(1+ 5%)^{6}

**PV =$373,107.70**

- To what present value would $1,500,000 received in twenty years, assuming an annual discount rate of 9%?

PV = FV/(1 + r)^{n})

PV = $1,500,000/(1+ 9%)^{20}

**= **$1,500,000/5.6044

**PV =$267,646.85**

- To what present value would $1,000,000 received in ten years, assuming an annual discount rate of 2%?

PV = FV/(1 + r)^{n})

PV = $1,000,000/(1+ 2%)^{10}

**= **$1,000,000/1.219

**PV =$820,344.54**

- To what present value would $650,000 received in five years, assuming an annual discount rate of 5%?

PV = FV/(1 + r)^{n})

PV = $650,000/(1+ 5%)^{5}

**= **$650,000/1.276

**PV =$509,404.39**

- The Mega Million payout today is $244,000,000 received in 20 years, assuming an annual discount rate of 3%. What would be the cash option if you win?

PV = FV/(1 + r)^{n})

PV = $244,000,000/(1+ 3%)^{20}

**= **$244,000,000/1.8061

**PV =$135,097,724.40**