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# Determination of PV (Research Paper Sample)

Instructions:

Assignment:
NOTE: This assignment is in two parts, one is quantitative problem, the other a short paper. You need to turn in both Part I and Part II to receive full credit for this assignment.
Part I: This part of the assignments tests your ability to calculate present value.
A. Suppose your bank account will be worth $7,000.00 in one year. The interest rate (discount rate) that the bank pays is 8%. What is the present value of your bank account today? What would the present value of the account be if the discount rate is only 3%?
B. Suppose you have two bank accounts, one called Account A and another Account B. Account A will be worth $4,000.00 in one year. Account B will be worth $9,600.00 in two years. Both accounts earn 5% interest. What is the present value of each of these accounts?
C. Suppose you just inherited an gold mine. This gold mine is believed to have three years worth of gold deposit. Here is how much income this gold mine is projected to bring you each year for the next three years:
Year 1: $42,000,000
Year 2: $62,000,000
Year 3: $99,000,000
Compute the present value of this stream of income at a discount rate of 8%. Remember, you are calculating the present value for a whole stream of income, i.e. the total value of receiving all three payments (how much you would pay right now to receive these three payments in the future). Your answer should be one number - the present value for this gold mine at a 8% discount rate but you have to show how you got to this number.
Now compute the present value of the income stream from the gold mine at a discount rate of 6%, and at a discount rate of 4%. Compare the present values of the income stream under the three discount rates and write a short paragraph with conclusions from the computations.
Part II: Read the following three sample business plans:
Ice Dreams
R J Wagner & Associates Realty
Interstate Travel Center
Which of these three projects do you think should have the highest risk from the point of view of investors (potential providers of funds) and would therefore be evaluated using the highest discount rate? Which one do you think should have the lowest? Write a paper explaining your reasoning.
In your assessment of the business plans consider the possible risk of each plan. Risk is one of the main considerations when deciding whether a plan should be evaluated and discounted to present value using a high or a low discount rate.
Note: you are not expected to fully analyse the numbers and financial statements in these business plans. There are only forecasts and projections. Nobody really believes them anyway. Use your intuition rather than calculations to assess risk and potential of each of these plans.
Assignment Expectations:
Turn in both Part I and Part II in one Word document. Part I should be two pages long and contain your calculations. Part II should be two pages long
source..

Content:

Determination of PV

Part I

* Suppose your bank account will be worth $7,000.00 in one year. The interest rate (discount rate) that the bank pays is 8%.

What is the present value of your bank account today?

PV = C/ (1+i) t

= 7,000/ (1+0.08)1= $ 6,481.48

What would the present value of the account be if the discount rate is only 3%?

= 7000/ (1+0.03)1 =$ 6,796.12

* Suppose you have two bank accounts, one called Account A and another Account B. Account A will be worth $4,000.00 in one year. Account B will be worth $9,600.00 in two years. Both accounts earn 5% interest.

What is the present value of each of these accounts?

Account A

PV = C/ (1+i) t

= 4000/ (1+0.05)1

= 3,809.52

Account B

PV = C/ (1+i) t

= 9600/ (1+0.05)1

= $9,142.86

* PV = C/ (1+i) t

I= 8%

1st year

= 42,000,000/ (1+0.08)1

=$38,888,888.89

2nd year

=62,000,000/ (1+0.08)2

=$53,155,006.86

3rd year

=99,000,000/ (1+0.08)3

=$78,589,391.86

PV = C/ (1+i) t

I= 6%

1st year

= 42,000,000/ (1+0.06)1

=$39,622,641.51

2nd year

=62,000,000/ (1+0.06)2

=$55,179,779.28

3rd year

=99,000,000/ (1+0.06)3

=$83,122,309.02

PV = C/ (1+i) t

I=4%

1st year

= 42,000,000/ (1+0.04)1

=$40,384,615.38

2nd year

=62,000,000/ (1+0.04)2

=$55,117,774.24

3rd year

=99,000,000/ (1+0.04)3

=$88,010,639.51

As the interest rate decreases the present value increases. This implies that in order to have substantial benefits with less investments, the interest rates must be high.

Part II: Evaluation of Projects

In this scenario, we are provided with three ...

Part I

* Suppose your bank account will be worth $7,000.00 in one year. The interest rate (discount rate) that the bank pays is 8%.

What is the present value of your bank account today?

PV = C/ (1+i) t

= 7,000/ (1+0.08)1= $ 6,481.48

What would the present value of the account be if the discount rate is only 3%?

= 7000/ (1+0.03)1 =$ 6,796.12

* Suppose you have two bank accounts, one called Account A and another Account B. Account A will be worth $4,000.00 in one year. Account B will be worth $9,600.00 in two years. Both accounts earn 5% interest.

What is the present value of each of these accounts?

Account A

PV = C/ (1+i) t

= 4000/ (1+0.05)1

= 3,809.52

Account B

PV = C/ (1+i) t

= 9600/ (1+0.05)1

= $9,142.86

* PV = C/ (1+i) t

I= 8%

1st year

= 42,000,000/ (1+0.08)1

=$38,888,888.89

2nd year

=62,000,000/ (1+0.08)2

=$53,155,006.86

3rd year

=99,000,000/ (1+0.08)3

=$78,589,391.86

PV = C/ (1+i) t

I= 6%

1st year

= 42,000,000/ (1+0.06)1

=$39,622,641.51

2nd year

=62,000,000/ (1+0.06)2

=$55,179,779.28

3rd year

=99,000,000/ (1+0.06)3

=$83,122,309.02

PV = C/ (1+i) t

I=4%

1st year

= 42,000,000/ (1+0.04)1

=$40,384,615.38

2nd year

=62,000,000/ (1+0.04)2

=$55,117,774.24

3rd year

=99,000,000/ (1+0.04)3

=$88,010,639.51

As the interest rate decreases the present value increases. This implies that in order to have substantial benefits with less investments, the interest rates must be high.

Part II: Evaluation of Projects

In this scenario, we are provided with three ...

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