Present Value Case

Present Value Case

PART I

This part of the assignments tests your ability to calculate present value.

A. Suppose your bank account will be worth $15,000.00 in one year. The interest rate (discount rate) that the bank pays is 7%. 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 4%?

Data:

FV = $15,000.00

Interest Rate = 7%

Discount Rate = 4%

Using Present Value formula,

PV = FV / ( 1 + r)

A

B

Future Value (FV)

15000

15000

Discount Rate

7%

4%

Present Value (PV)

14018.69

14423.08

B. Suppose you have two bank accounts, one called Account A and another Account B. Account A will be worth $6,500.00 in one year. Account B will be worth $12,600.00 in two years. Both accounts earn 6% interest. What is the present value of each of these accounts?

Account A

Account B

FV

$ 65,000.00 $ 12,600.00

Discount Rate

6.00%

6.00%

PV

$ 61,320.75 $ 11,886.79

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: $49,000,000Year 2: $61,000,000Year 3: $85,000,000

Compute the present value of this stream of income at a discount rate of 7%. 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 7% 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 5%, and at a discount rate of 3%. Compare the present values of the income stream under the three discount rates and write a short paragraph with conclusions from the computations.

Year

1

2

3

Cash Flow

$ 49,000,000 $ 61,000,000 $ 85,000,000

Discount Rate

7%

7%

7%

Discount Factor @ 7%

0.9346

0.8734

0.8163

Discounted Cash Flows $ 45,794,393 $ 53,279,762 $ 69,385,320

Present Value

$ 168,459,474

Year

1

2

3

Cash Flow

$ 49,000,000 $ 61,000,000 $ 85,000,000

Discount Rate @ 5%

5%

5%

5%

Discount Factor

0.9524

0.9070

0.8638

Discounted Cash Flows $ 46,666,667 $ 55,328,798 $ 73,426,196

Present Value

$ 175,421,661

Year

1

2

3

Cash Flow

$ 49,000,000 $ 61,000,000 $ 85,000,000

Discount Rate

3%

3%

3%

Discount Factor @ 3%

0.9709

0.9426

0.9151

Discounted Cash Flows $ 47,572,816 $ 57,498,350 $ 77,787,041

Present Value

$ 182,858,207

Conclusion

The calculations for ...