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Principles of Finance

Present Value

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%?

PV=FV/(1+r)t, PV=7,000/1.08 = $6,481.48 at 8%

PV=7,000/1.03, = $6,796.12 at 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?

Account A PV=FV/(1+r)t, PV=4,000/1.05 = $3,809.52

Account B PV=FV/(1+r)t, PV=9,600/1.1025 = $8,707.48

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 oil well at a 8% discount rate but you have to show how you got to this number.

PV=(FV/(1+r)t1)+(FV/(1+r)t2)+ (FV/(1+r)t3)

PV=(42,000,000/(1.08)t1)+(62,000,000/(1.08)t2)+ (99,000,000/(1.08)t3)

PV=(42,000,000/1.08)+(62,000,000/1.1664)+(99,000,000/1.259712)

PV=38,888,888.88 + 53,155,006.86 + 78,589,391.86

PV=$170,633,287.61

Now compute the present value of the income stream from the gold mine at a…...

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