TUI University

FIN301-Principles of Finance

December 2012

Elaine Ust

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%? SOLUTION:

Formula for Present Value:

PV = FV n {[1/ (1 + i) n}

Where PV = the present value of the future sum of money

FV n = the future value of the investment at the end of n years

n = the number of years until the payment (or stream) will be received

i = the annual discount or interest rate

in the problem:

FV n = $ 15,000

n = 1 year

i = 7%

PV = $15,000 (1 / (1 + .07) 1

= $ 15,000 (1/ 1.07) = $15,000 (.9356)

PV = $ 14,019

At i = 4%

PV = $15,000 (1 / (1 + .04) 1

= $ 15,000 (1/ 1.04) = $15,000 (. 9615)

PV = $ 14,422.50

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?

Solution:

PV = FV n {[1/ (1 + i) n}

Where PV = the present value of the future sum of money

FV n = the future value of the investment at the end of n years

n = the number of years until the payment (or stream) will be received

i = the annual discount or interest rate

in the problem:

For Account A

FV n = $ 6,500

n = 1 year

i = 6%

PV = $ 6,500 (1 / (1 + .06) 1

= $ 6,500 (1/ 1.06) = $ 6,500 (.9434)

PV = $ 6,132.08

For Account B

FV n = $ 12,600

n = 2 years

i = 6%

PV = $ 12,600 (1 / (1 + .06) 2

= $ 12,600 (1/ (1.06) 2

=$12,600 (1/1.1236)

= $12,600 (.8899)

PV = $ 11,212.74

C. Suppose you just inherited a 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: $49,000,000

Year 2: $61,000,000

Year 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.

SOLUTION:

Same formula of present value will be used. However, in this problem, it will be the sum of all the present values of the future stream of amounts to be received.

PV = FV n {[1/ (1 + i) n}

Where PV = the present value of the future sum of money

FV n = the future value of the investment at the end of n years

n = the number of years until the payment (or stream) will be received

i = the annual discount or interest rate

PV = PV = $ 49,000,000 {[1/ ( 1 + .07 ) 1 } + $ 61,000,000 {[1/ ( 1 + .07 ) 2 }

+ $ 85,000,000 {[1/ (1 + .07) 3}

= $ 49,000,000 (1/1.07) + $61,000 [1/ (1 .07) 2] + $85,000,000 [1/ (1 .07) 3] = $ 49,000,000 (.9346) + $61,000,000 (.8734) + $85,000,000 (.8163) = $ 45,794,392.52 + $53,277,400 + $69,385,500

PV= $ 168,457,292.50

At a discount rate of 7% ( or possibly an inflation rate of 7 %), the expected earnings for the gold mine for the three year-period as valued today will be $ 168,457,292.50 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...

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