The concept of present value is very important in corporate finance, and in any business because "The time value of money (TVM) is the basic mathematics of investing and is the basis of all financial calculations" (Investing in Mutual Funds, 2010, paragraph 1). It is suggested that corporations have a good understanding of the time value of money concept by utilizing the company's present value to determine "expected and actual returns on investments" (Investing in Mutual Funds, 2010, paragraph 1).
A corporation that utilizes the present values calculation is better able to make effective financial decision in terms of interest and non interest earned, bad debt generated from loans, budgeting, and various other corporate financial decisions (University of West Florida, n.d). Calculating the present value can act as financial road map for corporations.
Future Value Calculations
$500 if invested for five years at a 4% interest rate
$500.00 (1 + 4%)5th =
$500.00 (1.04)5th = $608.00
End of Year:
1
2
3
4
5
Principal:
$500
$520
$540.80
$562.43
$608.33
Interest:
$20
$20.8
$21.63
$22.5
Total:
$520.00
$540.80
$562.43
$608.33
To determine the Future Value of $500 dollars invested for 5 years at a 4% interest rate, the Future Value: $500 was multiplied by 1 plus the interest rate 4% (1.04) times the number of years invested (5). After one year of investing $500 at a 4% (1.04) the future value is $520.00 with $20 of accrued interest. The interest accrued was determined by multiplying the principal of $500 by 1 plus 4% (1.04), which equals $520.00 (Principal after one year), then, $520.00 (Principal after one year) minus $500 (beginning Principal) = $20. This step is repeated for the 5 year increment by multiplying the year end total with 1 plus 9% (1.09) to determine the future value of $500 if invested for five years at a 4% interest rate. To determine the interest gained per year each years principal was subtracted by the year ends total
b. $150 if invested for three years at a 9% interest rate
150.00 (1 + 9%)3rd =
150.00 (1.09)3rd = $194.25
To determine the Future Value of $150 dollars invested for 3 years at a 9% interest rate, the Future Value: $150 was multiplied by 1 plus the interest rate 9% (1.09) times the number of years invested. After one year of investing $150 at a 9% (1.09) the future value is $163.5 with $13.50 of accrued interest. The interest accrued was determined by multiplying the principal of $150 by 1 plus 9% (1.09), which equals $163.50 (Principal after one year), then, $163.50 (Principal after one year) minus $150.00 (beginning Principal) = $13.50. This step is repeated for the 3 year increment by multiplying the year end total with 1 plus 9% (1.09) to determine the future value of $150 if invested for three years at a 9% interest rate. To determine the interest gained per year each years principal was subtracted by the year ends total.
c. $9100 if invested for seven years at an 3% interest rate:
Same formula was used as in the above sections. However the answer for c is as follows.
$9100.00 (1 + 3%)7th =
$9100.00 (1.03)7th = $11,147.89
d. $1000 if invested for ten years with a 0.5% interest rate:
Same formula was used as in the above sections. However the answer for c is as follows.
$1000.00 (1 + 0.05%)10th =
$1000.00 (1.005)10th = $1,051.14
Present Value Calculations
$7700 to be received three years from now with a 5% Interest rate
To determine the present value of $7700 to be received 3 years from now with an interest rate of 5% the following calculations were used:
$7700 (Future value) x 5% (interest per yr.) = $385.00 (interest gained, yr. 3)
$7700 (Future Value) - $385.00 (interest gained) = $7315 (2nd yr. future value)
$7315 (2nd yr. future value) x 5% (interest) = $365.75 (interest gained, yr. 2)
$7315 (2nd yr. future value) - $365.75 (gained) = $6949.25 (1st yr. future value)
$6949.25 (1st yr. future value) x 5% (interest) = $347.47 (interest gained, yr. 1)
$6949.25 (1st yr. future value) - $347.47 (gained) = $6601.98
Present value = $6601.98
b. $1500 to be received five years from now with a 7% interest rate
To determine the present value of $1500 to be received 5 years from now with an interest rate of 7% the following calculations were used:
$1500 (Future value) x 7% (interest per yr.) = $105.00 (interest gained, yr. 5)
$1500 (Future Value) - $105.00 (interest gained) = $1395 (5th yr. future value)
$1395 (4th yr. future value) x 7% (interest) = $97.65 (interest gained, yr. 4)
$1395 (4th yr. future value) - $97.65 (gained) = $1297.35 (4th yr. future value)
$1297.35 (3rd yr. future value) x 7% (interest) = $90.81 (interest gained, yr. 3)
$1297.35 (3rd yr. future value) - $90.81 (gained) = $1206.84 (5th yr. future value)
$1206.84 (2nd yr. future value) x 7% (interest) = $84.48 (interest gained yr, 2)
$1206.84 (2nd yr. future value) - $84.48 (gained) = $1,122.36
$1,122.36 (1st yr. future value) x 7% = $78.57 (interest gained, yr. 1)
$1,122.36 (1st yr. future value) - $78.57 (gained) = $1043.79
Present value = $1,122.36
c. $7200 to received two years from now with a 11% interest rate:
To determine the present value of $7200 to be received 2 years from now with an interest rate of 11% the following calculations were used:
$7200 (Future value) x 11% (interest per yr.) = $792.00 (interest gained, yr. 2)
$7200 (Future Value) - $792.00 (interest gained) = $6408 (2nd yr. future value)
$6408 (1st yr. future value) x 11% (interest) = $704.88 (interest gained, yr. 1)
$6408 (1st yr. future value) - $704.88 = 5703.12
Present value = $5,703.12
d. $680,000 to be received eight years from now with a 9% interest rate:
To determine the present value of $680,000 to be received 8 years from now with an interest rate of 9% the following calculations were used:
$680,000 (Future value) x 9% (interest per yr.) = $61,200 (interest gained, yr. 8)
$680,000 (Future Value) - $61,200 (interest gained) = $618,800 (8th yr. FV)
$618,800 (7th yr. future value) x 9% (interest) = $55,692 (interest gained, yr. 7)
$618,800 (7th yr. future value) - $55,692 (gained) = $563,108 (7th yr. FV)
$563,108 (6th yr. future value) x 9% (interest) = $50,679.72 (interest gained, yr. 6)
$563,108 (6th yr. future value) - $50,679.72 (gained) = $512,428.28 (6th yr. FV)
$512,428.28 (5th yr. future value) x 9% (interest) = $46,118.55 (interest gained yr, 5)
$512,428.28 (5th yr. future value) - $46,118.55 (gained) = $466,309.73 (5th yr. FV)
$466,309.73 (4th yr. future value) x 9% = $41,967.85 (interest gained, yr.4)
$466,309.73 (4th yr. future value) - $41,967.85 (gained) = $424,341.88 (4th yr. FV)
$424,341.88 (3rd yr. future value) x 9% (interest) = $38,109.77 (interest gained, yr. 3)
$424,341.88 (3rd yr. future value) - $38,109.77 (gained) = $386,151.08 (3rd yr FV).
$386,151.08 (2nd yr. future value) x 9% (interest) = $34,753.60 (interest gained yr. 2)
$386,151.08 (2nd yr. future value) - $34,753.60 = $351,397.48 (2nd yr FV)
$351,397.48 (1st yr. future value) x 9% (interest) = $31,674.37 (interest gained yr. 1)
$351,397.48 (1st yr. future value) - $31,674.37 (gained) = $319,723.11
Present value = $5,703.12
Suppose you are to receive a stream of annual payments (also called an "annuity") of $3000 every year for three years starting this year. The interest rate is 3%. What is the present value of these three payments? The present value of these three payments is: year 1: 2738.02, year 2: $2822.70 and year 3: $2910
$3000 (3rd yr future value) x 3% (interest per year) = $90 (interest gained yr. 3)
$3000 (3rd. yr future value) - $90 (gained) = $2910 (present value)
$2910 (2nd yr. future value) x 3% (interest per year) = $87.30 (interest gained yr. 2)
$2910 (2nd yr. future value) - $87.30 (gained) = $2822.70 (present value)
$2822.70 (1st yr. future value) x 3% (interest per year) = $84.68 (interest gained yr. 1)
$2822.70 (1st yr. future value) - $84.68 (gained) = $2738.02 (present value).
Suppose you are to receive a payment of $5000 every year for three years. You are depositing these payments in a bank account that pays 2% interest. Given these three payments and this interest rate, how much will be in your bank account in three years? After three years there will be $5,294.04 in my bank account.
$5000 (3rd yr future value) x 2% (interest per year) = $100 (interest gained yr. 3)
$5000 (3rd. yr future value) - $100 (gained) = $4900 (present value)
$4900 (2nd yr. future value) x 2% (interest per year) = $98.00 (interest gained yr. 2)
$4900 (2nd yr. future value) - $98.00 (gained) = $4802 (present value)
$4802 (1st yr. future value) x 2% (interest per year) = $96.04 (interest gained yr. 1)
$4802 (1st yr. future value) - $96.04 (gained) = $4705.96 (present value).
