Time Value

TIME VALUE OF MONEY PV = Present Value FV = Future Value i = Interest Rate Future value of $100 earning 10% interest in one year FV = 100 + (100* .10) = $110 FV = PV + Interest FV = PV + (PV * i) Future value of 100 in two years earning 10% per year is FV=[100+(100 * .10)] +[100 + (100 *.1)]*.10 = $121 FV =[ PV +( PV * i)] + [PV +(PV * i)]* i FV = PV(1+i)(1+i) FV = PV(1+i)(1+i) FV = PV(1+i)N N=number of periods (years)

TIME VALUE OF MONEY Financial Calculator - BA II PLUS Calculate the future value of $100 in 2 years earning 10% interest per year 2nd FV (clears calculator of any numbers) 2ND I/Y 1 Enter CE/C (computes interest on yearly basis) 2nd . 6 Enter CE/C (6 decimal places) 2 N (2 year period) 10 I/Y (10% interest rate) - 100 PV (100 is the present value amount) CPT FV (computes future value = 121) Calculate FV of 10,000 in 10 years at 15%

TIME VALUE OF MONEY Present value amount - find the amount of money to invest today to have $1000 in 5 years if the investment earns 10%. PV = FV(1/1+i)N PV = 1000(1/1+.1)5 PV = 1000(.62092) = $620.92 Financial Calculator 2nd FV (Clears calculator) 5 N ( 5 years) 10 I/Y (10% interest) 1000 FV (1000 in 5 years) CPT PV (Finds present value amt=$620.92) Find PV of $1,000,000 in 30 yrs at 15%

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RULE OF 72 72 / % = number of years to double investment If you earn 10% on your money per year, how long will it take to double your investment? 72 / 10 = 7.2 years

If your investment doubles in 10 years, what return per year did you make. ANNUITIES Find the future value of four $100 payments made at the end of each year for four years if you earn 10%per year. FV = $100(1+.10)3 + $100(1+.10)2 +$100(1+.10)1 +$100 FV = $100[(1+.10)3 + (1+.10)2 + (1+.10)1 + 1] FV = $100(4.6410) = $464.10 Financial Calculator 2nd FV (clear calculator) 4 N (4 payments) 10 I/Y (10% interest) - 100 PMT (100 payments) CPT FV (Calculates future value = $464.10) Find PV 4N 10 I/Y 100 PMT CPT PV (PV=-316.99) Find PMT 10000 Loan 10% 5 year monthly payments 5*12 = 60 N 10/12 I/Y -10,000 PV CPT PMT (212.47)

TIME VALUE OF MOMEY

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ANNUITIES Find the present value of four $100 payments made at the end of each of the next four years earning a return of 10% per year. PV = 100(1/1+.1)1 + 100(1/1+.1)2 + 100(1/1+.1)3 + 100(1/1+.1)4 = PV = 100[(1/1+.1)1 + (1/1+.1)2 +(1/1+.1)3 + (1/1+.1)4] = 100(3.1698) = $316.98 Financial Calculator 2nd FV (clears calculator) 4 N (4 payments) 10 I/Y (10% interest) 100 PMT ($100 payments) CPT PV (calculates present value = 316.98)

TIME VALUE OF MONEY PERPETUITIES Find the present value of $100 payment made at the end of each and every year forever if it earns 10% interest per year. PV = 100 / .10 = 1000 PV (Perpetuity) = Payment / Interest Rate CAPITAL BUDGETING TECHNIQIUES WITH THE BA II PLUS

Required Return = 10% I = 10% Year 0 1 2 3 4

Cash Flows - $110,000 43,332 45,976 35,928 54,964

Find the NPV & IRR 2nd CE/C CFo -110000 Enter ↓ 43332 Enter ↓ ↓

[Clears Calculator] [CFo=0.0000] [CFo=-110000] [C01 0.0000] [C01 = 43332] [F01= 1.000] [C02 0.0000] 3

45976 Enter ↓ ↓ 35928 Enter ↓ ↓ 54964 Enter NPV 10 Enter ↓ CPT IRR CPT

[C02= 45976] [F02= 1.000] [C03 0.0000] [C03= 35928] [F03= 1.000] [C04 0.0000] [C04= 54964] [I = 0.00000] [I = 10.0000] [NPV= 0.0000] [NPV= 31,923.8112] [IRR= 0.0000] [IRR= 22.4824]

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