1. Importance of Present Value
The importance of time value of money has over powered finance and financial calculations. Be it a simple compound interest calculation or a complex derivative, time value calculations are involved in all of them. The reason for its indispensible use is the time frame in which financial decisions are made. For example any investment decision or loan grant decision has to be made today, but its cash flows will occur in the future. The disparity between cash flow timing and your decision to take the project/ investment or not, is the root concept of all present value analysis.
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"The present value of a cash flow due n years in the future is the amount which, if it were on hand today, would grow to equal the future amount." (Brigham, & Gapenski, 1994) The concept of present value is based on the principle that a dollar in hand today is worth more than the same dollar in future. Reason being you can invest that dollar today and start earning interest on it. The investment discounted back to get present value is done so using the opportunity cost. The present value takes into account the riskiness of future payments when they are discounted back by the opportunity cost or hurdle rate.
Thus, present value is the value today of a cash flow. It is used by firms in their capital budgeting decisions. The discounted cash flow techniques namely Net Present Value, the Internal Rate of Return and Modified Rate of Return all involve present value calculations. Therefore, present value is the basis for all capital budgeting decisions and that is why it is the most fundamental principle taught first and foremost in finance courses. "Thus, the largest impact is usually the time value of money. The present and future value formulas provide a basis for comparing and combining the value of cash flows occurring at different times." (Mc Crary, 2010)
The formulae used for generating answers to the assignment questions are taken from Eugene, 1994.
FVn = PV (1+i)n
PV= Present value
n=Number of years
2. Calculating Future Value
a. $600 if invested for five years at a 9% interest rate
= $ 923.17
b. $1750 if invested for three years at a 2% interest rate
c. $9900 if invested for seven years at an 4% interest rate
d. $5000 if invested for ten years with a 2.9% interest rate
FV=5000(1+0.029)10 = $6,654.63
3. Calculating Present Value
a. $500 to be received three years from now with a 7% Interest rate
PV=500/(1+0.07)3 = $408.15
b. $4500 to be received five years from now with a 1% interest rate
PV=4500/(1+0.01)5 = $4281.60
c. $2400 to received two years from now with a 11% interest rate
PV=2400/(1+0.11)2 = $1947.89
d. $900,000 to be received eight years from now with a .5% interest rate.
PV=900,000/(1+0.05)8 = $ 609,155.43
4. Suppose you are to receive a stream of annual payments (also called an "annuity") of $6000 every year for three years starting this year. The interest rate is 3%. What is the present value of these three payments?
0 1 2
6000 6000 6000
PV= PV0 + PV1 + PV2
=6000/ (1+0.03)0 + 6000/ (1+0.03)1 + 6000/ (1+0.03)2
=6000+ 5,825.24 + 5,655.58
5. Suppose you are to receive a payment of $100,000 every year for three years. You are depositing these payments in a bank account that pays 8% interest. Given these three payments and this interest rate, how much will be in your bank account in three years?
0 1 2 3
100,000 100,000 100,000
FV= FV1 +FV2 +FV3