# Quiz 14: The Effects of Time and Risk on Value

Present value Present value refers to the value of an asset or a project which it would generate in future, at present. It is the current value of the cash inflow that the project will yield in future to an investor. It facilitates an investor in determining the profitability and the feasibility which acts as the deciding factor in carrying out the project further. The formula to compute the Present Value of annuity received at the end of each year is as follows: Where, In the above equation we can express variable as .Thus, the above formula can be written as below: Where, Given: Substitute: Hence the PVA is calculated as Now, we can compare the both amounts easily because both are in Present Value. When we compare the both Present Values, it is better to accept to pay him $20,000 today. Because the Present Value $20,000 is greater than the Present Value of $3,200 pay at the end of each of the next 10 years. He chooses the annuity plan; the NPV will be $19,662.61. Using your financial calculator, enter the values shown in Table: Table Hence, Dr. Jackson should choose the lump sum payment of $20,000.

The time value of money is different at different time intervals. Compounding is used to calculate the future value of cash flows at a given required rate of return. And discounting is used to calculate the present value of future cash flows at a given discount rate. The future value can be calculated using following formula: Here, The future value is FV. The present value is PV. The required rate of return is r. The time period is T. The present value (PV) is $50. The time period (T) is 20 years. Annual interest rate is 10% (or 0.10) Calculate the future value (FV) as follows: Therefore, the $50 deposit made today is worth of $336.37 in 20 years at an annual interest rate of 10%. Therefore, the correct option is .

This is simply a yield calculation problem. Like any time-value-of-money problem, we are given four inputs and are asked to solve for the fifth. In this case, we must solve for the interest rate as follows: Solving this setup tells us the above loan yields a 15 percent return.