Present Value of a Single Amount

Present Value of a Single Amount is current value of a future amount of money evaluated at a given interest rate. Compare all points of cash flow at present time. Should compare Apples with Apples.

 

Present value of single amount (annual discounting)

The value of single amount (one time cash flow) at present time evaluated at a given interest rate assuming that discounting take place one time in a year (annually). Two methods for calculation:

present value

 

Formula

Formula Sheet Download

present value formula

PVn = Present Value for n time

FV = Future Value

i = Interest Rate

PVIF = Present Value of Interest Factor



Example # 1:

Designs Co. is opening a showcase office to display and sell its computer designed poster art. Designs expect cash flows to be $100,000, 6 years hence, if Designs uses 10 percent as its discount rate, what is the present value of the cash flow by above three equations?

present value example

present value example and solution

 

Present Value of a Single Amount Table Download

present value factor

 

Example # 2:

For each of the following, compute the present value by factor table?

Present Value of a Single Amount Table Download

present value factor calculator

 

Example # 3:

ABC Company expects cash flows to be $160,000 in the first year, $200,000 in the second year, $240,000 in the third year, $260,000 in fourth year and $300,000 in fifth year. If company uses 14 percent as its discount rate, what is the present value of the cash flows?

how to calculate present value



Example # 4:

Mr. Aamir will receive cash of $10,000,000 in 4 years if discount rate is 9% for first year, 10% for second year, 11% for third year and 12% for fourth year. What is the present value of the cash flow?

what is present value

 

Example # 5:

Find the present value of $10,000 to be received at the end of 10 periods at 8% per period. Solve this problem by scientific calculator and by Excel sheet?

present value calculator

present value spread sheet

 

>> Practice Present Value of a Single Amount MCQs   

Present Value of single amount (Intra-year discounting)

The value of lump sum amount (one time cash flow) at present time evaluated at a given interest rate assuming that discounting take place more than one time in a year (Intra-year). Interest rate reduced while periods of time increase by frequency of discounting (m) i.e. i/m and n*m. Two methods for calculation:

present value intra-year discounting

 

Formula

Time Value of Money Formula Sheet Download

present value intr-year discounting formula

 

Example # 6:

Your brother, who is 6 years old, just received a trust fund that will be worth $25,000 when he is 21 years old. If the fund earns 10 percent interest discounted semi-annually, what is the value of the fund today?

present value question and answer

 

Present Value of a Single Amount Table Download

present value of money example

 

Present Value / Continuous Discounting

When interest is discounted “many times”, we say that the interest is discounted continuously. It can be done annually or intra-yearly (No matter it is annually or intra yearly, answer will be same for all)

present value continuous discounting

 

Formula

Time Value of Money Formula Sheet Download

present value continuous discounting formula

PVn = Present value for n time

FV = Future value

e = Exponent with constant value 2.718

i = Interest rate / Discount rate / Opportunity cost

n = Number of year

 

Example # 7:

What is the present value of an offer of $2,000 two years from now if the opportunity cost of capital (discount rate) is 12% per year discounted continuously

       (a) Annually

       (b) Monthly?

pv example

present value continuous compounding example

 

When time (n) or i (interest) is unknown

In situation if we have future value and present value of lump sum with interest rate, than we can find time. In situation if we have future value and present value of lump sum with time, than we can find interest rate:

interest finding

 

interest finding formula

 

>>> Practice Present Value of a Single Amount MCQs   

 

Example # 8:

If you invested $40,000 at one point in time and received back $100,000 at 13.98% rate, how much time required?

finding number of years

 

Example # 9:

If you invested $40,000 at one point in time and received back $100,000 seven years later, what annual interest rate would you have obtained?

interest unknown

 

>>> Practice Present Value of a Single Amount Quiz 1.