present value of a lump sum - dcf

Question

Present Value of a Lump Sum - DCF Technique

Generally an investor would want to know how much he or she would stop currently to get a provided amount in year 1, 2, ... n.  In this condition he would have to decide at what rate of discount identified also as time preference rate, he or she will employ to discount the anticipated lump sum using this rate applying with the following formula as:

P_v = L / (1+K)ⁿ

Whereas:    P_v = Present value

                    L   = Lumpsum

                     K = Cost of finance or time preference rate

                     n = given year.

This implies there if the time preference rate is 10 percent the present value of 1/= to e obtained at the end of year 1 is as:

                   P_v = 1/1.1

                        = 0.909

Here value of inflows to be obtained in the 2^nd year to N^th year, will be equivalent to as:

P_v = A / (1+K)ⁿ

Where:       A = annual cash flows

                   N = Number of years

The present value also of a shilling to be obtained at a given point in time can in addition to by the above formula is found with the present value tables.

Assume that an investor can expect to obtain as:

 40,000 at the end of year 2

 70,000 at the end of year 6

 100,000 at the end of year 8

Calculate his present (value) if his time preference is 12 percent.

P_v = L / (1+K)^N

= 40,000 / (1.12)² + 70,000 / (1.12)⁶ - 100,000 / (1.12)⁸

=  Kshs.107,740.26

With using tables like:

= 40,000(0.7992) + 70,000(0.5066) + 100,000(0.4039)

= 107,820