Present Value Exercise: A lump sum cash flow of $$1,000\mathrm{.}00$ will be received in $10$ periods. For this cash flow, the appropriate discount rate per period is $9\mathrm{.}0\%.$ What is the present value of this lump sum cash flow? There are three alternative approaches to calculate the present value of this lump sum cash flow. First, we will calculate the present value using a time line, where each column corresponds to a period of calendar time. Second, we use a formula for the present value. Third, we use Excel$$s PV function for the present value. The assignment is to create a file following the instructions below. Procedure: $1.$ Inputs: Enter the inputs $($FV$,$ r and n$)$ in the range B$2$:B$4.2.$ Present Value using a Time Line: Create a time line from period $0$ to period $10.$ Enter the single cash flow in period $10.$ Calculate the present value of each cash flow and sum the present values as follows. $$ Period: Enter $0,1,2,...,10.$ in the range B$7$:L$7.$ Cash Flows: Enter $$0\mathrm{.}00$ in cell B$8$ and copy it to the range C$8$:K$8.$ Enter $=$B$2$ in cell L$8.$ Present Value of Each Cash Flow $=($Cash Flow$)/((1+$ Discount Rate per Period$)^$ Period$).$ o Enter $=$B$8/((1+$$B$$3)^$B$7)$ in cell B$9$ and copy it across. o The $ signs in $B$$3$ lock the column as B and the row as $3$ when copying. $$ Present Value $=$ Sum over all periods of the Present Value of Each Cash Flow. o Enter $=$SUM$($B$9$:L$9)$ in cell B$10.3.$ Present Value using the Formula: For a lump sum single cash flow, the formula is Present Value $=($Cash Flow$)/((1+$ Discount Rate per Period$)^$ Period$).$ Enter $=$B$2/((1+$B$3)^$B$4)$ in cell B$13.4.$ Present Value using the PV Function: The Excel PV function can be used to calculate the present value of a single cash flow, the present value of an annuity, or the present value of a bond. For a single cash flow, the format is $=-$PV$($Discount Rate per Period, Number of Periods, $0,$ Single Cash Flow$).$ Enter $=-$PV$($B$3,$B$4,0,$B$2)$ in cell B$16.$ The Present Value of this Single Cash Flow is $$422\mathrm{.}41.$ Notice you get the same answer all three ways: using the time line, using the formula, or using the PV function! A B C D E F G H I J K L $1$ Inputs $2$ Single Cash Flow $$1,000\mathrm{.}003$ Discount Rate per Period $9\mathrm{.}0\%4$ Number of Periods $1056$ Present Value using a Time Line $7$ Period $0123456789108$ Cash Flows $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$1,000\mathrm{.}009$ Present Value of Each Cash Flow $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$0\mathrm{.}00$ $$422\mathrm{.}4110$ Present Value $$422\mathrm{.}411112$ Present Value using the Formula $13$ Present Value $$422\mathrm{.}411415$ Present Value using the PV Function $16$ Present Value $$422\mathrm{.}41$