Worked Solution (Formula Solution)

In order to decide which investments that Tom Alexander should take, all cash flows must be in the same time period, so you need to find the present value of each cash flow today before you can compare these values with the quoted purchase price for each investment. The present value,

PV,

of some future amount,

FVn,

to be received n periods from now, assuming an interest rate (or opportunity cost) of

r,

is calculated as follows:

PV=FVn(1+r)n.

Substituting

FVn=$22,021,

r=0.10,

and

n=6

into the present value equation yields:

PV=$22,021(1+0.10)6=$12,430.28.

Thus, the value of Investment A today is

$12,430.28.

The present value of Investment B is:

PV=$2,281(1+0.10)21=$308.23.

The present value of Investment C is:

PV=$6,738(1+0.10)11=$2,361.63.

The present value of Investment D is:

PV=$25,571(1+0.10)41=$513.63.

Compare your answers (the present value of each investment) to the price of each investment. You should recommend that Tom purchases any of the four investments which have a present value that is greater than the price. Thus, if Tom can earn 10% on his investments, he should purchase investments

A and C.

Worked Solution (Financial Calculator Solution)

When solving for the present value of a single cash flow using a financial calculator, you will need to input the values of

N,

I,

PMT,

and

FV.

Make sure you enter a zero for

PMT,

which is not used in the problem. Since compounding is annual, the periods per year setting on your calculator should be set at 1, P/Y = 1. On many calculators, the present value will be preceded by a minus sign for a cash outflow. If a minus sign appears on your calculator, ignore it here. The present value of Investment A is computed as follows:

Input	Function
22,021	FV
6	N
10	I
	CPT
	PV
Solution
12,430.28

The present value of Investment B is computed as follows:

Input	Function
2,281	FV
21	N
10	I
	CPT
	PV
Solution
308.23

The present value of Investment C is computed as follows:

Input	Function
6,738	FV
11	N
10	I
	CPT
	PV
Solution
2,361.63

The present value of Investment D is computed as follows:

Input	Function
25,571	FV
41	N
10	I
	CPT
	PV
Solution
513.63

Compare your answers (the present value of each investment) to the price of each investment. You should recommend that Tom purchases any of the four investments which have a present value that is greater than the price. Thus, if Tom can earn 10% on his investments, he should purchase investments

A and C.

Worked Solution (Spreadsheet Solution)

Excel offers a mathematical function that makes the calculation of present values easy. The format of that function is PV(rate,nper,pmt,fv,type). The terms inside the parentheses are inputs that Excel requires to calculate the present value. The terms "rate" and "nper" refer to the interest rate and the number of time periods respectively. The term "fv" represents the lump sum (or future value) that you will receive in the future. The term "pmt" refers to the annual payment that an annuity offers. The term "type" is an input that lets Excel know whether the annuity being valued is an ordinary annuity (in which case the input value for "type" is 0 or omitted) or an annuity due (in which case the correct input value for "type" is 1). For now, we will ignore the two inputs, "pmt" and "type," and enter a value of zero. The present value of Investment A is computed as follows:

	A	B
1	PRESENT VALUE OF A SINGLE AMOUNT
2	Future value	$22,021
3	Interest rate, pct per year compounded annually	10%
4	Number of years	6
5	Present value	$12,430.28
Entry in Cell B5 is=PV(B3,B4,0,B2,0) The minus sign appears before PV to change the present value to a positive amount.

The present value of Investment B is computed as follows:

	A	B
1	PRESENT VALUE OF A SINGLE AMOUNT
2	Future value	$2,281
3	Interest rate, pct per year compounded annually	10%
4	Number of years	21
5	Present value	$308.23
Entry in Cell B5 is=PV(B3,B4,0,B2,0) The minus sign appears before PV to change the present value to a positive amount.

The present value of Investment C is computed as follows:

	A	B
1	PRESENT VALUE OF A SINGLE AMOUNT
2	Future value	$6,738
3	Interest rate, pct per year compounded annually	10%
4	Number of years	11
5	Present value	$2,361.63
Entry in Cell B5 is=PV(B3,B4,0,B2,0) The minus sign appears before PV to change the present value to a positive amount.

The present value of Investment D is computed as follows:

	A	B
1	PRESENT VALUE OF A SINGLE AMOUNT
2	Future value	$25,571
3	Interest rate, pct per year compounded annually	10%
4	Number of years	41
5	Present value	$513.63
Entry in Cell B5 is=PV(B3,B4,0,B2,0) The minus sign appears before PV to change the present value to a positive amount.

Compare your answers (the present value of each investment) to the price of each investment. You should recommend that Tom purchases any of the four investments which have a present value that is greater than the price. Thus, if Tom can earn 10% on his investments, he should purchase investments

A and C. .

its year of receipt are given for each investment. Which purchase recommendations would you make, assuming that Tom can earn 10% on his investments? Click the icon to see the Worked Solution (Formula Solution). Click the icon to see the Worked Solution (Financial Calculator Solution). Click the icon to see the Worked Solution (Spreadsheet Solution). The present value of Investment A is $ The present value of Investment B is 9 The present value of Investment C is s The present value of Investment D is s (Round to the nearest cent.) (Round to the nearest cent.) (Round to the nearest cent.) (Round to the nearest cent.) Which purchase recommendations would you make, assuming that Tom can earn 10\% on his investments? (Select the best answer below.) A. Investments A and C B. Investment D C. Investment B D. Investments B and C 4: Data Table (Click on the icon here in order to copy the contents of the data table below into a spreadsheet) \begin{tabular}{crcc} \hline Investment & \multicolumn{1}{c}{ Price } & Single cash inflow & Year of receipt \\ \hline A & $11,300 & $22,021 & 6 \\ B & $339 & $2,281 & 21 \\ C & $2,147 & $6,738 & 11 \\ D & $565 & $25,571 & 41 \\ \hline \end{tabular} Data table (Click on the icon here in inder to copy the contents of the data table below into a spreadsheet.)