Chapter 26: Q9SE (page 1466)

Use the Present Value of $1 table (Appendix A, Table A-1) to determine the present value of $1 received one year from now. Assume a 8% interest rate. Use the same table to find the present value of $1 received two years from now. Continue this process for a total of five years. Round to three decimal places.
Requirements
1. What is the total present value of the cash flows received over the five-year period?
2. Could you characterize this stream of cash flows as an annuity? Why or why not?
3. Use the Present Value of Ordinary Annuity of $1 table (Appendix A, Table A-2) to determine the present value of the same stream of cash flows. Compare your results to your answer to Requirement 1.
4. Explain your findings.

Short Answer

Expert verified

(1) Total present value equals $3.993.

(2) Yes, it can be classified as annuity, as similar amount is received for the fixed period of time.

(3) Present value equals $3.993, and it is same as Requirement 1.

(4) Adding the present value of similar cash flows, and calculating the present value of annuity will give the same result.

Step by step solution

Definition of present value

The current value of any sum of money that will be received in the future time period is known as the present value. This concept states that the value of money today is higher than the value of the same amount of money in future.

Calculation of present value over five years and total

Year	Future value	X	Present value factor	=	Present value
1	$1	X	0.926	=	$0.926
2	$1	X	0.857	=	$0.857
3	$1	X	0.794	=	$0.794
4	$1	X	0.735	=	$0.735
5	$1	X	0.681	=	$0.681
					$3.993

Classification of cash flow as an annuity

The stream of cash flows can be classified as annuity because the cash flows are received at a specified time and also they are equal.

Present value ordinary annuity

$\begin{array}{rcl} P r e s e n t v a l u e o r d i n a r y a n n u i t y & = & F u l u r e v a l u e \times P r e s e n t v a l u e o r d i n a r y a n n u i t y f a c t o r \\ = & $ 1 \times 3.993 \\ = & $ 3.993 \end{array}$

Explanation of findings

Findings of requirement 1 and requirement 3 are same because it is fact that the total of individual cash flow is same as the present value ordinary annuity determined collectively.

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	Project X	Project Y	Project Z
ARR	13.25%	6.58%	10.47%

	Equipment A	Equipment B	Equipment C
Present value of net cash inflows	\(1,647,351	\)1,969,888	\(2,064,830
Initial investment	(1,484,100)	(1,641,573)	(1,764,812)
NPV	\)163,251	\(328,315	\)300,018

Short Answer

Step by step solution

Definition of present value

Calculation of present value over five years and total

Classification of cash flow as an annuity

Present value ordinary annuity

Explanation of findings

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