Chapter 7, Problem 65P

To determine

i.

Present worth analysis.

Answer to Problem 65P

As alternative B has the highest present worth, Alternative B is selected.

Explanation of Solution

Given:

Time: 10 years

Alternative A has a cost of $10000

Annual benefits of $4500

Alternative B costs $25000

Annual benefits of $8800.

Calculation:

Alternative A

The rates are discounted to the present value at 8%

$\begin{array}{l}P{W}_A=746(P/A,i,n)-2500\\ =746(P/A,8\%,5)-2500\\ =746(3.993)-2500\\ 746(P/A,i,n)-2500\\ =2978.778-2500\\ =\$478.778\end{array}$

Alternative B

$\begin{array}{l}P{W}_A=1664(P/A,i,n)-6000\\ =1664(P/A,8\%,5)-6000\\ =1664(3.993)-6000\\ 746(P/A,i,n)-2500\\ =6644-6400\\ =\$644.352\end{array}$.

Conclusion:

As alternative B has the highest present worth, Alternative B is selected.

To determine

ii.

Annual Cash Flow.

Answer to Problem 65P

Alternative B has the highest cash flow.

Explanation of Solution

Given:

Time: 10 years

Alternative A has a cost of $10000

Annual benefits of $4500

Alternative B costs $25000

Annual benefits of $8800.

Calculation

Calculate annual cash flow as follows:

(EUAB-EAUC)_B = 1664-6000(A/P,8%,5)

= 1664-6000(0.2505)

= 1664-1503

= $161.

Conclusion:

Alternative B has the highest cash flow.

Thus alternative B is selected.

To determine

ii.

Rate of return analysis.

Answer to Problem 65P

Alternative A is selected.

Explanation of Solution

Given:

Two mutually exclusive alternatives are being considered. Both have lives of 10 years. Alternative A has a cost of $10000 and annual benefits of $4500. Alternative B costs $25000 and has annual benefits of $8800.

Calculation:

For A = $\begin{array}{l}=\frac{-2500}{{(1+r)}^0}+\frac{746}{{(1+r)}^1}+\frac{746}{{(1+r)}^2}+\frac{746}{{(1+r)}^3}+\frac{746}{{(1+r)}^4}+\frac{746}{{(1+r)}^5}+\frac{746}{{(1+r)}^6}+\frac{746}{{(1+r)}^7}+\frac{746}{{(1+r)}^8}+\frac{746}{{(1+r)}^9}+\frac{746}{{(1+r)}^{10}}\\ r=27.14\%\end{array}$ For B

$\begin{array}{l}=\frac{-6000}{{(1+r)}^0}+\frac{1664}{{(1+r)}^1}+\frac{1664}{{(1+r)}^2}+\frac{1664}{{(1+r)}^3}+\frac{1664}{{(1+r)}^4}+\frac{1664}{{(1+r)}^5}+\frac{1664}{{(1+r)}^6}+\frac{1664}{{(1+r)}^7}+\frac{1664}{{(1+r)}^8}+\frac{1664}{{(1+r)}^9}+\frac{1664}{{(1+r)}^{10}}\\ r=24.68\%\end{array}$

Year	Alternative A	Alternative B
0	-2500	-6000
1	746	1664
2	$746	1664
3	746	1664
4	746	1664
5	746	1664
6	746	1664
7	746	1664
8	746	1664
9	746	1664
10	746	1664
IRR	27.14%	24.68%

Conclusion:

Alternative A is selected.