Chapter 15, Problem 29P

To determine

(a)

The projects that should be approved.

Answer to Problem 29P

The projects B, C, D, E, H, and J should be approved.

Explanation of Solution

Given:

Salvage Value is $0$.

Duration is $5$ years.

Calculation:

Write the expression to calculate the present worth.

$PW=-P+A\frac{{\left(1+i\right)}^n-1}{{\left(1+i\right)}^n\times i}$ ...... (I)

Substitute $14\%$ for $i$ and $5$ for $n$ in Equation (I)

$\begin{array}{c}PW=-P+A\frac{{\left(1+0.14\right)}^5-1}{{\left(1+0.14\right)}^5\times 0.14}\\ =-P+A\left(3.433\right)\end{array}$ ...... (II)

Find the table to calculate the present worth.

Project	PV(thousand)(COST)	Uniform annual benefits	Rate of return	PW	PW/COST
A	$\$10$	$\$2.98$	$15\%$	$-\$0.01$	$-0.001$
B	$\$15$	$\$5.58$	$25\%$	$\$0.006$	$0.0004$
C	$\$5$	$\$1.53$	$16\%$	$\$0.0096$	$0.00192$
D	$\$20$	$\$5.55$	$12\%$	$\$.0065$	$0.000325$
E	$\$15$	$\$4.37$	$14\%$	$\$0.0026$	$0.000173$
F	$\$30$	$\$9.81$	$19\%$	$-\$0.0046$	$-0.000153$
G	$\$25$	$\$7.81$	$17\%$	$-\$0.013$	$-\$0.00052$
H	$\$10$	$\$3.49$	$22\%$	$\$5.86$	$\$0.586$
I	$\$5$	$\$1.67$	$20\%$	$-\$0.0056$	$-0.00112$
J	$\$10$	$\$3.20$	$18\%$	$\$0.00694$	$\$0.000694$

Here, the present worth has been calculated using Equation (I).

Conclusion:

Therefore, the projects B, C, D, E, H, and J should be approved.

To determine

(b)

The ranking order of all the acceptable projects.

Answer to Problem 29P

The ranking has been shown below.

Project	PW/COST	Ranking
H	$\$0.586$	$1$
C	$0.00192$	$2$
J	$\$0.000694$	$3$
B	$0.0004$	$4$
D	$0.000325$	$5$
E	$0.000173$	$6$
F	$-0.000153$	$7$
G	$-\$0.00052$	$8$
A	$-0.001$	$9$
I	$-0.00112$	$10$

Explanation of Solution

Calculation:

Rank the project according to the $PW/COST$

Project	PW/COST	Ranking
H	$\$0.586$	$1$
C	$0.00192$	$2$
J	$\$0.000694$	$3$
B	$0.0004$	$4$
D	$0.000325$	$5$
E	$0.000173$	$6$
F	$-0.000153$	$7$
G	$-\$0.00052$	$8$
A	$-0.001$	$9$
I	$-0.00112$	$10$

Conclusion:

Rank the project according to the $PW/COST$

Project	PW/COST	Ranking
H	$\$0.586$	$1$
C	$0.00192$	$2$
J	$\$0.000694$	$3$
B	$0.0004$	$4$
D	$0.000325$	$5$
E	$0.000173$	$6$
F	$-0.000153$	$7$
G	$-\$0.00052$	$8$
A	$-0.001$	$9$
I	$-0.00112$	$10$

To determine

(c)

The projects to be approve if only $\$70000$ is available.

Answer to Problem 29P

The project to be approve if only $\$70000$ available are H, C, J, B, D, and A.

Explanation of Solution

Calculation:

Project	PW/COST	Ranking
H	$\$0.586$	$1$
C	$0.00192$	$2$
J	$\$0.000694$	$3$
B	$0.0004$	$4$
D	$0.000325$	$5$
E	$0.000173$	$6$
F	$-0.000153$	$7$
G	$-\$0.00052$	$8$
A	$-0.001$	$9$
I	$-0.00112$	$10$

If the project budget is $\$70000$ then the project with best return should be selected.

The project to be approve if only $\$70000$ available are H, C, J, B, D, and A.

$\begin{array}{c}\text{Sum}=\$10000+\$5000+\$10000+\$15000+\$20000+\$10000\\ =\$70000\end{array}$

Hence, the chosen project is correct.

Conclusion:

Therefore, the project to be approve if only $\$70000$ available are H, C, J, B, D, and A.

To determine

(d)

If the result will be the same if the projects are ranked on IRR and calculate the opportunity cost of capital.

Answer to Problem 29P

No, there will be change in the rank of the project if they are ranked on IRR.

The opportunity cost of capital is $20\%$.

Explanation of Solution

Make the table to calculate the present worth.

Project	PV(thousand)(COST)	Uniform annual benefits	Rate of return	PW	PW/COST
A	$\$10$	$\$2.98$	$15\%$	$-\$0.01$	$-0.001$
B	$\$15$	$\$5.58$	$25\%$	$\$0.006$	$0.0004$
C	$\$5$	$\$1.53$	$16\%$	$\$0.0096$	$0.00192$
D	$\$20$	$\$5.55$	$12\%$	$\$.0065$	$0.000325$
E	$\$15$	$\$4.37$	$14\%$	$\$0.0026$	$0.000173$
F	$\$30$	$\$9.81$	$19\%$	$-\$0.0046$	$-0.000153$
G	$\$25$	$\$7.81$	$17\%$	$-\$0.013$	$-\$0.00052$
H	$\$10$	$\$3.49$	$22\%$	$\$5.86$	$\$0.586$
I	$\$5$	$\$1.67$	$20\%$	$-\$0.0056$	$-0.00112$
J	$\$10$	$\$3.20$	$18\%$	$\$0.00694$	$\$0.000694$

Here, the present worth has been calculated using Equation (I).

The project with highest PW is project H and the opportunity cost will be equal to its rate of return that is $22\%$.

Conclusion: No, there will be change in the rank of the project if they are ranked on IRR.

The opportunity cost of capital is $20\%$.