Chapter 5, Problem 74P

To determine

Stock to be purchased.

Answer to Problem 74P

Since the benefit-cost is highest for the stock of S. Products, investment should be made in S Products.

Explanation of Solution

Given information:

Minimum rate of return = 10%.

Six stocks are available.

Calculate the ratio of PW of benefits and PW of costs for each stock.

$\begin{array}{l}B/CratioforW.H.=\frac{PWofbenefits}{\begin{array}{l}PWof\cos ts\\ =\frac{1.25(P/A,10\%,4)+32(P/F,10\%,4)}{23.75}\end{array}}\\ =\frac{1.25(3.170)+32(0.6830)}{23.75}\\ =\frac{25.8185}{23.75}\\ =1.0871\end{array}$

$\begin{array}{l}B/CratioforF.F.=\frac{PWofbenefits}{\begin{array}{l}PWof\cos ts\\ =\frac{4.50(P/A,10\%,4)+45(P/F,10\%,4)}{45}\end{array}}\\ =\frac{4.50(3.170)+45(0.6830)}{45}\\ =\frac{45}{45}\\ =1\end{array}$

$\begin{array}{l}B/CratioforM.M=\frac{PWofbenefits}{\begin{array}{l}PWof\cos ts\\ =\frac{0(P/A,10\%,4)+42(P/F,10\%,4)}{30.6250}\end{array}}\\ =\frac{0+42(0.6830)}{30.6250}\\ =\frac{28.686}{30.6250}\\ =0.9367\end{array}$

$\begin{array}{l}B/CratioforS.P.=\frac{PWofbenefits}{\begin{array}{l}PWof\cos ts\\ =\frac{0(P/A,10\%,4)+20(P/F,10\%,4)}{12}\end{array}}\\ =\frac{0+20(0.6830)}{12}\\ =\frac{13.66}{12}\\ =1.1383\end{array}$

$\begin{array}{l}B/CratioforU.T.=\frac{PWofbenefits}{\begin{array}{l}PWof\cos ts\\ =\frac{2.00(P/A,10\%,4)+40(P/F,10\%,4)}{33.3750}\end{array}}\\ =\frac{2.00(3.170)+40(0.6830)}{33.3750}\\ =\frac{33.66}{33.3750}\\ =1.0085\end{array}$

$\begin{array}{l}B/CratioforW.P.=\frac{PWofbenefits}{\begin{array}{l}PWof\cos ts\\ =\frac{3.00(P/A,10\%,4)+60(P/F,10\%,4)}{52.50}\end{array}}\\ =\frac{3.00(3.170)+60(0.6830)}{52.50}\\ =\frac{50.49}{52.50}\\ =0.9617\end{array}$.

Conclusion:

Since the benefit-cost is highest for the stock of S. Products, investment should be made in S Products.