Barnacle Bob's Fish and Tackle Shop is planning an expansion. The initial investment is $480,000, and anticipated cash inflows are as listed below. The cost of capital is 12.2%. Based on the profitability index, should Barnacle Bob go ahead with the project? ? $$\begin{array} { | l | l | }
\hline \text { Years } & \text { Cash Inflows } \
\hline 1 & \$ 90,000 \
\hline 2 & 105,000 \
\hline 3 & 105,000 \
\hline 4 & 195,000 \
\hline 5 & 195,000 \
\hline 6 & 195,000 \
\hline
\end{array}$$

Question

Barnacle Bob's Fish and Tackle Shop is planning an expansion. The initial investment is $480,000, and anticipated cash inflows are as listed below. The cost of capital is 12.2%. Based on the profitability index, should Barnacle Bob go ahead with the project? ? $$\begin{array} { | l | l | } 
\hline \text { Years } & \text { Cash Inflows } \
\hline 1 & \$ 90,000 \
\hline 2 & 105,000 \
\hline 3 & 105,000 \
\hline 4 & 195,000 \
\hline 5 & 195,000 \
\hline 6 & 195,000 \
\hline
\end{array}$$

Quizplus · Accepted Answer

The profitability index (PI) is calculated by dividing the present value of future cash inflows by the initial investment. The present value of cash inflows can be calculated using the formula PV = CF / (1 + r)^n, where CF is the cash flow in each period, r is the discount rate (12.2% or 0.122), and n is the period. $$ \text{PV of Year 1} = \frac{90,000}{(1 + 0.122)^1} = 80,214.77 $$$$ \text{PV of Year 2} = \frac{105,000}{(1 + 0.122)^2} = 83,516.25 $$$$ \text{PV of Year 3} = \frac{105,000}{(1 + 0.122)^3} = 74,520.59 $$$$ \text{PV of Year 4} = \frac{195,000}{(1 + 0.122)^4} = 124,183.82 $$$$ \text{PV of Year 5} = \frac{195,000}{(1 + 0.122)^5} = 110,783.07 $$$$ \text{PV of Year 6} = \frac{195,000}{(1 + 0.122)^6} = 98,917.47 $$Adding these together gives the total present value of cash inflows:$$ \text{Total PV} = 80,214.77 + 83,516.25 + 74,520.59 + 124,183.82 + 110,783.07 + 98,917.47 = 572,136.97 $$The profitability index (PI) is then calculated as:$$ \text{PI} = \frac{\text{Total PV of Cash Inflows}}{\text{Initial Investment}} = \frac{572,136.97}{480,000} = 1.19 $$Rounding to two decimal places, the profitability index is approximately 1.18, indicating that for every dollar invested, the project returns $1.18. Therefore, the project is profitable and should be undertaken.

Barnacle Bob's Fish and Tackle Shop Is Planning an Expansion