You are analyzing a project and have prepared the following data: $$\begin{array} { | l | l | }
\hline \text { Year } & \text { Cad Flow } \
\hline 0 & -£ 169,000 \
\hline 1 & £ 46,200 \
\hline 2 & £ 87,300 \
\hline 3 & £41,000 \
\hline 4 & £ 39,000 \
\hline
\end{array}$$ Required payback period: 2.5 years
Required AAR: 7.25%
Required return: 8.50%
Based on the payback period of _____for this project,you should _____ the project.
A)1.87 years; accept
B)2.87 years; accept
C)2.87 years; reject
D)3.13 years; reject
E)3.87 years; reject

Question

You are analyzing a project and have prepared the following data: $$\begin{array} { | l | l | } 
\hline \text { Year } & \text { Cad Flow } \
\hline 0 & -£ 169,000 \
\hline 1 & £ 46,200 \
\hline 2 & £ 87,300 \
\hline 3 & £41,000 \
\hline 4 & £ 39,000 \
\hline
\end{array}$$ Required payback period: 2.5 years
Required AAR: 7.25%
Required return: 8.50%
Based on the payback period of _____for this project,you should _____ the project.
A)1.87 years; accept
B)2.87 years; accept
C)2.87 years; reject
D)3.13 years; reject
E)3.87 years; reject

Quizplus · Accepted Answer

The payback period for this project is calculated by adding up the cash flows until they reach the initial investment. In this case, that is £169,000. Adding up the cash flows of years 1 and 2 gives a total of £133,500, leaving a remaining balance of £35,500. The cash flow in year 3 is £41,000, which is greater than the remaining balance, so the payback period falls between years 2 and 3. To calculate the exact payback period, we use the formula: Payback period = Year before full recovery + (Unrecovered cost at the start of year)/(Cash flow during year). In this case, 2 + (35,500/41,000) = 2.87 years, which is greater than the required payback period of 2.5 years. Therefore, the project should be rejected.

To calculate the AAR, we use the formula: AAR = Average annual net income / Average investment. The average annual net income is the total net income divided by the number of years, or [(46,200 + 87,300 + 41,000 + 39,000)/4] = £53,625. The average investment is the sum of the initial investment and the final salvage value (assuming there is one) divided by 2, or [(169,000 + 0)/2] = £84,500. Therefore, the AAR is 63.39%, which is greater than the required AAR of 7.25%, indicating that the project is acceptable.

To calculate the NPV using the required return of 8.50%, we use the formula: NPV = CF0 + (CF1/(1+r)^1) + (CF2/(1+r)^2) + (CF3/(1+r)^3) + (CF4/(1+r)^4), where CF0 is the initial investment and CF1-CF4 are the cash flows. Plugging in the values, we get NPV = -169,000 + (46,200/1.085) + (87,300/1.085^2) + (41,000/1.085^3) + (39,000/1.085^4) = -£17,739.39, which is negative and indicates that the project should be rejected.

Since two out of three evaluation methods (payback period and NPV) indicate that the project should be rejected and only one (AAR) indicates that it is acceptable, we should rely on the methods that take into account the timing and size of cash flows (payback period and NPV) and reject the project. Therefore, the best choice is C.

You Are Analyzing a Project and Have Prepared the Following