A project manager is using the payback method to make the final decision on which project to undertake.The company has a 15% required rate of return and expects a 5% rate of inflation for the following five years.What is the discounted payback of a project that has cash flows as shown in the table? $$\begin{array} { | l | l | }
\hline \text { Year } & \text { Cash Flow } \
\hline 0 & - \$ 500,000 \
\hline 1 & \$ 50,000 \
\hline 2 & \$ 75,000 \
\hline 3 & \$ 150,000 \
\hline 4 & \$ 150,000 \
\hline 5 & \$ 750,000 \
\hline
\end{array}$$
A) 3.9 years
B) 4.3 years
C) 4.6 years
D) 4.1 years

Question

A project manager is using the payback method to make the final decision on which project to undertake.The company has a 15% required rate of return and expects a 5% rate of inflation for the following five years.What is the discounted payback of a project that has cash flows as shown in the table? $$\begin{array} { | l | l | } 
\hline \text { Year } & \text { Cash Flow } \
\hline 0 & - \$ 500,000 \
\hline 1 & \$ 50,000 \
\hline 2 & \$ 75,000 \
\hline 3 & \$ 150,000 \
\hline 4 & \$ 150,000 \
\hline 5 & \$ 750,000 \
\hline
\end{array}$$
A) 3.9 years
B) 4.3 years
C) 4.6 years
D) 4.1 years

Quizplus · Accepted Answer

To calculate discounted payback, we need to discount each cash flow by the company's required rate of return adjusted for inflation.

Year 0: - $500,000 (no discounting needed) 
Year 1: $50,000/(1.15*1.05) = $41,904.76 
Year 2: $75,000/(1.15^2*1.05^2) = $57,017.54 
Year 3: $150,000/(1.15^3*1.05^3) = $97,065.14 
Year 4: $150,000/(1.15^4*1.05^4) = $83,011.67 
Year 5: $750,000/(1.15^5*1.05^5) = $405,669.15

We can then find the cumulative discounted cash flows:

Year 0: - $500,000 
Year 1: - $458,095.24 ($41,904.76) 
Year 2: - $401,077.70 ($41,904.76 + $57,017.54) 
Year 3: - $304,012.55 ($41,904.76 + $57,017.54 + $97,065.14) 
Year 4: - $221,000.88 ($41,904.76 + $57,017.54 + $97,065.14 + $83,011.67) 
Year 5: $184,668.27 ($41,904.76 + $57,017.54 + $97,065.14 + $83,011.67 + $405,669.15)

The discounted payback is the point at which the cumulative discounted cash flows become positive. In this case, that occurs in Year 4.

Cumulative discounted cash flows at the end of Year 3: - $304,012.55 
Remaining discounted cash flow in Year 4: $83,011.67 
Years of cash flows: 3 + ($83,011.67/$221,000.88) = 4.37

Therefore, the discounted payback period is 4.37 years. However, since we are asked to choose from the given options, the closest answer is 4.3 years, or choice B.

A Project Manager Is Using the Payback Method to Make