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Question 10.2: A project costs $100,000 in year 0. Cash inflows are Y1 = $3...

A project costs $100,000 in year 0. Cash inflows are Y1 = $30,000, Y2 = $50,000, Y3 = $70,000, where year 0 is the present, and Y1, Y2, and Y3 are the inflows in one, two, and three years, respectively. Assume a discount rate of 12%. Figure 10–2 provides a format for computing discounted payback.

F I G U R E 10–2
Format for Computing Discounted Payback

\begin{array}{lccc}& {\text { Year 1 }} & {\text { Year 2 }} & {\text { Year 3 }} \\\\\hline \text { Discounting inflows } & \cfrac{\$ 30,000}{(1+12 \%)} & \cfrac{\$ 50,000}{(1+12 \%)^2} & \cfrac{\$ 70,000}{(1+12 \%)^3} \\\\& \$ 30,000 / 1.12 & \$ 50,000 / 1.254 & \$ 70,000 / 1.405 \\\\& \$ 26,786 & \$ 39,872 & \$ 49,822\end{array}

 

\begin{array}{lr}\text { Outflows } &\qquad& \$ 100,000 \\\text { Less DF Y1 } & \qquad&-\$ 26,786 \\\text { Less DF Y2 } &\qquad& -\$ 39,872 \\\quad \text { Residue } &\qquad&\overline{ \$ 33,342}\end{array}

 

Residue/inflow in year 3=\$ 33,342 / \$ 49,822=0.669
Payback =2 years +0.669=2.669 years

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