Question

At the end of 2017, Sawyer Company is conducting an impairment test and needs to develop a fair value estimate for machinery used in its manufacturing operations. Given the nature of Sawyer’s production process, the equipment is for special use. (No secondhand market values are available.) The equipment will be obsolete in 2 years, and Sawyer’s accountants have developed the following cash flow information for the equipment.

Net Cash Flow Probability Year Estimate Assessment 2018 \(6,000 40% 9,000 60% 2019 \) (500) 20% 2,000 60% 4,000 20% Scrap Value 2019 $ 500 50% 900 50%

Instructions Using expected cash flow and present value techniques, determine the fair value of the machinery at the end of 2017. Use a 6% discount rate. Assume all cash flows occur at the end of the year.

Short answer

The fair value of machine at the end will be $9,672.52.

Step-by-step solution

Calculation of PV of cash flow of 2018

$\begin{array}{rcl}\mathrm{Present}\mathrm{value}\mathrm{of}\mathrm{cash}\mathrm{flow}2021& =& \mathrm{Expected}\mathrm{cash}\mathrm{flow}\times \mathrm{PV}\mathrm{factor}\\ & =& \left(6,000\times 40\%+9,000\times 60\%\right)\times 0.9434\\ & =& \left(2,400+5,400\right)\times 0.9434\\ & =& \$7,358.52\end{array}$

Calculation of PV of cash flow of 2018

$\begin{array}{rcl}\mathrm{Present}\mathrm{value}\mathrm{of}\mathrm{cash}\mathrm{flow}2019& =& \mathrm{Expected}\mathrm{cash}\mathrm{flow}\times \mathrm{PV}\hspace{0.17em}\mathrm{factor}\\ & =& \left(-500\times 20\%+2,000\times 60\%+4,000\times 20\%\right)\times 0.8900\\ & =& \left(-100+1,200+800\right)\times 0.8900\\ & =& \$1,691\end{array}$

Computation of PV of scrap value

$\begin{array}{rcl}\mathrm{PV}\mathrm{of}\mathrm{scrap}\mathrm{value}& =& \mathrm{Expected}\mathrm{value}\times \mathrm{PV}\hspace{0.17em}\mathrm{factor}\\ & =& \left(250+450\right)\times 0.8900\\ & =& \$623\\ \mathrm{Fair}\mathrm{value}\mathrm{of}\mathrm{machinery}& =& \mathrm{PV}\hspace{0.17em}\mathrm{value}\mathrm{of}\mathrm{expected}\mathrm{cash}\mathrm{flow}\mathrm{of}2018\mathrm{and}2019+\mathrm{PV}\mathrm{of}\mathrm{scrap}\mathrm{value}\\ & =& 7,358.52+1,691+623\\ & =& \$9,672.52\end{array}$