Question

At the end of 2020, Sheffield 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 Sheffield’s production process, the equipment is for special use. (No secondhand market values are available.) The equipment will be obsolete in 2 years, and Sheffield’s accountants have developed the following cash flow information for the equipment.

Year		Net Cash Flow Estimate				Probability Assessment
2021		$5,440				40%
		9,500				60%
2022		$(460	)			20%
		2,180				60%
		3,800				20%
		Scrap value
2022		$530				50%
		970				50%

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Using expected cash flow and present value techniques, determine the fair value of the machinery at the end of 2020. Use a 6% discount rate. Assume all cash flows occur at the end of the year. (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

Fair value of the machinery at the end of 2020

$

Answer 1

Ans:- Sheffield Company Table Showing expected cash flow and present value at 6% discount rate.

Year	Net Cash Flow Estimate	Probability Assessment	Expected Cash Flow
2021	$ 5,440	40%	$ 2,176
	$ 9,500	60%	$ 5,700
	Total		$ 7,876
2022	$ (460)	20%	$ (92)
	$ 2,180	60%	$ 1,308
	$ 3,800	20%	$ 760
	Total		$ 1,976
	Scrap Value
2022	$ 530	50%	$ 265
	$ 970	50%	$ 485
	Total		$ 750

According to above calculation, the expected cash flow in 2021 is $ 7,876 and in 2022 ($1,976 + $750) is $2,726.

Formula of Cash Flow:

Factor table 1: 1 year @ 6% discount =1.0600

2021 Present Value = $ 7,876/(1.0600)^1= $7,430.18868

2022 Present Value = $ 2,726/(1.0600)^2= $2,426.13030

The Total Present Value of the 2 cash flow = $7,430.18868+ $2,426.13030 = $9,856

Using Factor table 2:

2021 Present Value= $7,876 x 0.9434=$7,430.2184

2022 Present Value= $2,726 x 0.8900= $2,426.14

The Total Present Value of the 2 cash flow = $7,430.2184+ $2,426.14 = $9,856

Thus, Fair value of the machinery at the end of 2020 is $9,856.

Note:- The Factor Table:- You can see future table for future rate.