Question

The managers of a company are considering an investment with the following estimated cash flows. The MARR is 15% per year. Capital investment Annual profits Market value Useful life $50,000 15,000 5,000 5 years The company is inclined to make the investment as the PW(15%) = $2,769. However, you wish to examine the sensitivity of the decision to errors in estimating annual profits and the market value. a) Determine the sensitivity of the decision to invest to changes in annual profits. Hold all other factors constant at their original estimated values. b) Determine the sensitivity of the decision to invest to changes in the market value. Hold all other factors constant at their original estimated values. c) Explain to management why the decision to invest is more sensitive to changes in annual profits or to changes in the market value.

Answer 1

	I	Initial Cash flow (Capital investment)	($50,000)
	Rate	MARR	15%
	Nper	Number of years of Useful life	5
	Pmt	Annual profit	$15,000
	Fv	Market Value	$5,000
	PV	Present Value of Cash Inflows	$52,768	(Using PV function of excel with Rate=15%,Nper=5,Pv=-15000,Fv=-5000)
	PW=PV+I	Present Worth	$2,768
	a)	Sensitivity to changes in annual profits
			A	I
			Annual Profit	Initial Cash Flow	PV	PW=PV+I	(PV using Rate =15%, Nper=5, Pv=-A,Fv=-5000)
		30% less	$10,500	($50,000)	$37,684	($12,316)
		20% Less	$12,000	($50,000)	$42,712	($7,288)
		10% less	$13,500	($50,000)	$47,740	($2,260)
		Base amount	$15,000	($50,000)	$52,768	$2,768
		10% higher	$16,500	($50,000)	$57,796	$7,796
		20% higher	$18,000	($50,000)	$62,825	$12,825
		30% higher	$19,500	($50,000)	$67,853	$17,853
	b)	Sensitivity to changes in market Value
			M	I
			Market Value	Initial Cash Flow	PV	PW=PV+I	(PV using Rate =15%, Nper=5, Pv=-15000,Fv=-M)
		30% less	$3,500	($50,000)	$52,022	$2,022
		20% Less	$4,000	($50,000)	$52,271	$2,271
		10% less	$4,500	($50,000)	$52,520	$2,520
		Base amount	$5,000	($50,000)	$52,768	$2,768
		10% higher	$5,500	($50,000)	$53,017	$3,017
		20% higher	$6,000	($50,000)	$53,265	$3,265
		30% higher	$6,500	($50,000)	$53,514	$3,514
	c)	Sensitivity to change in annual profit is much higher than the sensitivity to changes in market Value
		Reasons:
		1.Market Value is much lower than Annual Profit
		2.Market Value is only one time cash flow , annual profit is for all 5 years
		3. Market value is at the end of useful life . Thus the discounted present Value is low
						G9 x fc =PV(G5, G6,-G7,-68) B C D E G H J K L M ($50,000) 15% Rate Nper Pmt Initial Cash flow (Capital investment) MARR Number of years of Useful life Annual profit Market Value Present Value of Cash Inflows FV PV $15,000 $5,000 $52,768 (Using PV function of excel with Rate=15%,Nper=5,Pv=-15000, Fv=-5000) 115 - x fc =PV(15%,5,-G15,-5000) G H I J K L M N O ($50,000) 15% Initial Cash flow (Capital investment) Rate MARR Nper Number of years of Useful life Pmt Annual profit FV Market Value PV Present Value of Cash Inflows PW=PV+I Present Worth $15,000 $5,000 $52,768 $2,768 (Using PV function of excel with Rate=15%,Nper=5,Pv=-15000, Fv=-5000) Sensitivity to changes in annual profits Initial Cash Annual Profit Flow PV $10,500 ($50,000)| (PV using Rate =15%, Nper=5, Pv=-A, Fv=-5000) P W=PV+I $37,684 30% less 127 X foc =PV(15%,5,-15000,-G27) K L L M N O Base amount 10% higher 20% higher 30% higher $15,000 $16,500 $18,000 $19,500 $50,000) ($50,000) $50,000) ($50,000) $52,768 $57,796 $62,825 $67,853 J $2,768 $7,796 $12,825 $17,853 Sensitivity to changes in market value Initial Cash Market Value Flow PV $3,500 ($50,000) $52,022 (PV using Rate =15%, Nper=5, Pv=-15000,Fv=-M) PW=PV+I $2,022 30% less an