Risk and Managerial Options in Capital Budgeting 14

Risk and Managerial Options in Capital Budgeting 14 -1

An Illustration of Total Risk (Discrete Distribution) ANNUAL CASH FLOWS: YEAR 1 PROPOSAL A State Deep Recession Mild Recession Normal Minor Boom Major Boom 14 -2 Probability. 05. 25. 40. 25. 05 Cash Flow $ -3, 000 1, 000 5, 000 9, 000 13, 000

Probability Distribution of Year 1 Cash Flows Proposal A Probability . 40. 25 . 05 3, 000 1, 000 5, 000 9, 000 Cash Flow ($) 14 -3 13, 000

Expected Value of Year 1 Cash Flows (Proposal A) CF 1 $ - 3, 000 1, 000 5, 000 9, 000 13, 000 14 -4 P 1. 05. 25. 40. 25. 05 S=1. 00 (CF 1)(P 1) $ -150 2, 000 2, 250 650 CF 1=$5, 000

Variance of Year 1 Cash Flows (Proposal A) 14 -5 (CF 1)(P 1) (CF 1 - CF 1)2(P 1) $ -150 2, 000 2, 250 650 $5, 000 ( -3, 000 - 5, 000)2 (. 05) ( 1, 000 - 5, 000)2 (. 25) ( 5, 000 - 5, 000)2 (. 40) ( 9, 000 - 5, 000)2 (. 25) (13, 000 - 5, 000)2 (. 05)

Variance of Year 1 Cash Flows (Proposal A) 14 -6 (CF 1)(P 1) (CF 1 - CF 1)2*(P 1) $ -150 2, 000 2, 250 650 $5, 000 3, 200, 000 4, 000, 000 3, 200, 000 14, 400, 000

Summary of Proposal A The standard deviation = SQRT (14, 400, 000) = $3, 795 The expected cash flow = $5, 000 14 -7

An Illustration of Total Risk (Discrete Distribution) ANNUAL CASH FLOWS: YEAR 1 PROPOSAL B State Deep Recession Mild Recession Normal Minor Boom Major Boom 14 -8 Probability. 05. 25. 40. 25. 05 Cash Flow $ -1, 000 2, 000 5, 000 8, 000 11, 000

Probability Distribution of Year 1 Cash Flows Proposal B Probability . 40. 25 . 05 -3, 000 1, 000 5, 000 9, 000 Cash Flow ($) 14 -9 13, 000

Expected Value of Year 1 Cash Flows (Proposal B) CF 1 P 1 $ -1, 000 2, 000 5, 000 8, 000 11, 000 . 05. 25. 40. 25. 05 S=1. 00 14 -10 (CF 1)(P 1) $ -50 500 2, 000 550 CF 1=$5, 000

Variance of Year 1 Cash Flows (Proposal B) (CF 1)(P 1) $ -50 500 2, 000 550 $5, 000 14 -11 (CF 1 - CF 1)2(P 1) ( -1, 000 - 5, 000)2 (. 05) ( 2, 000 - 5, 000)2 (. 25) ( 5, 000 - 5, 000)2 (. 40) ( 8, 000 - 5, 000)2 (. 25) (11, 000 - 5, 000)2 (. 05)

Variance of Year 1 Cash Flows (Proposal B) (CF 1)(P 1) $ -50 500 2, 000 550 $5, 000 14 -12 (CF 1 - CF 1)2(P 1) 1, 800, 000 2, 250, 000 1, 800, 000 8, 100, 000

Summary of Proposal B The standard deviation SQRT (8, 100, 000) = = $2, 846 The expected cash flow = $5, 000 The standard deviation of Proposal B < Proposal A. ( $2, 846 < $3, 795 ) 14 -13

Coefficient of variation(COV) u. The ratio of the standard deviation of a distribution to the expected value of the distribution. u. Higher the COV, higher the relative risk would be. 14 -14