Question

Cash flow series

	Annual Cash Flow ($ per year)	Annual Cash Flow ($ per year)	Annual Cash Flow ($ per year)
Year	Prob = 0.3	Prob = 0.22	Prob = 0.48
0	–5000	–6000	–4000
1	1000	500	3100
2	1000	1500	1200
3	1000	2000	100

Determine the expected present worth of the following cash flow series if each series may be realized with the probability shown at the head of each column. Let i = 20% per year.

The present worth when the probability is 0.3 is $

The present worth when the probability is 0.22 is $

The present worth when the probability is 0.48 is $

The expected present worth value is $  .

Answer 1

a)

Let us take the case, when probability=0.30

Initial Cash flow-Co=-$5000

Cash flow in year 1=CF1=$1000

Cash flow in year 2=CF2=$1000

Cash flow in year 3=CF3=$1000

Interest rate=i=20%

PW (p=0.30)=-Co+CF1*(P/F,20%,1)+CF2*(P/F,20%,2)+CF3*(P/F,20%,3)

Let us calculate interest factors

(P/F,20%,1)=1/(1+20%)^1=0.833333

(P/F,20%,2)=1/(1+20%)^2=0.694444

(P/F,20%,3)=1/(1+20%)^3=0.578704

PW (p=0.30)=-5000+1000*0.833333+1000*0.694444+1000*0.578704=-$2893.52

b)

Let us take the case, when probability=0.22

Initial Cash flow-Co=-$6000

Cash flow in year 1=CF1=$500

Cash flow in year 2=CF2=$1500

Cash flow in year 3=CF3=$2000

Interest rate=i=20%

PW (p=0.22)=-Co+CF1*(P/F,20%,1)+CF2*(P/F,20%,2)+CF3*(P/F,20%,3)

PW (p=0.22)=-6000+500*0.833333+1500*0.694444+2000*0.578704=-$3384.26

c)

Let us take the case, when probability=0.48

Initial Cash flow-Co=-$4000

Cash flow in year 1=CF1=$3100

Cash flow in year 2=CF2=$1200

Cash flow in year 3=CF3=$100

Interest rate=i=20%

PW (p=0.48)=-Co+CF1*(P/F,20%,1)+CF2*(P/F,20%,2)+CF3*(P/F,20%,3)

PW (p=0.48)=-4000+3100*0.833333+1200*0.694444+100*0.578704=-$525.46

d)

Expected present worth=0.30*(-2893.52)+0.22*(-3384.26)+0.48*(-525.46)=-$1864.81