The following equivalence equation is used to calculate the present worth of a n

Question

The following equivalence equation is used to calculate the present worth of a non-uniform cash flow series:
PW=$800(P/A,8%,6)-$150(P/G,8%,6)+$200(P/G,8%,5)(P/F,8%,2)-$2000

PW: present sum of money
G: arithmetic gradient
P: present sum of money
F: future some of money at the end of the nth interest period, which is equivalent to P with interest rate i

1. The value of the net cash flow in year 5
2. The value of the net cash floe in year 2
3. The value of the net cash floe in year 7
4. The value of the net cash floe in year 4

Can u please show me the formula and the solution steps ?, Life Saver !

Explanation / Answer

(P/A,8%,6) means find P when A is at 8% for n=6 Yrs (P/G,8%,6) means find P for a series groth rate g at 8% for 6 yrs (P/F,8%,2) means find P when future value F for 8% for 2 yrs PW=$800(P/A,8%,6)-$150(P/G,8%,6)+$200(P/G,8%,5)(P/F,8%,2)-$2000 ie PW = 800*4.6229-150*10.5233+200*7.3724*0.8573-2000 = $1,383.90 1. For n=5 PW=$800(P/A,8%,5)-$150(P/G,8%,5)+$200(P/G,8%,5)(P/F,8%,5)-$2000 ie PW = 800*3.9927 -150*7.3724 +200*7.3724*0.6806-2000 = $1,091.83 2. for n=2 PW=$800(P/A,8%,2)-$150(P/G,8%,2)+$200(P/G,8%,2)(P/F,8%,2)-$2000 ie PW = 800*1.7833 -150*0.8573+200*0.8573*0.8573-2000 = $(554.96) 3. n=7 PW=$800(P/A,8%,7)-$150(P/G,8%,7)+$200(P/G,8%,7)(P/F,8%,7)-$2000 ie PW = 800*5.2064 -150*14.0242 +200*14.0242*0.5835 -2000 = $1,698.11 4. n=4 PW=$800(P/A,8%,4)-$150(P/G,8%,4)+$200(P/G,8%,4)(P/F,8%,4)-$2000 ie PW =800*3.3121-150*4.6501+200*4.6501*0.7350-2000 = $635.73 The factors are taken from the growth series tables. For want of time, I am not able to share formula. Pl PM & will send you.

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