Question

use FW

Q6. [20 marks] The estimated annual cash flows of an investment project along with associated probabilities are given below. Determine the expected equivalent worth of this cash flow series at an interest rate of 12% per year (If your student ID number is even, use the FW method. Otherwise, use the PW method). EOY 0 Probability = 0.45 Probability = 0.25 Probability = 0.3 -$10,000 -$20,000 -$12,000 $4,200 $3,500 $3,100 $3,250 $3,500 $3,100 $6,000 $5,000 $3,100 2-6 7

Answer 1

Ans)- Using Future worth method :-

Expected outflow at the end of year ‘0’ = 0.45*(-10,000) + 0.25*(-20,000) + 0.3*(-12,000)

= $13,100

Expected inflow at the end of year ‘1’ = 0.45*4,200 + 0.25*3,500 + 0.3*3,100

                                                                  = $3,695

Expected inflow at the end of year ‘(2-6)’ =0.45*3,250 + 0.25*3,500 + 0.3*3,100

                                                                  = $3,267.5

Expected inflow at the end of year ‘7’ = 0.45*6,000 + 0.25*5,000 + 0.3*3,100

                                                                  = $4,880

Hence, using formula for future worth

Future Worth (FW) = A (1+r)” + A1(1+r)n-1 + A2(1+r)n-2 + ...An

Where,

A₀,A₁, A₃, … ,A_n are the cash flows at the end of year 0,1,2,…,n respectively.

r: interest rate

here,

n=7 and r=12%=0.12

Hence,

Future Worth (FW) = A. (1+r)? + A(1+r)6 + A2(1+r)5 + ... Az

FW = -13,100(1 + 0.12) + 3695(1 + 0.12)6 + 3267.5(1 + 0.12)5 +3267.5(1 + 0.12)4 + 3267.5(1 + 0.12)3 + 3267.5(1 + 0.12) +3267.5(1 + 0.12): + 4880

FW = -28,960 +7,293+5,758 +5,141 +4,590 +4,099 + 3,660+ 4880

FW = $6,461(Approximately)

Hence, required Expected future worth (FW) is $6,461