Question

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 1 Probability = 0.45 -$10,000 $4,200 $3,250 $6,000 Probability = 0.25 -$20,000 $3,500 $3,500 $5,000 Probability = 0.3 -$12,000 $3,100 $3,100 $3,100 2-6 7 ga I co search

FW please :)

Answer 1

The expected initial investment = 0.45 $\times$ - $ 10,000 - 0.25 $\times$ - $ 20,000 - 0.3 $\times$ - $ 12000 = - $ 13100

Expected cash flow in year 1 = 0.45 $\times$ $ 4200 + 0.25 $\times$ $ 3500 + 0.3 $\times$ $ 3100 = $ 3695

Expected cash flow from year 2 to 6 = 0.45 $\times$ $ 3250 + 0.25 $\times$ $ 3500 + 0.3 $\times$ $ 3100 = $ 3267.5

Expected cash flow year 7 =  0.45 $\times$ $ 6000 + 0.25 $\times$ $ 5000 + 0.3 $\times$ $ 3100 = $ 4880

Expected equivalent worth = Future worth $\times$ Capital recovery factor

Future worth = - $ 13100 $\times$ ( 1 + 0.12)⁷ + $ 3695 $\times$ ( 1 + 0.12)⁶ + $ 3267.5 $\times$ ( 1 + 0.12)⁵ + $ 3267.5 $\times$ ( 1 + 0.12)⁴  + $ 3267.5 $\times$ ( 1 + 0.12)³ + $ 3267.5 $\times$ ( 1 + 0.12)² + $ 3267.5 $\times$ ( 1 + 0.12)¹ + $ 4880 $\times$ ( 1 + 0.12)⁰

Future worth = $ 6462.23

Expected equivalent worth =  Future worth $\times$ Capital recovery factor

Expected equivalent worth =  $ 6462.23 $\times$ (A/P, 12%, 7 years) =   $ 6462.23 $\times$ 0.2191

Expected equivalent worth = $ 1415.9 $\approx$ $ 1416