5) Determine the value of EUAw from the cash flow diagram shown below, i-9%. 200

Question

5) Determine the value of EUAw from the cash flow diagram shown below, i-9%. 2000 0 4 7,500 A. $328.25 B. S377.75 C. $569.75 D. $451.06 Compute the rate of return represent flow.- ed by the cash Year Cash Flow S I 4.000 5.000 5.500 6.000 6.500 2 3 Symbol Formula to Fi given /P to P given F to A given F to A given P to F given A to P given A to P given G Single Payment (FIP, i%, n) Single Payment Present Worth Uniform Series Sinking Fund Capital Recovery (A/P, i%, n) Uniform Series (FIA, i%, n) Compound Amount Uniform Series Present Worth (0+-1 Uniform Gradient (PG, ion, n ) (FG, i%, n) (40, i%, n) Present Worth Uniform Gradient Future Worth to F given G Uniform Gradient Uniform Series to A given G

Explanation / Answer

ANSWER:

5) IN ORDER TO FIND THE EQUIVALENT ANNUAL WORTH WE WILL USE THIS FORMULA:

P = R * PV / ( 1 - ( 1 + R) ^ - N )

AND BEFORE THAT WE WOULD NEED TO FIND THE PRESENT VALUE .

INITIAL INVESTMENT = $7,500

ANNUAL CASH FLOW RECIEVED = $2,000

PV = -7,500 + 2,000 (P/A,I,N)

WHERE I = 9%

AND N = 6

PV = -7,500 + 2,000(P/A,9%,6)

PV = -7,500 + 2,000 * 4.486

PV = -7,500 + 8,972

PV = $1,472

NOW FOR FINDING THE EUAW WE WILL USE THE FORMULA:

P = R * PV / ( 1- ( 1+R) ^ - N)

P = 9% * 1,472 / ( 1 - ( 1 + 9% ) ^ -6)

P = 132.48 / ( 1 - (1.09) ^ -6 )

P = 132.48 / ( 1 - 0.5962)

P = 132.48 / 0.4037

P = $328.13 (APPROX)

AND HENCE THE CORRECT OPTION IS A.

6) IN ORDER TO FIND THE RATE OF RETURN , WE WILL HAVE TO EQUATE THE PV TO ZERO OF THE CASH FLOWS.

PV = -14,000 + 5,000(P/A,I,N) + 5,500(P/A,I,N) + 6,000(P/A,I,N) + 6,500(P/A,I,N)

0 = -14,000 + 5,000(P/A,I,1) + 5,500(P/A,I,2) + 6,000(P/A,I,3) + 6,500(P/A,I,4)

14,000 =  5,000(P/A,I,1) + 5,500(P/A,I,2) + 6,000(P/A,I,3) + 6,500(P/A,I,4)

NOW, WE SOLVE FOR VARIOUS VALUES OF I , BY TRIAL AND WE GET I = 22.12% OR 22% APPROX.

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