You are considering two investment options In option A you h

You are considering two investment options. In option A, you have to invest $4500 now and $1000 three years from now. In option B, you have to invest $3500 now, $1000 a year from now, and $1000 three years from now. In both options, you will receive four annual payments of $2000 each (you will get the first $2000 payment a year from now). Which of these two options would you choose based on AE criterion? Assume the interest rate is 10%.

Solution

Option A

Initial Investment = $4500

Investment at 3^rd year = $1000

Annual Benefits = $2000 each for 4 years

Rate of interest is 10%

NPW = -$4500 – $1000 (P/F, 10%, 3) + $2000 (P/A, 10%, 4)

NPW = -$4500 – $1000 (0.75131) + $2000 (3.1699) = 1088.49

AE = NPW (A/P, 10%, 4)

AE = 1088.49 (A/P, 10%, 4)

AE = 1088.49 (0.31547)

AE = 343

Option B

Initial Investment = $3500

Investment at 1^st year = $1000

Investment at 3^rd year = $1000

Annual Benefits = $2000 each for 4 years

Rate of interest is 10%

NPW = -$3500 – $1000 (P/F, 10%, 1) – $1000 (P/F, 10%, 3) + $2000 (P/A, 10%, 4)

NPW = -$3500 – $1000 (0.90909) – $1000 (0.75131) + $2000 (3.1699) = 1179.4

AE = NPW (A/P, 10%, 4)

AE = 1179.4 (A/P, 10%, 4)

AE = 1179.4 (0.31547)

AE = 372

OPTION B is a better option as it has AE more than option A.