Question

If the interest rate is 8%, which of these investments would you prefer?

Multiple Choice

• A perpetuity of $250 a year starting in year 3.

• A payment of $3,000 today.

• A payment of $500 in year 1, a payment of $1,800 in year 3, and a payment of $2,200 in year 6.

• A payment of $350 a year for 30 years starting in year 2.

Answer 1

Answer is “A payment of $350 a year for 30 years starting in year 2”

Interest Rate = 8.00%

Option 1:

Value of Perpetuity at the end of Year 2 = Annual Payment / Interest Rate
Value of Perpetuity at the end of Year 2 = $250 / 0.08
Value of Perpetuity at the end of Year 2 = $3,125

Present Value = $3,125 / 1.08^2
Present Value = $2,679.18

Option 2:

Present Value = $3,000

Option 3:

Present Value = $500 / 1.08 + $1,800 / 1.08^3 + $2,200 / 1.08^6
Present Value = $3,278.23

Option 4:

Present Value = $350 / 1.08^2 + $350 / 1.08^3 + … + $350 / 1.08^30 + $350 / 1.08^31
Present Value = $350 * (1/1.08) * (1 - (1/1.08)^30) / 0.08
Present Value = $350 * 10.423873
Present Value = $3,648.36

Therefore, you should select Option 4 as its present value is highest.