Suleiman must make a choice between two investment alternatives. Alternative 1 will provide him returns of $300 000 at the end of second year and $700 000 at the end of fifth year. Alternative 2 will provide him returns $180 000 at the end of each of the next six years. Alternative 3 will provide him returns $370 000 at the end of second, fourth and sixth years. Which alternative is preferable if money is worth 9.4%?
A) Alternative 1
B) Alternative 2
C) Alternative 3
D) Alternative 2 or Alternative 3, as both are essentially same
E) Alternative 1 or Alternative 3, as both are essentially same

Question

Quizplus · Accepted Answer

To determine the preferable alternative, we calculate the present value (PV) of each alternative using the given interest rate of 9.4%. The formula for PV of a single future payment is PV = FV / (1 + r)^n, where FV is the future value, r is the interest rate, and n is the number of years until payment. For an annuity (equal payments at regular intervals), the formula is slightly different, incorporating the annuity factor.- Alternative 1: PV = $300,000 / (1 + 0.094)^2 + $700,000 / (1 + 0.094)^5 = $252,294.23 + $519,413.95 = $771,708.18- Alternative 2: This is an annuity, so we use the annuity formula. The PV of an annuity can be calculated using the formula PV = P * [(1 - (1 + r)^-n) / r], where P is the payment per period. For Alternative 2, P = $180,000, r = 0.094, and n = 6. PV = $180,000 * [(1 - (1 + 0.094)^-6) / 0.094] = $180,000 * 4.355 = $783,900- Alternative 3: PV = $370,000 / (1 + 0.094)^2 + $370,000 / (1 + 0.094)^4 + $370,000 / (1 + 0.094)^6 = $307,087.79 + $252,294.23 + $207,174.85 = $766,556.87Alternative 2 has the highest present value, making it the preferable investment option.

Suleiman Must Make a Choice Between Two Investment Alternatives