Question

You are comparing two investment options that each pay 6 percent interest, compounded annually. Both options will provide you with $12,000 of income. Option A pays $2,000 the first year followed by two annual payments of $5,000 each. Option B pays three annual payments of $4,000 each.

Which one of the following statements is correct given these two investment options? Assume a positive discount rate. (No calculations needed.)

a) Option A has a higher future value at the end of year three.
b) Option B has a higher present value at time zero.
c) Option B is a perpetuity.
d) Option A is an annuity.

Answer 1

Option B has a higher present value at time zero is correct

as shown below:

Option A future value at the end of three years = 2000*(1.06)^2+5000*(1.06)^1+5000*(1.06)^0= $12,547

Option B future value at the end of three years = 4000*(1.06)^2+4000*(1.06)^1+4000*(1.06)^0=$12,734

Option B has higher future value as determined above, so first option is wrong.

Option A present value at time zero = 2000/(1.06)^1+5000/(1.06)^2+5000/(1.06)^3= $10,535

Option B present value at time zero = 4000/(1.06)^1+4000/(1.06)^2+4000/(1.06)^3=$10,692

Option B has higher present value as determined above, so second option is correct.

Third option is wrong as Option B is not perpetuity as B has three years life.

Fourth option is wrong as Option A is not ANNUITY as A CASH FLOW amounts is not equal , it varies on annual basis.