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. Both options are of equal value since they both provide $12,000 of income. a. Option A has the 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

Answer choice b - Option B has a higher present value at time zero is the correct answer.

Step-by-step explanation:

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

as shown below:

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

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

From the calculation above, option B has higher future value, so the first option is wrong.

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

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

From the calculation above, option B has higher present value, so second option is correct.

The third option is wrong as Option B is not perpetuity as B has three years of life.

The fourth option is wrong as Option A is not annuity as cash flow, amounts is not equal, it varies on an annual basis.