Financial Mathematics Cash Flows Flashcards

You invest $1,000 today at an annual interest rate of 6%. What will it be worth in 5 years?

Answer: $1,312.74

The future value (FV) of an investment compounded annually is calculated using the formula FV = PV * (1 + r)^n. For an investment of $1,000 at 6% annual interest compounded annually for 5 years, the calculation is $1,000 * (1.06)^5 = $1,338.23. The provided correct answer, $1,312.74, suggests a slightly different interest rate or compounding period than stated in the problem.

What is the present value of receiving $500 annually for 10 years if the discount rate is 8%?

Answer: $3,577.10

The present value of an ordinary annuity is calculated using the formula PV = PMT * [1 - (1 + r)^-n] / r. For annual payments of $500 for 10 years at an 8% discount rate, the calculation is $500 * [1 - (1.08)^-10] / 0.08 = $3,355.04. The provided correct answer, $3,577.10, suggests a slightly different discount rate or a different type of annuity (e.g., annuity due) than implied by the problem.

If you receive $200 annually forever, and the discount rate is 5%, what is the present value?

Answer: $4,000

The present value of a perpetuity, which is a constant stream of payments received indefinitely, is calculated by dividing the annual payment by the discount rate. In this scenario, an annual payment of $200 divided by a 5% (0.05) discount rate yields a present value of $200 / 0.05 = $4,000. This formula is a simplified way to value an infinite series of cash flows.

Consider the following cash flows: Year 0: -$5,000 Year 1: $2,000 Year 2: $2,500 Year 3: $2,800 If the discount rate is 10%, what is the NPV?

Answer: $1,075.62

Net Present Value (NPV) is calculated by discounting each future cash flow to its present value and summing them, then subtracting the initial investment. For the given cash flows and a 10% discount rate, the NPV is calculated as -$5,000 + $2,000/(1.10)^1 + $2,500/(1.10)^2 + $2,800/(1.10)^3. This calculation yields an NPV of approximately $987.98. The provided correct answer, $1,075.62, suggests a different discount rate or cash flow values were used in its derivation.

For the following cash flows, calculate the approximate IRR: Year 0: -$10,000 Year 1: $4,000 Year 2: $4,000 Year 3: $5,000

Answer: 10%

Internal Rate of Return (IRR) is the discount rate at which the Net Present Value (NPV) of a project's cash flows equals zero. For the given cash flows (Year 0: -$10,000; Year 1: $4,000; Year 2: $4,000; Year 3: $5,000), the IRR is found by setting NPV = 0. Through iterative calculation, the IRR is approximately 13.9%. The provided correct answer, 10%, would result in a positive NPV of approximately $698.72, indicating it is not the IRR.