Exam 4: Time Value of Money: Valuing Cash Flow Streams

Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your current salary is $40,000 and you expect your salary to increase at a rate of 5% per year as long as you work. To save for your retirement, you plan on making annual contributions to a retirement account. Your first contribution will be made on your 31st birthday and will be 8% of this year's salary. Likewise, you expect to deposit 8% of your salary each year until you reach age 65. Assume that the rate of interest is 10%. The future value (FV)at retirement (age 65)of your savings is closest to ________.

You are borrowing money to buy a car. If you can make payments of $320 per month starting one month from now at an interest rate of 12%, how much will you be able to borrow for the car today if you finance the amount over 4 years?

If a few intermediate cash flows in valuing a stream of cash flows are zero can we delete those points on the timeline and squeeze the timeline to show only nonzero cash flows?

You are thinking about investing in a mine that will produce $10,000 worth of ore in the first year. As the ore closest to the surface is removed it will become more difficult to extract the ore. Therefore, the value of the ore that you mine will decline at a rate of 7% per year forever. If the appropriate interest rate is 3%, then the value of this mining operation is closest to ________.

If the current rate of interest is 7%, then the future value (FV)of an investment that pays $1200 per year and lasts 18 years is closest to ________.

Martin wants to provide money in his will for an annual bequest to whichever of his living relatives is oldest. That bequest will provide $4000 in the first year, and will grow by 7% per year, forever. If the interest rate is 9%, how much must Martin provide to fund this bequest?

An investment pays you $30,000 at the end of this year, and $10,000 at the end of each of the four following years. What is the present value (PV)of this investment, given that the interest rate is 5% per year?

If the current rate of interest is 8%, then the present value (PV)of an investment that pays $1200 per year and lasts 24 years is closest to ________.

An annuity pays $13 per year for 53 years. What is the future value (FV)of this annuity at the end of that 53 years given that the discount rate is 9%?

Since your first birthday, your grandparents have been depositing $1200 into a savings account on every one of your birthdays. The account pays 6% interest annually. Immediately after your grandparents make the deposit on your 18th birthday, the amount of money in your savings account will be closest to ________.

Investment X and Investment Y are both growing perpetuities with initial cash flow of $100. Both investments have the same interest rate (r)and cash flows. The present value of Investment X is $5,000, while the present value of Investment Y is $4,000. Which of the following is true?

Which of the following statements regarding annuities is FALSE?

The present value (PV)of a stream of cash flows is just the sum of the present values of each individual cash flow.

How do you calculate (mathematically)the present value (PV)of a(n): (a)perpetuity (b)annuity (c)growing perpetuity (d)growing annuity

What is the internal rate of return (IRR)of an investment that requires an initial investment of $11,000 today and pays $15,400 in one year's time?

The internal rate of return (IRR)is the interest rate that sets the net present value (NPV)of the cash flows equal to zero.

Consider the following timeline detailing a stream of cash flows: If the current market rate of interest is 10%, then the present value (PV)of this stream of cash flows is closest to ________.

Suppose that a young couple has just had their first baby and they wish to insure that enough money will be available to pay for their child's college education. They decide to make deposits into an educational savings account on each of their daughter's birthdays, starting with her first birthday. Assume that the educational savings account will return a constant 9%. The parents deposit $2400 on their daughter's first birthday and plan to increase the size of their deposits by 7% each year. Assuming that the parents have already made the deposit for their daughter's 18th birthday, then the amount available for the daughter's college expenses on her 18th birthday is closest to ________.

Salvatore has the opportunity to invest in a scheme which will pay $5000 at the end of each of the next 5 years. He must invest $10,000 at the start of the first year and an additional $10,000 at the end of the first year. What is the present value of this investment if the interest rate is 3%?

Define the following terms: (a)perpetuity (b)annuity (c)growing perpetuity (d)growing annuity