Exam 4: The Time Value of Money

Damon is contemplating taking a deal with his uncle,who is a very successful entrepreneur.He must pay his uncle $50,000 this year and an additional $50,000 at the end of both the fifth and tenth year.This would allow him to receive a perpetual annual cashflow of $12,000.What is the NPV of this offer if the interest rate is 10%?

You are considering purchasing a new home.You will need to borrow $250,000 to purchase the home.A mortgage company offers you a 15-year fixed rate mortgage (180 months)at 9% APR (0.75% month).If you borrow the money from this mortgage company,your monthly mortgage payment will be closest to:

Which of the following investments has a higher present value,assuming the same (strictly positive)interest rate applies to both investments?

Cash flows from an annuity occur every year in the future.

What is the future value of this annuity?

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 8% per year forever.If the appropriate interest rate is 6%,then the value of this mining operation is closest to:

How do the growth perpetuity results differ with negative and positive growths of similar magnitude,assuming everything else remains unchanged?

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:

Alex buys a consol (perpetual bond)for $90,000.This consol promises him a fixed cash flow of $10,000 every year,forever,starting at the end of the year.If the current market rate is 10%,what is the net present value of his purchase?

Use the table for the question(s) below. -What is the decision criteria for the Net Present Value rule?

Use the information for the question(s) below. Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your current salary is $45,000 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 7%. -The future value (FV)at retirement (age 65)of your savings is closest to:

An annuity will pay you $12,000 per year for 20 years.What is the PV of this annuity if your cost of capital is 7%?

Micha offers to pay an investor of a lump sum in her business today $1000 in one year's time,$2000 in two years' time,$3000 in three years' time and $4000 in 4 years' time.If the interest rate is 8%,what is the minimum value of the lump sum she must ask of an investor if the net present value (NPV)is to be equal to zero?

What is the difference between a perpetuity and an annuity?

A growing perpetuity' with a first payment of $17,500 grows at a constant rate,g.If the present value of this perpetuity is $1,000,000,what is the growth rate of the cash flows,given that the interest rate is 6%?

Why must a growing perpetuity have a growth rate less than the discount rate?

Which of the following investments has the highest net present value (NPV),given that the interest rate is 5.5%?

Jackie & her husband started a savings account for their twin daughters when they were 2 years old.They have been saving $100,000 a year at an interest rate of 10%,and intend on keeping up with their annual contribution to the fund until the girls are 21.What is the future value of their investment?

Clarissa wants to fund a growing perpetuity that will pay $5000 per year to a local museum,starting next year.She wants the annual amount paid to the museum to grow by 5% per year.Given that the interest rate is 8%,how much does she need to fund this perpetuity?