FINANCE - CHAPTER 6

You have decided to fund an account that will pay your descendants the inflation-adjusted equivalent of $100 per year forever. You assume inflation will equal 3% per year, and you expect the account to earn 7% per year. How much do you need to put in the account today to ensure your gift will continue forever?

$2,500 This is a growing perpetuity, because you want the $100 to grow at the inflation rate every year. So its value is PV=C/(r-g) = 100/(0.07-0.03) = $2,500 today.

Ralph has $1,000 in an account that pays 10 percent per year. Ralph wants to give this money to his favorite charity by making three equal donations at the end of the next 3 years. How much will Ralph give to the charity each year?

$402.11

Use your financial calculator to find the future value of an annuity of $400 per year for 10 years at 5%.

$5,031.16 Enter 400 for pmt, 10 for N, and 5 for I/Y. Solve for FV. This is the answer you would get for the FV of a single sum.

What is the present value of an ordinary annuity that pays $100 per year for 20 years if the interest rate is 10 percent per year?

$851.36

The formula for the present value of an annuity due is:

(1+r) x (PV of an ordinary annuity)

Which of the following is true about growing annuity?

- The cash flows grow for a finite period. - The cash flows grow at a constant rate.

Which of the following should be valued using a perpetuity formula?

- preferred stock - cash flows from a product whose sales are expected to remain constant forever - a consol (bond that pays interest only and does not mature)

To find the present value of an annuity of $100 per year for 5 years at 10 percent per year using the tables, look up the present value interest factor which is _____ and multiply that by _____.

3.7908; $100

You are planning to buy a CD for $1,352. You will receive $1,500 in 2 years. Use a financial calculator to find the interest rate you will receive on that investment assuming annual compounding.

5.33%

The annuity present value factor for a 30-year annuity with an interest rate of 10 percent per year is _____.

9.4269

Which of the following spreadsheet (Excel) functions will calculate the $614.46 present value of an ordinary annuity of $100 per year for 10 years at 10 percent per year?

=PV(0.10, 10,-100,0,)

Which of the following is the formula for the future value of an annuity?

FV = C [((1+r)^t -1) /r]

True or false: The formula for the present value interest factor for annuities is Annuity present value factor = {1-[1/(1+r)^t]}/r

True

An annuity due is a series of payments that are made _____.

at the beginning of each period

In almost all multiple cash flow calculations, it is implicitly assumed that the cash flows occur at the _____ of each period.

end

A single cash flow is also known as a:

lump sum

Most investments involve:

multiple cash flows

The present value formula for a(n) _____ is PV = C/r, where C is the constant and regularly timed cash flow to infinity, and r is the interest rate.

perpetuity

$100 at the end of each year forever at 10 percent per year is worth how much today?

$1,000 The word forever means this is a perpetuity. The formula is PV for a perpetuity = C/r. In this case, PV = $100/0.10 = $1000.

Which of the following processes can be used to calculate future value for multiple cash flows?

- Compound the accumulated balance forward one year at a time - Calculate the future value of each cash flow first and then add them up

Suppose you need $5,000 in one year, $4,300 in two years, and $5,000 in three years. Match each present value amount to the corresponding cash flow assuming a discount rate of 17%.

Present Value of the Year 1 Cash Flow: $4,273.50 Present Value of the Year 2 Cash Flow: $3,141.21 Present Value of the Year 3 Cash Flow: $3,121.85 Year 1: $5000/1.17 Year 2: $4300/(1.17)^2 Year 3: $5000/(1.17)^3

You are considering an investment that will earn the following cash flows over the next three years. You expect to earn 6% return on the investment. Match each cash flow with its present value, then match the total amount you should pay for the investment today to the appropriate box. Year 1: $5,000 Year 2: $6,000 Year 3: $5,500

Year 1: $4,716.98 Year 2: $5,339.98 Year 3: $4,617.91 Amount you should pay for the investment: $14,674.87 Discount for 1 period: 5000/(1.06) = $4,716.98 Discount for 2 periods: 6000(1.06)^2 = $5,339.98 Discount for 3 periods: 5500/(1.06)^3 = $4,617.91 You should not pay more than the PV of the cash flows, which is the sum of the discounted cash flows.

You expect to receive bonuses with your job at the end of each year for the next five years. Assume you can invest all of your bonuses at 4.5%, and the bonuses are as shown below, match each amount to its future value at the end of five years, then match the total to the appropriate box. Year 1: $500 Year 2: $1,200 Year 3: $1,000 Year 4: $2,400 Year 5: $2,200

Year 1: $596.26 Year 2: $1,369.40 Year 3: $1,092.03 Year 4: $2,508.00 Year 5: $2,200.00 Total after 5 years: $7,765.68