Exam 2 Lecture 8

A company's preferred stock sells for $10/share today and pays a dividend of $1 each quarter. What is the rate of return per quarter?

10 = 1/r. So r = 1/10 = 10%.

GSU offers a one-year scholarship that pays you a monthly stipend of $2,000. Suppose that you can invest at a 4% rate of return. For simplicity, assume 4% is monthly. What is the present value of this scholarship for you?

C = $2,000, t = 12, r = 4% 𝑃𝑉𝐴 =2000×(1−[1⁄(1+4%)12])/4%=$18,770.15 If 4% is APR, not monthly return, you need to make r = 4%/12 in the calculation.

You really want an Audi A4 that sells at $35,000. After carefully going over your budget, you determine that you can afford to pay $800 per month toward a new car. You call up an Audi dealer and find out that they can provide financing at a rate of 0.5% per month for 48 months. The first payment is due when you sign the contract. How much can you borrow? Is it enough for you to buy this Audi A4?

C = $800, r = 0.5% per month, t = 48 months 1 − 1⁄1.00548 𝑃𝑉 = $800 × (1-1/0.005^48)/.005) × 1.005) = $34,234.58 So it is not enough to buy that Audi A4. A down payment of about $765.42 is needed.

Financial calculator operation: PMT = _____, N = _____, I/Y = ____ (in percentage), compute PV or FV (future value at t)

C;t;r

Peter plans to retire in 30 years. His expenses after retirement are expected to be $1M. Peter's bank provides a retirement CD account with annual interest rate of 8%. How much does Peter have to deposit today in order to achieve his retirement fund need in 30 years?

FV = $1M, r = 8% per year, t = 30 years PV = $1𝑀/1.08^30 = $99,377.33

_____value: The equivalent value of the present cash flow at some point of time in the future.

Future

Your Bank of America representative tells you that BOA recently released a new product, "Super CD" that gives you 5% interest rate. How much money can you withdraw at maturity if you deposit $1,000 in a one- year Super CD at BOA? What about a two-year Super CD? And, a five-year Super CD? How do you interpret them?

One-year CD: $1,000×1.05 = $1,050 Two-year CD: $1,000×1.052 = $1,102.5 Five-year CD: $1,000×1.055 = $1,276.28 It is equivalent between $1,000 today and $1,050 in one year, $1,102.5 in two years and $1,276.28 in five years.

Example of perpetutity: ____ stock

Preferred

examples of annuities are _____ payments of your apartment, _____payments, leasing fees, etc.

Rent;mortgage

You plan to deposit $1,000 into a savings account in one year, and then deposit $2,000 in two years, and finally $3,000 in three years. The savings account earns a 3.5% interest rate. How much can you withdraw at the end of the fourth year? Alternatively, you may make a single deposit now and withdraw it in four years. How much do you need to deposit now to achieve the same saving goal?

This is the find the future value and present value of the cash flows. Future value is 𝐹𝑉 = $1,000 × 1.0353 + $2,000 × 1.0352 + $3,000 × 1.035 = $6,358.17. Present value is 𝑃𝑉 = $6,356.17 /1.035^4= $5,539.03.

________ is almost the same as annuity except for the timing of the cash flows. It is an annuity shifted one period backward on the time line.

annuity due

The extra future cash flow is ____for being patient,It compensates for opportunity costs, its also reward to risk.

compensation

Perpetuity: A series of ____ cash flows that last forever.

constant

Annuity Due: A series of _____ cash flows that occur at the ______ of each period for some fixed number of periods.

constant ;beginning

Growing annuity: Cash flows that grow at a ____rate g for some ____ number of periods

constant ;fixed

One dollar at the current time is worth _____from (usually more than) one dollar in one year

differently

Convention of cash flow timing: Without specific instruction, we assume that cash flows occur at the _____of each period

end

Growing perpetuity: Cash flows that ____at a constant rate g forever

grow

We often use the tool of "Time Line" to assist the analysis. It shows a. Period ___ (day, month, year, etc.), and number of periods b. ______ rate of return for each period c. _______flows in each period d.Convention of cash flow _____

intervals;Effective ;Cash;timing

Annuity due is ____valuable than annuity because the cash flow arrives earlier Value of annuity due = Value of annuity × (1 + 𝑟)

more

To be equivalent, _____ than one dollar has to be given for one dollar of today

more

Annuities: A series of constant cash flows that occur at the end of each ______for some ___ number of periods

period;fixed

You are ready to buy a house and you have $20,000 for a down payment and closing costs. Closing costs are estimated to be 4% of the loan value and cannot be financed. You have an annual salary of $36,000 and the bank is willing to allow your monthly mortgage payment to be equal to 28% of your monthly income. The interest rate on the loan is 0.5% per month for a 30-year fixed rate loan. How much money will the bank lend to you? How much can you offer for the house? Assume mortgage payments are at the end of each month.

𝐶 = $36,000/12 × 0.28 = $840 𝑡 = 30 × 12 = 360 months, 𝑟 = 0.5% per month 𝑃𝑉 = $840 × (1−1⁄1.005^360)/.005 = $140,104.96, that is what the bank lends to you. 0.005 Closing cost = $140,104.96 × 0.04 = $5,604.20. Down payment = $20,000 - $5,604.20 = $14,395.80 So you can afford a house up to $154,500.76 = $140,104.96 + $14,395.80.

The present value of a perpetuity:

𝐶/𝑟

The present value of growing perpetuity:

𝐶1 /𝑟−𝑔

The present value of a growing annuity:

𝐶1: the first cash flow; g: growth rate; r: rate of return; t: number of periods (cash flows).

How much money will you receive next year if you invest $100 today and the expected rate of return is 10%?

𝐹 = $100 + $100 × 0.1 = 100 × (1 + 0.1) = $110. The $100 is called the future value of the present $100. $110 in one year is equivalent to $100 today given the return of 10%

relation between present value and future value is

𝐹𝑉𝑡 =𝑃𝑉×(1+𝑟)^𝑡.

Your broker called again and recommended an investment opportunity that pays $100 in one year and then the paybacks grow at a rate of 2% each year indefinitely. What is the highest price that you will pay for the investment? Assume required return is 5%.

𝑃𝑉 = 100/(5%−2%) = $3,333.33

Present value of an annuity of 𝐶 dollars per period for 𝑡 periods when the rate of return is 𝑟:

𝑃𝑉𝐴 =𝐶×(1−[1⁄(1+𝑟)𝑡])/r