Chapter 6,7,8- Business Finance

What is the formula for the present value of a perpetuity?

PV = C / r, where C is the cash flow and r is the interest rate.

What is an ordinary annuity?

A finite series of equal payments that occur at regular intervals, with the first payment at the end of the period.

What is an annuity due?

A finite series of equal payments that occur at regular intervals, with the first payment at the beginning of the period.

How do you adjust the present value of an annuity due?

Multiply the present value of an ordinary annuity by (1 + r).

How do you find the future value of multiple cash flows?

Calculate the future value of each cash flow at the desired future date and sum them.

What is the future value of an investment of $4,000 for three years at 8% interest?

The future value is $21,803.58 after three years.

What is the future value of $500 invested today and $600 invested in one year at 9% interest over two years?

The future value is $1,248.05.

How do you calculate the present value of uneven cash flows?

Find the present value of each cash flow and sum them.

What is the present value of receiving $200 in one year, $400 in two years, $600 in three years, and $800 in four years at 12% interest?

The present value is $1,432.93.

What does the CF key do on a financial calculator?

It allows you to enter cash flows for calculations involving multiple cash flows.

What should you do if your broker offers an investment that requires a return higher than the calculated present value?

You should decline the investment if the present value is less than the amount you would pay.

How much would you be willing to invest today for five annual payments of $25,000 each beginning in 40 years at 12% interest?

You would be willing to invest $1,084.71.

What is the formula for finding the payment (C) on a loan?

C = P[r(1 + r)^n] / [(1 + r)^n - 1], where P is the loan amount, r is the interest rate per period, and n is the number of payments.

What is the monthly payment for a $20,000 loan at 8% interest compounded monthly over 4 years?

The monthly payment is $488.26.

How do you calculate the number of payments needed to pay off a loan?

Use the formula for loan payments to solve for n, the number of payments.

What is the present value of a $10 million sweepstakes paid in equal annual installments of $333,333.33 over 30 years at a 5% discount rate?

The present value is $5,124,150.29.

What is the effect of compounding on investment returns?

Compounding increases the total returns on an investment over time due to interest being earned on previously earned interest.

What is the future value of $100 deposited in one year and $300 deposited in three years at 8% interest after five years?

The future value is $485.97.

What is the total future value of cash flows of $7,000 today and $4,000 each year for three years at 8% interest?

The total future value in three years is $21,803.58.

What is the significance of the interest rate in discounted cash flow analysis?

The interest rate determines the present value of future cash flows and affects investment decisions.

How do you clear cash flow keys on a financial calculator?

Press the CF key and then CLR Work to clear the cash flow entries.

What is the formula for calculating the present value of an annuity?

PV = PMT × [(1 - (1 + r)^-n) / r]

How do you find the monthly interest rate when borrowing $10,000 with a payment of $207.58 per month for 60 months?

The monthly interest rate is 0.75%.

What is the trial and error process for finding the interest rate on an annuity?

Choose an interest rate, compute the present value (PV) of payments, and adjust the rate until the computed PV equals the loan amount.

How much will you have in 40 years if you deposit $2000 per year at an interest rate of 7.5%?

You will have $454,513.04.

What is the future value of an annuity due with annual payments of $10,000 at 8% for 3 years?

The future value is $35,061.12.

What are perpetuities in finance?

Perpetuities are annuities where cash flows continue indefinitely.

How do you calculate the present value of a perpetuity?

PV = Cash Flow / Required Rate of Return.

If an investment offers a perpetual cash flow of $500 annually at a required return of 8%, what is its value?

The value of the investment is $6,250.

What is the formula for the Effective Annual Rate (EAR)?

EAR = (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1.

What is the difference between APR and EAR?

APR is the annual rate quoted by law, while EAR accounts for compounding during the year.

How do you compute the APR from a monthly interest rate of 0.5%?

APR = 0.5% × 12 = 6%.

What is the monthly payment for a $3500 computer system loan at 16.9% interest over 2 years?

The monthly payment is $172.88.

What is the required APR if you want an effective rate of 12% with monthly compounding?

You need to calculate the APR based on the compounding frequency.

What is the significance of truth-in-lending laws in the U.S.?

They require lenders to disclose the APR on consumer loans.

What is the formula for calculating the future value of an ordinary annuity?

FV = PMT × [(1 + r)^n - 1] / r.

What happens if the computed present value of an annuity is greater than the loan amount?

The interest rate is too low.

How do you compare two savings accounts with different compounding periods?

Calculate the EAR for both accounts and compare them.

What is the formula for computing the future value of an annuity due?

FV = PMT × [(1 + r)^n - 1] / r × (1 + r).

What is the relationship between APR and effective interest rates?

APR does not equal EAR; they are calculated differently.

What is the effective annual rate for an investment of $100 at 8% compounded quarterly?

The EAR is approximately 8.24%.

What is the formula for the present value of preferred stock?

PV = D / R, where D is the dividend and R is the required return.

What is the value of preferred stock with a price of $40 and a quarterly dividend of $1?

The required return is 2.5%.

What is the future value of an annuity with a first payment made today?

It is calculated by adjusting the future value of an ordinary annuity.

Bond

A debt security that represents a loan made by an investor to a borrower.

Par value (face value)

The amount paid back to the bondholder at maturity.

Coupon rate

The annual interest rate paid on a bond, expressed as a percentage of the face value.

Coupon payment

The actual dollar amount paid to bondholders, typically on a semiannual basis.

Maturity date

The date on which the bond's principal amount is to be paid in full.

Yield or Yield to maturity

The total return anticipated on a bond if held until it matures.

Discount bond

A bond that sells for less than its par value.

Premium bond

A bond that sells for more than its par value.

Bond Value

The present value of future cash flows, including coupon payments and par value.

Present Value of Cash Flows

The current worth of a cash flow or series of cash flows that are expected to be received in the future.

Valuing a Discount Bond with Annual Coupons

Using the formula: B = PV of annuity + PV of lump sum.

Valuing a Premium Bond with Annual Coupons

Using the formula: B = PV of annuity + PV of lump sum.

Annuity

A series of equal payments made at regular intervals.

Lump Sum

A single payment made at a specific time.

N

The number of payments, not years.

I/YR

The interest rate per year.

PV

Present Value, the current value of a future sum of money.

FV

Future Value, the value of an investment after a specified period.

p/yr

Payments per year, which should be 2 for semi-annual bonds.

Rates Climb to 12%

Indicates a scenario where interest rates increase to 12%.

Rates Fall to 6%

Indicates a scenario where interest rates decrease to 6%.

Bond Prices: Relationship Between Coupon and Yield

If YTM = coupon rate, then par value = bond price; if YTM > coupon rate, then par value > bond price; if YTM < coupon rate, then par value < bond price.

Impact of Inflation on Interest Rates

Inflation affects the real return on bonds and can lead to fluctuations in interest rates.

Term Structure of Interest Rates

The relationship between interest rates and the time to maturity of debt.

Bonds

Debt securities issued by corporations or governments to borrow money from the public on a long-term basis.

Interest-only loans

Loans where only interest payments are made during the term, with the principal repaid at the end.

Coupon

The stated interest payment made on a bond.

Face value (par value)

The principal amount of a bond that is repaid at the end of the term.

Maturity

The specified date on which the principal amount of a bond is paid.

Yield to Maturity (YTM)

The rate implied by the current bond price.

Present value (PV)

The current worth of a future sum of money or stream of cash flows given a specified rate of return.

Annuity present value

The present value of a series of equal payments made at regular intervals.

Total bond value

The sum of the present value of the coupon payments and the present value of the face value.

Semiannual coupon payment

The coupon payment made every six months.

Price Risk

The change in price due to changes in interest rates.

Reinvestment Rate Risk

Uncertainty concerning rates at which cash flows can be reinvested.

Interest Rate Risk

The risk that changes in interest rates will affect the price of a bond.

Long-term bonds

Bonds that typically have more price risk than short-term bonds.

Low coupon rate bonds

Bonds that have more price risk than high coupon rate bonds.

High coupon rate bonds

Bonds that have more reinvestment rate risk than low coupon rate bonds.

Trial and error for YTM

The process of estimating the yield to maturity if a financial calculator is not available.

Sign convention for YTM

PMT and FV need to have the same sign, while PV needs to have the opposite sign.

Bond with 10% annual coupon rate

A bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1,000, with a current price of $928.09.

YTM with Semiannual Coupons

Yield to maturity (YTM) for a bond with a 10% coupon rate, semiannual coupons, face value of $1,000, 20 years to maturity, selling for $1,197.93 is 8%.

Periods

There are 40 periods for the bond with semiannual coupons.

Current Yield

Current Yield is calculated as annual coupon divided by price.

Yield to Maturity

Yield to maturity is the sum of current yield and capital gains yield.

Capital Gain Yield

Capital gain yield is calculated as (1,193.68 - 1,197.93) / 1,197.93 = -0.0035 = -0.35%.

Bond Pricing Theorems

Bonds of similar risk and maturity will yield about the same return, regardless of the coupon rate.

Debt Characteristics

Debt does not represent ownership interest and creditors do not have voting rights.

Interest Tax Deductibility

Interest on debt is considered a cost of doing business and is tax deductible.

Creditor's Legal Recourse

Creditors have legal recourse if interest or principal payments are missed.

Financial Distress from Excess Debt

Excess debt can lead to financial distress and bankruptcy.

Equity Characteristics

Equity represents ownership interest and common stockholders vote for the board of directors.

Dividends Tax Treatment

Dividends are not considered a cost of doing business and are not tax deductible.

Legal Recourse for Stockholders

Stockholders have no legal recourse if dividends are not paid.