Finance: Time Value of Money, Interest Rates, Bonds, and Risk Concepts

[CH5 TVM] What does the time value of money mean?

A dollar today is worth more than a dollar in the future because it can earn interest.

[CH5 TVM] What is the formula for the future value of a single lump sum?

FV = PV (1 + r)ⁿ shows how much one deposit grows after compounding for n periods.

[CH5 TVM] If the interest rate or number of periods increases, what happens to the future value?

Future value increases since the investment compounds faster or for more periods.

[CH5 TVM] What is the formula for present value of a future amount?

PV = FV / (1 + r)ⁿ discounts future cash to today's dollars.

[CH5 TVM] What happens to present value when the discount rate rises?

Present value decreases because higher discounting reduces current worth.

[CH5 TVM] Define n and r in TVM formulas.

n = total compounding periods r = interest rate per period.

[CH5 TVM] What is the effective annual rate (EAR) and its formula?

EAR = (1 + r / m)ᵐ − 1 converts nominal APR to a true annual yield.

[CH5 TVM] Which rate should you use to compare two loans with different compounding?

The effective annual rate (EAR) it standardizes rates to one-year equivalents.

[CH5 TVM] Example find EAR for an 8 percent nominal rate with monthly compounding.

EAR = (1 + 0.08 / 12)¹² − 1 = 8.30 percent.

[CH5 TVM] Formula for the present value of an ordinary annuity.

PV = PMT × [1 − (1 + r)⁻ⁿ] / r values equal end-of-period payments.

[CH5 TVM] Formula for the future value of an ordinary annuity.

FV = PMT × [(1 + r)ⁿ − 1] / r compounds equal payments to the future.

[CH5 TVM] How do you adjust annuity formulas for an annuity due?

Multiply the ordinary-annuity PV or FV by (1 + r) because payments occur at the beginning.

[CH5 TVM] What is a perpetuity and its formula?

A stream of equal payments that never ends PV = PMT / r.

[CH5 TVM] Compute PV of $1 000 received in 5 years at 8 percent.

PV = 1 000 / (1.08)⁵ = 680.58.

[CH5 TVM] BA II Plus setup for that example.

N = 5 I/Y = 8 FV = 1 000 PMT = 0 CPT PV = − 680.58.

[CH5 TVM] When do you use TVM keys on your calculator?

When payments are evenly spaced and the rate per period is constant.

[CH6 Interest Rates] What is the general equation for a nominal interest rate?

r = r* + IP + DRP + LP + MRP sum of real rate and risk premiums.

[CH6 Interest Rates] Define each component (r*, IP, DRP, LP, MRP).

r* = real risk-free rate IP = inflation premium DRP = default risk premium LP = liquidity premium MRP = maturity risk premium.

[CH6 Interest Rates] If expected inflation rises, how does the yield curve change?

It becomes upward sloping because long maturities include higher inflation expectations.

[CH6 Interest Rates] What does an upward sloping yield curve indicate?

Investors expect higher inflation or higher real rates in the future.

[CH6 Interest Rates] What causes a downward (inverted) yield curve?

Expectations of falling inflation or interest rates often signaling a recession.

[CH6 Interest Rates] Which securities have the lowest risk premiums?

Short-term U.S. Treasury bills because they have no default or liquidity risk.

[CH6 Interest Rates] Typical maturity risk premium (MRP) formula?

MRP = (t − 1) × 0.1 percent premium rises with maturity.

[CH6 Interest Rates] How do default and liquidity premiums affect corporate bond yields?

They raise corporate yields above Treasury yields to compensate for extra risk.

[CH6 Interest Rates] If r* = 2.5 percent, IP = 3 percent, DRP = 1 percent, LP = 0.5 percent, MRP = 1 percent, find r.

r = 2.5 + 3 + 1 + 0.5 + 1 = 8.0 percent.

[CH6 Interest Rates] Why do longterm bonds usually yield more than short term bonds?

They carry a maturity risk premium for greater rate uncertainty.

[CH6 Interest Rates] How does a change in the real risk free rate affect all yields?

All yields shift equally because r* affects every maturity.

[CH6 Interest Rates] Why do corporate bonds offer higher yields than Treasuries of equal maturity?

They include default and liquidity risk premiums that Treasuries lack.

[CH7 Bonds] How are bond prices related to market interest rates?

They move inversely as market rates rise bond prices fall and vice versa.

[CH7 Bonds] Why do bond prices and yields move in opposite directions?

Because price equals the present value of future cash flows divided by (1 + r)ⁿ so a higher r reduces PV.

[CH7 Bonds] Define yield to maturity YTM.

The rate of return earned on a bond if it is held to maturity.

[CH7 Bonds] Define coupon rate.

The annual interest percentage of par that the issuer promises to pay.

[CH7 Bonds] When does a bond sell at a premium?

When the coupon rate is greater than YTM price is above par.

[CH7 Bonds] When does a bond sell at a discount?

When the coupon rate is less than YTM price is below par.

[CH7 Bonds] What happens to a bond's YTM if its market price rises above par?

YTM falls below the coupon rate because investors paid more for it.

[CH7 Bonds] What is the semiannual bond pricing equation?

PB = Σ [CPN ÷ 2 ÷ (1 + r ÷ 2)ᵗ] + FV ÷ (1 + r ÷ 2)²ᵀ.

[CH7 Bonds] Example 10 year 8 percent coupon bond semiannual YTM 10 percent find price.

N = 20 I/Y = 5 PMT = 40 FV = 1 000 PV = −875.38 so it sells at a discount.

[CH7 Bonds] Define current yield.

Annual coupon divided by current price showing income portion of return.

[CH7 Bonds] What is reinvestment rate risk?

The risk that coupon payments must be reinvested at lower rates than the bond's YTM.

[CH7 Bonds] What is price risk?

The risk that a bond's price will fall when market rates rise greater for long maturities or low coupons.

[CH7 Bonds] What is a call provision and when is it used?

It allows issuers to repurchase the bond early usually when interest rates fall.

[CH7 Bonds] Why do callable bonds offer higher yields?

They are riskier for investors since issuers can redeem them when prices rise.

[CH7 Bonds] Dirty price vs clean price.

Dirty price equals clean price plus accrued interest since the last coupon.

[CH7 Bonds] As a bond approaches maturity what happens to premium and discount prices?

Premium bond prices decline toward par while discount bond prices rise toward par.

[CH7 Bonds] How to find YTM on BA II Plus for semiannual bonds.

2nd CLR TVM N = years × 2 PV = negative price PMT = coupon ÷ 2 FV = 1 000 CPT I/Y × 2 gives YTM percent.

[CH7 Bonds] How does bond maturity affect price volatility?

Longer maturity means greater price sensitivity to changes in interest rates.

[CH8 Risk and Return] What is the formula for holding period return HPR?

HPR = (P1 − P0 + D) ÷ P0 measuring total percent return over one period.

[CH8 Risk and Return] What does standard deviation measure?

Total volatility or stand alone risk of returns.

[CH8 Risk and Return] What is the coefficient of variation CV and what does it show?

CV = standard deviation ÷ mean return showing risk per unit of return lower CV is better.

[CH8 Risk and Return] Which type of risk can diversification eliminate?

Unsystematic or firm specific risk.

[CH8 Risk and Return] Which type of risk cannot be diversified away?

Systematic or market risk.

[CH8 Risk and Return] Define beta.

A measure of systematic risk showing how sensitive a stock's returns are to market movements.

[CH8 Risk and Return] Interpret beta = 1.5 vs beta = 0.7.

Beta 1.5 is 50 percent more volatile than the market beta 0.7 is 30 percent less volatile.

[CH8 Risk and Return] Write the CAPM equation.

r = rF + beta × (rM − rF).

[CH8 Risk and Return] Example beta = 1.3 rF = 5 percent RPM = 6 percent find r.

r = 5 + 1.3 × 6 = 12.8 percent.

[CH8 Risk and Return] If investors become more risk averse what happens to the Security Market Line SML?

The slope increases because the market risk premium rises.

[CH8 Risk and Return] What does a steeper SML indicate?

Higher required returns for each level of risk.

[CH8 Risk and Return] What happens to the SML if investors become less risk averse?

It flattens because the market risk premium decreases.

[CH8 Risk and Return] Portfolio beta formula and example.

BetaP = Σ w × beta; example 0.75 × 0.9 + 0.25 × 1.2 = 0.975.

[CH8 Risk and Return] Portfolio required return if betaP = 0.975 rF = 6 percent RPM = 5 percent.

rP = 6 + 0.975 × 5 = 10.88 percent.

[CH8 Risk and Return] If beta = 1.5 and you want portfolio beta = 1 what percent in T bills?

(1.5 − 1) ÷ 1.5 = 33 percent in T bills 67 percent in stock.

[CH8 Risk and Return] If expected return is greater than required return how is the stock valued?

Under valued meaning it offers more return than required buy signal.

[CH8 Risk and Return] If expected return is less than required return how is the stock valued?

Over valued meaning it is priced too high for its risk sell signal.

[CH8 Risk and Return] How does increasing risk aversion affect the market risk premium?

The market risk premium rises as investors demand more compensation for risk.

[CH8 Risk and Return] What is the Security Market Line and its slope?

Graph of expected return versus beta with slope equal to the market risk premium.

[CH8 Risk and Return] Define risk premium.

The extra return above the risk free rate that compensates for taking risk equal to r − rF.

[CH8 Risk and Return] What happens to required return if RPM increases from 5 percent to 6 percent?

Required returns increase proportionally to each asset's beta.

[CH9 Stock Valuation] What is the constant growth Gordon model formula?

P0 = D1 ÷ (r − g) used when dividends grow at a constant rate g.

[CH9 Stock Valuation] How do you find D1 from D0?

D1 = D0 × (1 + g) the next dividend grows by g from the last one.

[CH9 Stock Valuation] Example D0 = 1.50 g = 4 percent r = 14.1 percent find P0.

P0 = 1.50 × 1.04 ÷ (0.141 − 0.04) = 15.45.

[CH9 Stock Valuation] What is the zero growth model?

P0 = D ÷ r used when dividends remain constant.

[CH9 Stock Valuation] If the growth rate g increases while r stays constant what happens to price?

Price rises because future dividends grow faster.

[CH9 Stock Valuation] If the required return r increases while g stays constant what happens to price?

Price falls because future dividends are discounted more heavily.

[CH9 Stock Valuation] If r is approximately equal to g what happens to valuation sensitivity?

Price becomes very sensitive to small changes in r or g.

[CH9 Stock Valuation] How do you use CAPM to find the required return for stock valuation?

Compute r = rF + beta × (rM − rF) then use that r in the Gordon model.

[CH9 Stock Valuation] If expected return is greater than CAPM required return what does that imply?

The stock is under valued buy signal.

[CH9 Stock Valuation] If expected return is less than CAPM required return what does that imply?

The stock is over valued sell signal.

[CH9 Stock Valuation] What is the dividend yield in the Gordon model?

Dividend yield = D1 ÷ P0 showing the cash return from dividends.

[CH9 Stock Valuation] What is the capital gains yield in the Gordon model?

Equal to the constant growth rate g.

[CH9 Stock Valuation] Total expected return on a stock.

Dividend yield plus capital gains yield equals D1 ÷ P0 + g.

[CH9 Stock Valuation] If inflation expectations rise how does that affect required returns and prices?

Required return increases so stock prices fall.

[CH9 Stock Valuation] What is the relation between growth payout and ROE?

g = (1 − payout ratio) × ROE higher retention or ROE increases growth.

[CH9 Stock Valuation] How can you estimate growth rate g from past dividends?

g = (Dn ÷ D0)^(1 ÷ n) − 1.

[CH9 Stock Valuation] Example D0 = 1.20 D5 = 1.55 find g.

g = (1.55 ÷ 1.20)^(1 ÷ 5) − 1 = 5.25 percent.