FIN 125 EXAM 2

formulas, definitions, etc.

What is the base concept of asset valuation?

The price of a security today is the present value of all cash flows.

What is a bond?

A loan you give to a company or government, where you are the lender, and they are the borrower.

When a company goes bankrupt, _______ are paid first, and _______ are paid last.

Bondholders; shareholders

What is the PV_bond formula? (with symbols)

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

What is the PV_bond formula? (in terms of other formulas)

PV of coupons + PV of par value OR PV of annuity + PV of lump sum

“At par” means that bonds are issued where PV = _______, and YTM = ________.

Principal; coupon rate

If a bond sells below par value, it is a…

Discount bond

If a bond sells above par value, it is a…

Premium bond

Bond prices and interest rates have an _______ relationship.

Inverse

The longer the period for which your money is tied up, the ________ (greater/lesser) the loss when the market starts to offer better interest rates, and correspondingly, the greater the drop in bond price.

Greater

What is the formula for “C” (coupon payments)?

(par value * coupon rate) / m

If YTM = coupon rate, then _______ = ________.

Par value = bond price

If YTM > coupon rate, _______ > ________.

Par value > bond price

If YTM < coupon rate, _______ < ________.

Par value < bond price

What is the formula for current yield?

annual coupon / bond’s price

Define current yield. What is the difference between current yield and YTM?

Current yield is the annual return you would receive if you bought a bond today and held it for one year while receiving coupons. YTM measures the total return rather than the annual return.

YTM is always quoted in the _____ format!

Annual

List the calculator shortcuts and their associated values used to calculate the PV of a bond.

PV (bond price), N (total # of coupon-paying periods), PMT (coupon amt in $$$), FV (principal), and i/yr (interest or your YTM)

Adjusting inputs is crucial to calculating the PV of any security. When calculating the PV of a bond, what inputs must you adjust if you have a coupon-payment period of anything other than a year? (semi-annual, quarterly, etc.)

N, i/yr, and PMT. 

Let’s say you have a bond that has semi-annual coupon payments instead of annual. You must adjust [input] by multiplying by 2, and [input] and [input] by dividing by 2.

N; i/yr and PMT

What is the formula for a zero-coupon bond?

PV_ZCB = FV/(1+r)^t

What is the formula for dirty price?

dirty price = clean price + accrued interest

What is the formula for accrued interest?

coupon per period x (days passed since start of period/ total days in the period)

Which government bonds are not tax-free?

Treasury securities

Which government bonds are tax-free?

Municipal securities

What is the formula for critical tax rate?

T = 1 - (r_m / r_c)

What is the equivalent taxable yield formula?

(r_m) / (1 - T) = ETY

What formula would you use to solve a problem such as "At which tax rate would you be indifferent between the 2 (bonds)?” Let’s say the taxable bond is “x” and the tax-free bond is “y” (yields are respectively x% and y%.

x% (1-T) = y%

What is the nominal rate of interest (or nominal return)?

Quoted interest rate not adjusted for inflation; change in the actual # of dollars.

What is the real rate of interest (real return)?

Interest rate adjusted for inflation; the actual change in your purchasing power.

What is the Fisher Effect? (Either equation)

Real rate = (Nominal rate - inflation) / (1 + inflation) OR = ((1 + nominal rate) / (1 + inflation)) - 1

What is the formula for the approximate real rate of return?

Real rate = nominal - inflation

If you are in a 30% tax bracket, and your investment provides you with a 12% return, and inflation runs at 8%, what is your real after-tax rate of return?

(12% * (1-0.3)) - 8% = 0.4%

The constant dividend (zero-growth) model is measured using the _______ formula.

Perpetuity

Provide the formula for the constant dividend (zero-growth) model.

P₀ = D₁ / r

The dividend growth (aka Gordon Growth) model is measured using the ________ formula.

Growing perpetuity

Provide the formula for the dividend growth (Gordon Growth) model.

P₀ = D₁ / (r-g) OR P₀ = D₀(1+g) / (r-g)

The two-stage dividend-discount model is compromised of measuring two parts: first of _________ growth and then of _________ growth

Rapid; stable

Provide the formula for the two-stage dividend-discount model.

P₀ = sum(D_t / (1+r)^t) + P_n/(1+r)^n

Within the two-stage dividend-discount model, P_n is part of measuring the period of ________ growth. Now provide the formula for P_n.

Stable ; P_n = (D_n+1) / (r_n - g_n) OR P_n = (D_n+1) / (r_n)

If the YTM < coupon rate, then the bond is a _________.

Premium bond

If the YTM > coupon rate, then the bond is a _________.

Discount bond.

If the YTM = coupon rate, then the bond is at _________.

Par value.

Dirty price is also known as ________ price.

Invoice

What is the breakdown of the required rate of return on a stock based on the Gordon Growth Model?

r = (D₁ / P₀) + g

What is the formula to find bond price using a quote%?

Price = FV * Quote%

What are the calculator shortcuts to find YTM? What would you solve for?

PV, FV, PMT, i/yr, N; solving for i/yr

What is the formula for stock valuation using multiples?

P_t = Benchmark PE ratio x EPS_t

What is the formula for NPV?

NPV = sum(CF_t / (1+r)^t) - cost

What are the calculator shortcuts for NPV?

CFj, i/yr, NPV

What is the formula for the exact payback period for annuities?

Payback period = initial investment / cash flow per period

What is the formula for the exact payback period for uneven cashflows?

Payback period = A + B/C

What is the approximate payback period?

PBP is the whole number of years before you recover the initial cost, without going over the initial cost

What is the formula for the internal rate of return (IRR)?

NPV = sum(CF_t / (1+r)^t) - cost, where you solve for r (IRR) OR sum(CF_t / (1+r)^t) = cost

What are the calculator shortcuts for IRR?

CFj, solve for IRR. 

What is the formula for the profitability index (PI)?

PI = (sum( CFt / (1+r)^t)) / cost

What is the definition of NPV?

The difference between the present value of future cash flows of the project and the project’s costs. How much value is created from undertaking the investment?

If the NPV is positive, we should _______ (accept/reject) the project. If the NPV is negative, we should _______ (accept/reject) the project.

Accept; reject

What is the definition of a “payback period”?

The length of time required for an investment to generate cash flows sufficient to recover its initial cost; that is, the time it takes for the project to ”pay back” its initial cost. How long does it take to get the initial cost back?

The discounted payback period tells us the value that a project adds to a firm. True or False?

False

When computing the value of a project, the ____ is the most reliable method.

NPV

What is the definition of the Internal Rate of Return (IRR)?

The discount rate that makes the NPV of an investment zero

What is the definition of the profitability index (PI)?

Measures the benefit per unit cost, based on the time value of money, measures “bang for the buck”