Finance Content

Question 1

Present Value to Future Value

Answer 1

FV = PV * (1/(1+r))^T - Note numerator 1 is unchanged by T

Question 2

How long to get from PV to a set FV

Answer 2

FV = PV * (1 + r)^T
FV/PV = (1+r)^T
ln(FV/PV) = ln(1+r)^T
T = ln(FV/PV)/ln(1+r)

Question 3

Compounding periods

Answer 3

FV = PV * (1 + (r/m))^(m*t)
m = periods a year
t = years

Question 4

Effective Annual Rate of Interest

Answer 4

Effective Annual Rate (EAR) is the annual rate that would provide the the same FV as the compounding rate being compared to for a year.

i.e. investing at 12.36% annually is the same as investing 12% semi annually.

r(EAR) = ((FV/PV)^(1/T)) -1

Question 5

Cash flow terms

Answer 5

Perpetuity: Constant for ever
Growing perpetuity: Growing t constant rate for ever
Annuity: Constant for fixed term
Growing annuity: Growing for fixed term

Question 6

Present value of cash flows

Answer 6

Perpetuity: C/r
Growing perpetuity: C/(r-g)
Annuity: (C/r)[1-(1/[q+r]^T)]
Growing annuity: (C/[r-g])[1-([1+g]/[1+r])^T]

Question 7

Bond terms

Answer 7

Par value: The amount of money the bondholder will receive at maturity.
Coupon rate: The fixed interest rate paid to the bondholder, expressed as a percentage of the face value.
Coupon Payment: The annual interest rate paid on a bond, expressed as a percentage of the face value and paid from issue date until maturity.
Maturity date: The date on which the principal amount of the bond is repaid to the bondholder.
Yield to maturity: Required market interest rate of the bond.
Yield: The annual return an investor can expect from the bond, considering both interest payments and any potential price appreciation or depreciation.

Question 8

Bond value/pricing equation

Answer 8

Bond value = C/r + FV/([1+r]^T)

C = coupon
r = yield to maturity (YTM)
FV = Par value
T = periods to maturity date

Question 9

Yield To Maturity (YTM)

Answer 9

Bond prices and market prices move in opositve directions:
Coupon rate= YTM then Price = Par value
Coupon rate > YTM then Price > Par value (Premium bond)
Coupon rate < YTM then Price > Par value (Discount bond)

YTM = RATE(nper, pmt, pv, fv)

Question 10

NPVGO

Answer 10

Net Present Value + Growth Opportunitites

Question 11

NPV excel

Answer 11

NPV(Rate, C1, C2…CT) +C0

Question 12

AAR

Answer 12

Annual Accounting Revenue: (Average Net Income/Net book value of investment)

Question 13

IRR

Answer 13

Internal Rate of Return: Discount rate that sets NPV to 0.
NPV = -1 + sum(CT/[1+IRR]^T) = 0

Question 14

PI Method

Answer 14

Profitability Index
PI = Total NPV of Future Cash Flows/Initial Investment

Question 15

FCF

Answer 15

Free Cash Flow: Operating Cash Flow - Net Capital Spending - Change in Net Working Capital

Question 16

Percentage Return

Answer 16

Dividend yield + Capital Gain Yield

Question 17

Average geometric returns

Answer 17

Arithmetic Average Return = (r1+r2….+rt)/t
Average geometric return = T(th)root([1+r1] + [1+r2]….)

Question 18

Variance and Standard deviation

Question 19

Risk Premium and T-bills

Answer 19

T-bill = Risk-free rate
Company risk premium = L(8.5%), M(13.6%), S(2.4%)
THe expected return would be Risk free rate + Company risk premium

Question 20

FV