Ch. 4 (Lecture 2 & 3)

Question 1

FV

Answer 1

= principal + interest

= C₁ (1 + r)

(compounding) = C₀ * (1 + r)^T

Question 2

PV of lump sum

Answer 2

= C₁ / (1+r)

(discounting) = FV_T/(1 + r)^T

Question 3

NPV

Answer 3

= PV of future cash flows - required investment

= C₁/(1 + r) + C₀

(for T periods) = -C₀ + Σ^t_i=1 [C_i/(1 + r)ⁱ]

_{If NPV is +, take it}

_{If NPV is -, leave it}

Question 4

r_a,m

Answer 4

annual interest rate compounded m times per year

Question 5

r

Answer 5

annual rate compounded annually (referred to as annual yield in class)

= r_a,1

= (1 + r_a,m/m)^m - 1

Question 6

R

Answer 6

interest rate for specified interval (not annualized)

= r_a,m / m

Question 7

(1 + r)

Answer 7

= (1 + r_a,m/m)^m = (1 + R)^m

= e^r_a,infinite

Question 8

APR

Answer 8

= (interest rate per period) * (# periods in year)

Question 9

EAR

Answer 9

effective annual yield/rate

= (1 + r/m)^m - 1

Question 10

Continuous Compounding

Answer 10

FV = C₀ * e^rT

Question 11

Perpetuity

Answer 11

constant stream of cash flows w/o end

PV = C/r

*C = cash flow to be received one period hence from date 0, @ time of first payment*

perpetuity value incr when interest rate decr

perpetuity value decr when interest rate incr

Question 12

Growing perpetuity

Answer 12

cash flow stream that rises a % per year indefinitely

PV = C/(r - g)

*C = cash flow to be received one period hence from date 0, @ time of first payment*

Question 13

Annuity

Answer 13

level stream of regular payments (of # N) that lasts for a fixed number of periods

PV = C [(1/r) - 1/r(1 + r)^N]

FV = C [(1 + r)^N/r - 1/r]

Question 14

Delayed annuities

Answer 14

when annuity begins @date many periods in future

1. calculate PV of annuity ⇒ PV @ period prior to 1st payment
2. discount PV of annuity back to date 0

Question 15

Infrequent annuities

Answer 15

payments occur < 1X a year

1. determine interest rate over x-year period
2. find PV

Question 16

Growing annuity

Answer 16

finite # of growing CF’s

= C [1 - (1 + g/1+r)^N] / [r - g]

= C [1/(r-g) - (1+g)^N / (r-g)(1+r)^N]

N = fixed # N years

Question 17

FV w/compounding

Answer 17

FV = C₀ (1 + r/m) ^mT

T = # of years

Question 18

FV w/ continuous compounding

Answer 18

FV = C₀ * e^rT

r = APR (stated annual rate)

Question 19

Infinite compounding, EAR =

Answer 19

EAR = e^r - 1