Ch16 Time Value of Money

Question 1

Quoted rates

Answer 1

aka. stated rates
nominal rates
TVM calculation must always use interest rates related to compounding period

Question 2

Effective annual interest rates (EAR)

Answer 2

EAR = (1 + r / n) ^ n -1

The higher the # of periods compounded during the year, the higher EAR will be

Question 3

Effective rate for compounding periods (r/n)

Answer 3

Effective compounding rate (r/n) = (EAR + 1) ^ (1 / n) -1

Question 4

Present value

Answer 4

Single cash flow: PV = FV / (1+i)^n

Question 5

Annuity

Answer 5

finite series of equal payments occuring at regular intervals

Ordinary annuity - payment at end-of-period

PV = PMT [1/i - 1/i(1+i)^n]

Annuity due - payment at beg-of-period

PV = PMT + PMT [1/i - 1/i(1+i)^(n-1)]

Question 6

Perpetuity

Answer 6

periodic same amount cash flows never end

no growth: PV = PMT / i
constant growth: PV = PMT / (i - g)

Question 7

Future value

Answer 7

Worth of a cash flow at a specific date in the future given a specified interest rate

single amount: FV = PV x (1+i)^n

Question 8

FV of an annuity

Answer 8

an ordinary annuity: FV = PMT [((1+i)^n-1) / i]
an annuity due: FV = (1+i) x PMT [((1+i)^n-1)/i]

Question 9

Mortgages

Answer 9

in Canada, mortgage rates are quoted as semi-annual rate - effective annul rate

pmt made monthy - effective monthly rate

monthly pmt are based on amortization period to maturity, while mortgage contract period is shorter

Question 10

Growing annuity

Answer 10

PV = PMT [ (1/(i-g)) - (1/(i-g)) x ((1+g)/(1+i))^n ]

Question 11

Inflation and real rates of return

Answer 11

Fisher effect:
(1+inflation rate) x (1 + real rate of return) = (1 + nominal rate of return)