Interest Rate Quotes and Adjustments

Question 1

Effective Annual Rate

Answer 1

• indicates the total amount of interest that will be earned at the end of one year
• considers the effect of compounding
• also referred to as the effective annual yield (EAY) or annual percentage yield (APY)

Question 2

Adjusting the Discount Rate to different time periods

Answer 2

earning a 5% return annually is not the same as earning 2.5% every 6 months

Question 3

General equation for discount rate period conversion

Answer 3

n-period discount rate

= (1+r)^n -1

therefore for 5% annual discount rate for 6 months:

= (1.05)^0.5 -1 = 2.47%. (0.5 is for half the period)

e.g bank pays effective annual rate of 6%. How much will you need to save each month to accumulate $100,000 in 10 years?

6% EAR = 1.06^1/12 -1 = 0.4868% per month

10 x12 = 120 monthly payments

use future value of annuity equation to get $615.47 per month

Question 4

Annual percentage rates (APR)

Answer 4

indicates the amount of simple interest earned in one year

simple interest = amount of interest earned without the effect of compounding

• APR typically less that EAR
• APR can’t be used as a discount rate
• the APR with k compounding periods is a way of quoting the actual interest earned each compounding period:

Interest rate per compounding period = APR/k periods a year

Question 5

Converting an APR to an EAR

Answer 5

1 + EAR = ( 1 + (APR/k))^k where k = periods a year

therefore EAR increases with the frequency of compounding

e.g if interest rate of 5% APR with semi-annual compounding

APR corresponds to a 6 month discount rate of 5/2 = 2.5%

converting to one-month discount rate then =

1.025^1/6 -1 = 0.4124% per month

Question 6

NPV decision rule

Answer 6

take investment decision with highest NPV as is equivalent to receiving its NPV in cash today

Question 7

Internal Rate of Return (IRR)

Answer 7

the discount rate that sets the NPV of the projects cash rates equal to zero

NPV = IRR = 0

• sometimes alternative investment rules may give same answer as NPV rule but others they disagree, always follow NPV rule

Question 8

IRR investment rule

Answer 8

take any investment where the IRR exceeds the cost of capital. Turn down if its below

In general works for a stand-alone project if all of the projects negative cash flows price its positive cash flows