
Suppose you are looking at the following possible cash flows: Year 1 CF = $100; Years 2 and 3 CFs = $200; Years 4 and 5 CFs = $300. The required discount rate is 7%. What is the value of the cash flows at year 5?
CF_{0} = 0; C01 = 100; F01 = 1; C02 = 200; F02 = 2; C03 = 300; F03 = 2; I = 7; CPT NPV = 874.17
PV = 874.17; N = 5; I/Y = 7; CPT FV = 1226.07

Suppose you are looking at the following possible cash flows: Year 1 CF = $100; Years 2 and 3 CFs = $200; Years 4 and 5 CFs = $300. The required discount rate is 7%. What is the value of the cash flows today?
CF0 = 0; C01 = 100; F01 = 1; C02 = 200; F02 = 2; C03 = 300; F03 = 2; I = 7; CPT NPV = 874.17

Suppose you are looking at the following possible cash flows: Year 1 CF = $100; Years 2 and 3 CFs = $200; Years 4 and 5 CFs = $300. The required discount rate is 7%. What is the value of the cash flows at year 3?
CF0 = 0; C01 = 100; F01 = 1; C02 = 200; F02 = 2; C03 = 300; F03 = 2; I = 7; CPT NPV = 874.17
PV = 874.17; N = 3; I/Y = 7; CPT FV = 1070.90

You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value?
PV

You want to receive $5,000 per month in retirement. If you can earn 0.75% per month and you expect to need the income for 25 years, how much do you need to have in your account at retirement?
PMT = 5000; N = 25*12 = 300; I/Y = .75; CPT PV = 595,808

You want to receive $5000 per month for the next 5 years. How much would you need to deposit today if you can earn 0.75% per month?
5(12) = 60 N; .75 I/Y; 5000 PMT; CPT PV = 240,867

You want to receive $5000 per month for the next 5 years. What monthly rate would you need to earn if you only have $200,000 to deposit?
200,000 PV; 60 N; 5000 PMT; CPT I/Y = 1.439%

Suppose you have $200,000 to deposit and can earn 0.75% per month. How many months could you receive a $5000 payment?
200,000 PV; .75 I/Y; 5000 PMT; CPT N = 47.73 (47 months plus partial payment in month 48)

Suppose you have $200,000 to deposit and can earn 0.75% per month. How much could you receive every month for 5 years?
200,000 PV; 60 N; .75 I/Y; CPT PMT = 4151.67

You want to have $1 million to use for retirement in 35 years. If you can earn 1% per month, how much do you need to deposit on a monthly basis if the first payment is made in one month?
35(12) = 420 N; 1,000,000 FV; 1 I/Y; CPT PMT = 155.50

You want to have $1 million to use for retirement in 35 years. If you can earn 1% per month, how much do you need to deposit on a monthly basis if the first payment is made today?
Set calculator to annuity due and use the same inputs as above. 35(12) = 420 N; 1,000,000 FV; 1 I/Y; CPT PMT = 153.96

You are considering preferred stock that pays a quarterly dividend of $1.50. If your desired return is 3% per quarter, how much would you be willing to pay?
PV = 1.50 / .03 = $50

What is the definition of an APR?
APR = period rate * # of compounding periods per year

What is the effective annual rate?
EAR is the rate we earn (or pay) after we account for compounding

Which rate should you use to compare alternative investments or loans?
You should use the EAR to compare alternatives.

Which rate do you need to use in the time value of money calculations?
We need the period rate and we have to use the APR to get it.

What is a pure discount loan? What is a good example of a pure discount loan?
 A pure discount loan is where the principal is reapid at some future date without any periodic interest payments.
 A good example of a pure discount loan is a treasury bill.

What is an interestonly loan? What is a good example of an interestonly loan?
 An interestonly loan is where the borrower pays interest each period and repays the entire principal at some point in the future.
 Good examples of interestonly loans are bonds issued by the Government of Canada, the provinces, and corporations.

What is an amortized loan? What is a good example of an amortized loan?
An amortized loan is where the borrower repays parts of the loan amount over time. Can be either fixed principal amount plus interest for the period or a fixed payment amount where the amount of principal paid each time increases.

