NPV, bonds and markets (Chapter 4-5)

Question 1

Why is a dollar more valuable today than in the future?

Answer 1

• It can be invested to make more dollars (intrest)
• It can be immediately consumed (utility)
• There is no doubt about its receipt (counterparty risk)

Question 2

What is the difference between simple and compound intrest?

Answer 2

With simple interest you withdraw the $90 from the market and reinvest only $1000 for the next year. You will therefore receive $90 in interest also for year 2.

With compound interest you also reinvest the interest for a total of $1090 the next year, giving you $98.10 interest for year 2, an amount $8.10 greater than the previous year.

Compound interest = Simple interest + Interest on interest

Question 3

FV - single period

Answer 3

Future Value: The value in the future of a sum invested today.

Question 4

PV - single period

Answer 4

Present value: The value today of a payment to be received in the future.

Question 5

PV - multi period

Answer 5

Question 6

FV - multi period

Answer 6

Question 7

NPV - single period

Answer 7

NPV = -Cost + PV

Question 8

NPV - multi period

Answer 8

Question 9

What is EAR?

Answer 9

Effective annual rate

What we have is a loan with a monthly interest rate of 1.5% or a yearly interest rate of 18%.
This is equivalent to a loan with an annual interest rate of 19.56%.

Question 10

Continious compounding

Question 11

Perpetuity PV

Answer 11

A constant stream of cash flows that lasts forever

Question 12

Growing Perpetuity PV

Answer 12

A stream of cash flows that grows at a constant rate forever

Question 13

Annuity PV

Answer 13

A stream of constant cash flows that lasts for a fixed number of periods

Mark Young won the state lottery, paying $50 000 for 20 years. This was advertised as a Million Dollar Lottery, since $50 000 * 20 = $1 000 000. But, what is the true value if the interest rate is 8%?
PV = 50 000 *[ (1 – (1 / 1.0820)) / 0.08] PV = 50 000 * 9.8181 PV = $490 905

Question 14

Growing Annuity PV

Answer 14

A stream of cash flows that grows at a constant rate for a fixed number of periods.

C is the cash flow to be received one period hence, g is the rate of growth per period and r is the appropriate discount rate.

The bracket term for annuity is called ”Annuity factor”, and tells us at what factor the periodic payment must be multiplied to get the present value.

Question 15

What are pure discount loans?

Answer 15

The simplest form of loan. The borrower receives money today and repays a single lump sum (principal and interest) at a future time.

Question 16

What are intrest only loans?

Answer 16

Require an interest payment each period, with full principal due at maturity.

Question 17

What are amortized loans?

Answer 17

Require repayment of principal over time, in addition to required interest. This is usually divided in two groups:
* Serial (regular amortized loan)
* Annuity (amortized loan with fixed principal payment)

Question 18

What is a firm worth?

Answer 18

Conceptually, a firm should be worth the present value of the firm’s cash flows. The tricky part is determining the size, timing and risk of those cash flows.

Question 19

What kind of securities are issued by corporations?

Answer 19

Equity – Ownership Interest
Debt – Short or Long Term Borrowing

Question 20

What is a bond?

Answer 20

A bond is a legally binding agreement between a borrower and a lender that specifies the:
* Par (face) value (F)
* Coupon rate (r)
* Coupon payment (C)
* Maturity Date (t)

The yield to maturity (YTM) is the required market interest rate on the bond.
Important: Do not confuse the coupon rate with the required market interest rate. Issues with original maturity of 10 years or less are often called notes. Longer-term issues are called bonds.

Bonds are classified as debt.

Question 21

Bond valuation - primary principle and formula

Answer 21

Value of financial securities = Present Value of expected future cash flows

Bond value is, therefore, determined by the present value of the coupon payments plus the present value of the par, or face, value. Interest rates are inversely related to present (i.e., bond) values.

Question 22

Bond concepts

Answer 22

• Bonds can be traded like any other financial asset, and the price is set by comparing the bond interest rate with the market interest rate.
• Bond prices and market interest rates move in opposite directions.
• With the current bond price, we can calculate the implied rate of return, called the Yield To Maturity (YTM).
• When coupon rate = YTM, price = par value
• When coupon rate > YTM, price > par value (premium bond)
• When coupon rate < YTM, price < par value (discount bond)

Question 23

What is intrest rate risk?

Answer 23

The risk that arises for bond owners from fluctuationg interest rates.
We need to keep the following in mind when looking at bonds
1. All other things being equal, the longer the time to maturity, the greater the interest rate risk.
2. All other things being equal, the lower the coupon rate, the greater the interest rate risk.

Question 24

Why does the bond value vary?

Answer 24

1. Price risk
   ▪ Change in price due to changes in
   interest rates
2. Reinvestment risk
   ▪ Uncertainty concerning rates at
   which cash flows can be reinvested
3. Default risk
   ▪ Uncertainty concerning the
   repayment of the face value