Fight Finance

Question 9  DDM, NPV

For a price of $129, Joanne will sell you a share which is expected to pay a $30 dividend in one year, and a $10 dividend every year after that forever. So the stock's dividends will be $30 at t=1, $10 at t=2, $10 at t=3, and $10 forever onwards.

The required return of the stock is 10% pa.

Would you like to the share or politely ?

Question 25  bond pricing, zero coupon bond, term structure of interest rates, forward interest rate

A European company just issued two bonds, a

• 2 year zero coupon bond at a yield of 8% pa, and a
• 3 year zero coupon bond at a yield of 10% pa.

What is the company's forward rate over the third year (from t=2 to t=3)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.

(a) 0.0374

(b) 0.0604

(c) 0.1204

(d) 0.1250

(e) 0.1411

Question 48  IRR, NPV, bond pricing, premium par and discount bonds, market efficiency

The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over- or under-priced. Buying or selling a fairly priced asset has an NPV of zero.

Considering this, which of the following statements is NOT correct?

(a) The internal rate of return (IRR) of buying a fairly priced bond is equal to the bond's yield.

(b) The Present Value of a fairly priced bond's coupons and face value is equal to its price.

(c) If a fairly priced bond's required return rises, its price will fall.

(d) Fairly priced premium bonds' yields are less than their coupon rates, prices are more than their face values, and the NPV of buying them is therefore positive.

(e) The NPV of buying a fairly priced bond is zero.

Question 178  bond pricing, premium par and discount bonds

Which one of the following bonds is trading at a discount?

(a) a ten-year bond with a $4000 face value whose yield to maturity is 6.0% and coupon rate is 6.5% paid semi-annually.

(b) a 6-year bond with a principal of $40,000 and a price of $45,000.

(c) a 15-year bond with a $10,000 face value whose yield to maturity is 8.0% and coupon rate is 10.0% paid semi-annually.

(d) a two-year bond with a $50,000 face value whose yield to maturity is 5.2% and coupon rate is 5.2% paid semi-annually.

(e) None of the above bonds are discount bonds.

Question 184  NPV, DDM

A stock is expected to pay the following dividends:

Cash Flows of a Stock
Time (yrs)	0	1	2	3	4	...
Dividend ($)	2	2	2	10	3	...

After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What is the current price of the stock?

(a) 62.9842

(b) 52.0526

(c) 50.5500

(d) 48.5009

(e) 47.1349

Question 207  income and capital returns, bond pricing, coupon rate, no explanation

For a bond that pays fixed semi-annual coupons, how is the annual coupon rate defined, and how is the bond's annual income yield from time 0 to 1 defined mathematically?

Let: ##P_0## be the bond price now,

##F_T## be the bond's face value,

##T## be the bond's maturity in years,

##r_\text{total}## be the bond's total yield,

##r_\text{income}## be the bond's income yield,

##r_\text{capital}## be the bond's capital yield, and

##C_t## be the bond's coupon at time t in years. So ##C_{0.5}## is the coupon in 6 months, ##C_1## is the coupon in 1 year, and so on.

(a) coupon rate = ##\dfrac{C_{0.5}+C_{1}}{F_T}##, ##r_\text{income, 0 to 1}=\dfrac{C_{0.5}(1+r_\text{total})^{0.5}+C_{1}}{P_0}##

(b) coupon rate = ##\dfrac{2 \times C_{0.5}}{F_T}##, ##r_\text{income, 0 to 1}=\dfrac{C_{0.5}(1+r_\text{capital})^{0.5}+C_{1}}{P_0}##

(c) coupon rate = ##\dfrac{2 \times C_{1}}{P_0}##, ##r_\text{income, 0 to 1}=\dfrac{C_{0.5}+C_{1}}{P_0}##

(d) coupon rate = ##\dfrac{2 \times C_{1}}{P_0}##, ##r_\text{income, 0 to 1}=\dfrac{2 \times C_{1}}{P_0}##

(e) coupon rate = ##\dfrac{2 \times C_{1}}{F_T}##, ##r_\text{income, 0 to 1}=\dfrac{C_{0.5}(1+r_\text{total})^{0.5}+C_{1}}{F_T}##

Question 266  bond pricing, premium par and discount bonds

Bonds X and Y are issued by the same company. Both bonds yield 10% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.

The only difference is that bond X pays coupons of 6% pa and bond Y pays coupons of 8% pa. Which of the following statements is true?

(a) Bonds X and Y are premium bonds.

(b) Bonds X and Y are discount bonds.

(c) Bond X is a discount bond but bond Y is a premium bond.

(d) Bond X is a premium bond but bond Y is a discount bond.

(e) Bonds X and Y are par bonds.

Question 298  interest only loan

A prospective home buyer can afford to pay $2,000 per month in mortgage loan repayments. The central bank recently lowered its policy rate by 0.25%, and residential home lenders cut their mortgage loan rates from 4.74% to 4.49%.

How much more can the prospective home buyer borrow now that interest rates are 4.49% rather than 4.74%? Give your answer as a proportional increase over the original amount he could borrow (##V_\text{before}##), so:

###\text{Proportional increase} = \frac{V_\text{after}-V_\text{before}}{V_\text{before}} ###

Assume that:

• Interest rates are expected to be constant over the life of the loan.

• Loans are interest-only and have a life of 30 years.

• Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates compounding per month.

(a) 0.055679

(b) 0.029631

(c) 0.029547

(d) 0.006245

(e) 0.0025

Question 518  DDM

A stock just paid a dividend of $1. Future annual dividends are expected to grow by 2% pa. The next dividend of $1.02 (=1*(1+0.02)^1) will be in one year, and the year after that the dividend will be $1.0404 (=1*(1+0.02)^2), and so on forever.

Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.

Calculate the current stock price.

(a) $10

(b) $12.254902

(c) $12.5

(d) $12.75

(e) $13.75

Question 872  duration, Macaulay duration, modified duration, portfolio duration

A fixed coupon bond’s modified duration is 20 years, and yields are currently 10% pa compounded annually. Which of the following statements about the bond is NOT correct?

(a) The Macaulay duration of the bond is 22 years.

(b) If yields-to-maturity suddenly fell by 1 percentage point then bond prices would suddenly rise by 20% or more.

(c) If yields-to-maturity suddenly rose by 2 percentage points then bond prices would suddenly fall by 40% or less.

(d) If the bond is a zero-coupon bond then its maturity is 20 years.

(e) The modified-duration-price-change formula assumes parallel shifts in the yield curve.