Topic 9 - Investments

Question 1

What are some of the major asset classes?

Answer 1

Government Bonds/Borrowing
Non Government Bonds/Borrowing
Equity type borrowing
Property

Question 2

What are the different types of government bonds/borrowing assets?

Answer 2

Government Bills – short duration
Government Bonds (Fixed interest and Index-linked) –medium to long duration

Question 3

What is a government bill?

Answer 3

• Typically short-dated securities issued by governments to fund short-term spending
• Normally issued at discount and redeemed at par with no coupon
• So reward for investor is difference between the discount price (P) and par value

Question 4

What is the typical term for a government bill?

Answer 4

3 months

Question 5

What are the advantages of a government bill?

Answer 5

Government bills are secure (low risk of default), highly

marketable (easy to sell) and unquoted (cannot be sold on stock market)

Question 6

What is a fixed interest government bond?

Answer 6

• Typically medium to long term securities issued by
  governments to fund spending (Called Gilts in the UK)
• They are quoted on stock exchange
• Investor will normally receive coupons (interest
  payments) half-yearly and receive return of capital at
  redemption at a specific date
• Bonds can also be redeemed below or above par
  (original capital value)

Question 7

What are some possible variations to traditional government bonds?

Answer 7

• May have variable redemption dates, where date is
  chosen by borrower or lender
• May allow coupons and redemption payments to be
  traded separately:
  • So a 10 year bond with half yearly coupons becomes 20 separate coupon payments with a single capital payment
  • Alternatively already stripped coupon and redemption payments can be combined to reconstruct a particular bond

Question 8

What is the reality for investors regarding earnings from coupon payments?

Answer 8

Majority of examples assume investor is tax-free,
if investor subject to tax at rate t1 a rate of (1-t1) is
applied to each coupon

Question 9

What are the advantages and disadvantages of a fixed interest government bond?

Answer 9

Advantages
Marketability – Gov bonds form largest part of market and are extremely liquid (easy to sell and can be quickly converted into cash)
Security – Bonds issued by governments of developed
countries are most secure (low risk of default)

Disadvantages
Coupons are fixed, income volatile relative to inflation

Question 10

What is an Index-linked government bond?

Answer 10

• Typically medium to long term securities issued by
  governments to fund spending (Called Gilts in the UK)
• They are quoted on stock exchange
• Investor will normally receive coupons (interest
  payments) half-yearly and receive return of capital at
  redemption at a specific date
• Bonds can also be redeemed below or above par
  (original capital value)
• Coupon and redemption payments linked to inflation
• Normally suffer from time lag until particular index is
  published

Question 11

What are the advantages and disadvantages of index-linked government bonds?

Answer 11

Advantages
Marketability – Gov bonds form largest part of market and are extremely liquid (easy to sell and can be quickly converted into cash)
Security – Bonds issued by governments of developed
countries are most secure (low risk of default)
Coupon and redemption payments linked to inflation

Disadvantages
Normally suffer from time lag until particular index is
published (Effectively no protection from inflation during the lag period)

Question 12

What are the different types of non government bonds/borrowing assets?

Answer 12

Corporate Bonds

Question 13

What are Corporate Bonds?

Answer 13

Similar to conventional gov bonds, but issued by companies

Question 14

What are the advantages and disadvantages of corporate bonds?

Answer 14

Disadvantages
- Corporate bonds less secure than gov bonds, because:
• Depends on type of bond (secured or unsecured)
• Depends on company that issued it
• Depends on term
- Corporate bonds less marketable than gov bonds because of smaller issue size

Advantages
- As a result the yield is higher than gov bonds

Question 15

What are the different types of Equity type borrowing?

Answer 15

Ordinary shares

Preference shares

Question 16

What is an ordinary share?

Answer 16

• Issued by companies and entitles holder to net profits
  (after interest on loans and bonds)
• Payment made to shareholder is a dividend, No legal
  requirement to pay dividends
• Any remaining profits are retained earnings
• Principle way companies are financed
• Lowest ranking form of finance

Question 17

What forms do the returns from an ordinary share take?

Answer 17

Returns made up of dividends and increase in market price

Question 18

What are the key features of a preference share?

Answer 18

• Less common than ordinary shares
• Dividends limited to set amount and almost always paid
• No ord dividend can be paid if pref dividends outstanding
• Rank above ordinary shares, only vote if dividends not paid
• Expected return lower than ordinary shares (lower risk)
• Similar characteristics to unsecured loan stock and similar marketability

Question 19

Analyse the pros and cons of ordinary shares

Answer 19

• Offers high potential return for high risk
• Initial running yield low (dividend/market price)
• Overall future return expected to be higher than most other classes of security to compensate for:
  Greater risk of default
  Variability of returns
• Marketability depends on size of issue and size of company
• Ordinary shareholders have voting rights

Question 20

State the differences between ordinary shares and preference shares

Answer 20

(1) Ordinary Shares (2) Preference Shares

(1) Signifies proportionate ownership of shareholders in the company
(2) Signifies preferential rights over the payment of dividend and repayment of capital at the time of liquidation

(1) Ordinary shares come with voting rights (2)Preference shares do not come with voting rights
(1) Dividends can be paid or not paid to ordinary shareholders as declared by the management. (2)Dividends will be paid at the fixed rate agreed at the time of the issue of the shares.

(1) At the time of liquidation, ordinary shareholders are repaid if anything is remaining after meeting all the liabilities.
(2) At the time of liquidation, preference shareholders are paid before ordinary shareholders.

(1)Ordinary shares cannot be redeemed. (2)Preference shares come with a redemption clause at the end of a specified period of time.

(1) Ordinary share is generally non-convertible.
(2) Some preference shares come with a clause of conversion to ordinary shares.

Question 21

What are the two types of property investment?

Answer 21

Direct Investment - Investing in land and/or buildings

Indirect Investment - via shares in a property firm

Question 22

What form do the returns from a property investment take?

Answer 22

Mixture of rental income and capital gains

Question 23

Why does property investment have a real return?

Answer 23

Property has a real return i.e. increase with inflation

Rents normally reviewed (upwards) every 3-5 yrs

Question 24

What are some of the negative features of property investment?

Answer 24

• Large unit size
• Each property unique –hard to value & costly
• Actual value on sale uncertain –subjective
• Trading expenses higher than for shares and bonds
• Net rental income reduced by maintenance expenses
• May be periods of when property unoccupied –voids
  Marketability poor due to above

Question 25

Calculating PV of cash flows and yields

In topic 9 what type of calculations will we carry out?

Answer 25

• Price P payable to secure a net yield of i% per annum
• Given a price P, what is the net yield per annum
  For bonds, equities and property
  Terminology may change –principles still apply

Question 26

What equation do we solve in order to calculate the price P of a fixed interest bond when the investor is tax exempt?

Answer 26

P = D𝑎n¬(p) + Rv^n at rate i% per annum
D is the coupon
R is the capital
i is known as gross redemption yield (GRY) 
D/P is known as the running (flat) yield

Question 27

What equation do we solve in order to calculate the price P of a fixed interest bond when the investor is subject to income tax?

Answer 27

P’= (1-t,1)D𝑎n¬(p) + Rv^n at rate i per annum
D is the coupon
R is the capital
t,1 is rate of income tax
Assume tax paid immediately
Coupons are income hence subject to income tax
Capital not income hence not liable for income tax
i becomes net redemption yield (NRY) allowing for tax
D/P’ is known as the running (flat) yield

Question 28

Question
An investor subject to income tax at 20%, purchases
£5,000 nominal of newly issued 10 year FI bonds,
redeemable at par. Paying ½ yrly coupons of 5% pa in
arrears. Calculate price they should pay to obtain a net yield of 10% pa.

Answer 28

P’= (1-0.2) x 250𝑎¬10(2) + 5000v^10 @10% pa
P’= 200 x 6.1446 x 0.1/0.097618 + 5000(1.1)^-10
P’= £3,187

Question 29

Question
An investor subject to income tax at 20%, purchases
£5,000 nominal of newly issued 10 year FI bonds,
redeemable at par. Paying ½ yrly coupons of 5% pa in
arrears. Calculate the net yield if the investor paid £3,500 for the issue.

Answer 29

3500 = (1-0.2) x 250𝑎10¬(2) + 5000v^10
We know i = 10% pa, P’= £3,187, try i = 8% pa
= 0.8x250x6.7101x0.08/0.078461 + 5000(1.08)^-10 =£3,684
Try 9% pa, = £3,424
i ≈0.08 + (3500−3684)/(3424−3684) x (0.09 –0.08) = 8.7% pa (check)

Question 30

What if investor subject to capital gains tax?

Answer 30

Carry out capital gains test:
R > (1-t1)D𝑎n¬(p) + Rv^n
R(1-v^n) > (1-t1)D(1-v^n)/i(p) 
R > (1-t,1)D/i(p) 
i(p) > (1-t1)D/R
If have capital gain and pay CGT at rate of t,2 then price is P’’ = (1-t,1)D𝑎n¬(p) + Rv^n  - t,2(R-P’’)v^n

Question 31

Example
An investor subject to income tax at 20% and CGT at
15%, purchases £5,000 nominal of newly issued 10 year FI bonds, redeemable at par. Paying ½ yrly coupons of 5% pa in arrears. Calculate price they should pay to obtain a net yield of 10% pa.

Answer 31

Example
Test if have capital gain
i(p) > (1-t1)D/R
0.097618 > (1-0.2)x250/5000, >0.04 so have CG
P’’= (1-0.2) x 250𝑎10¬(2) + 5000v^10 -0.15(5000-P’’)v^10
P’’= 200(1-1.1^-10)/0.097618 + 4250(1.1)^-10 +0.15P’’v^10
(1-0.15v^10)P’’ = 2897.45
P’’ = 2897.45/(1-0.15(1.1^-10)) = £3,075.30

Question 32

What equation do we solve in order to calculate the price P of an index linked bond when the investor is tax exempt?

Answer 32

So far we have discussed Fixed Interest Bonds
Now consider Index-Linked Bonds (IL Bonds)
IL Bonds are real assets
Coupon and capital are linked to an index of inflation
P = D𝑎n¬(p)’ + Rv’^n at rate i’ % per annum
We need an assumption for the assumed rate of inflation j
1+i’ = 1+i/1+j
i’ = i−j/1+j

Question 33

Example
An investor purchases £10,000 nominal of newly issued 5 year IL bonds, redeemable at par paying ½ yrly coupons of 5% pa in arrears. If expected inflation is 4% pa, calculate price she should pay to obtain a yield of 10% pa, ignore lags.

Answer 33

P = 500𝑎5¬(2)’ + 10000v’^5 @ i’ = (0.1−0.04)/1.04 = 5.77%
P = 500(1-1.0577^-5)/0.0569 + 10000(1.0577)^-5
= £9,704

Question 34

Question
An investor purchases £10,000 nominal of newly issued 5 year IL bonds, redeemable at par paying ½ yrly coupons of 5% pa in arrears. If expected inflation is 4% pa, calculate the yield if the investor paid £9,000 for the issue.

Answer 34

Question
Calculate the yield if the investor paid £9,000 for the issue.
9000 =500a5¬(2)’ + 10000v’^5
We know i’= 5.77% pa, P’= £9,703, try i’ = 7% pa
= 500x4.1002x0.07/0.068816 + 10000(1.07)^-5 =£9,215
Try 8% pa = £8,841
i’ ≈0.07 + (9000−9215)/(8841−9215) x (0.08 –0.07) = 7.57% (check)
i = (1+i’)/(1.04)-1 = 1.0757x1.04-1 = 11.9%

Question 35

Do investors who own equity receive coupons or dividends?

Answer 35

Rather than coupons investors receive dividends (D)

Question 36

What assumptions must we make in order to construct an equation to calculate the price P of a share?

Answer 36

To construct equation we need to assume the following

• Dividends are paid annually
• Dividends grow at a specific rate (g) , so dividend at t is D,t
• Dividends continue in perpetuity

Question 37

Construct a simple equation to calculate the price P of a share

Answer 37

P = ∑∞,t=1 D,t x v,i^t

i is the return on the share, given P
Dividend at t is D,t

Question 38

What is an ex-dividend equity trade?

Answer 38

Equities can be traded ex-dividend i.e. without the next

dividend. This may happen if a transaction occurs close to dividend payment date.

Question 39

Given that we assume dividends grow at a rate g what formulae can we construct for D,t and P?

Answer 39

D,t = D(1+g)^t
Since P = ∑∞,t=1 D,t x v,i^t
P = D[(1+g)v + (1+g)^2v^2 + (1+g)^3v^3 …….]
P = D[(1+g)/(1+i) + (1+g)^2/(1+i)^2 + (1+g)^3/(1+i)^3 …….]

1+i’ = 1+i/1+g therefore i’ = i−g/1+g
P = D𝑎∞¬ @i’ Since 𝑎∞¬ @i’ = 1/i′
so P = D(1+g)/i−g

Question 40

Example
An investor (20% taxed) has purchased 100 shares ex-dividend. Dividends are annual, grow at 3% pa and the next one is payable in 2 months time, the previous dividend was £5 per share. Calculate P if i is 10% pa.

Answer 40

100(5x1.03(1-0.2)v^0.167 + 5x1.03^2(1-0.2)v^1.167 + 5x1.03^3(1-0.2)v^2.167 +…)
However don’t receive first dividend
P = 100x5x1.03x0.8v^0.167(1x0 + 1.03v + 1.03^2v^2 +…)
P = 100x5x1.03x0.8v0.167(1.03v + 1.03^2v^2 +…….)
P = 100x5x1.03x0.8v^0.167 𝑎∞¬ @i’
i’ = 0.1−0.03/1.03 = 6.796%

P = 100x5x1.03x0.8v^0.167 x 1/0.06796
P = £5,967

Question 41

Question
An investor (20% taxed) has purchased 100 shares ex-dividend. Dividends are annual, grow at 3% pa and the next one is payable in 2 months time, the previous dividend was £5 per share. Calculate i if the price per share is £65.

Answer 41

£6,500 =100x5x1.03x0.8v^0.167 𝑎∞ @i’
 We know i’= 6.796%, P = £5,967, try i’ = 6% and i = 1.06x1.03-1 = 9.18%
= 500x1.03x0.8x1.0918^-0.167x 1/0.06 = £6,767
i’ ≈0.06 + (6500−6767)(5967−6767) x (0.06796 –0.06) = 6.27% (check)
i = (1+i’)(1.03)-1 = 1.0627x1.03-1 = 9.46%

Question 42

What are the similarities and differences between valuation of property by discounting future cashflows and valuation of equity?

Answer 42

Key similarities are:
- Require assumptions for increase in future income
- Income is real
Key differences are:
- Property rents (Dt) fixed for a number of years at a time
- Property contracts may be fixed term, so income may cease

Question 43

Give the formula for calculating the present value of future cashflows of a property investment given rent payable at a frequency of m

Answer 43

If rents paid at frequency m, so Dt/m is income t = 1/m, 2/m..
P = ∑∞,t=1 1/m x D,t/m x v^(t/m)