1. Time value of money Julian Hince, Technical development director
Notes Presentation Title Page
Type name of Presenters
Date

2. Choose one wheel to spin
Money now or later?
Which would you choose?
Choose one wheel to spin
£10,000
£10,000
Now
1 year

3. Concept of time value of money
Money now can be invested and earn interest
Present value (PV)
Interest rate (r)
Time period (n)
Future value (FV)

4. TVM in financial planning
What are the various returns available on different investments?
How well did this portfolio perform compared to other investments and inflation generally?
What yield will be needed on a capital sum of a series of payments to meet a know liability?
How much needs to be invested now to build up a specific sum in the future?
If I make withdrawals from a fund, how long will it last at different rates of return?

5. Of compounding interest
If you remember nothing else today remember this…
FV = PV (1+r)n
£1,000 invested at an interest rate of 2% for seven years;
FV = 1,000 (1+r)n
= 1,000 (1+0.02)7
= 1,000 (1.02)7
= 1,000 (1.149)
= £1,148.69
Care where interest is paid in arrears, add one n

6. Compounding your interest
FV = PV (1+r)n
£1,000 invested and after seven years was worth £1, What compound rate has been achieved?
1, = 1,000 (1+r)7
1,450.00/1,000 = (1+r)7
1.45 = (1+r)7
= 1+r
R = – 1
R = 5.45%

7. Compounding your interest further
FV = PV (1+r)n
£1,000 invested at 2% for four years and 5.45% three years?
FV = 1,000 x (1+r1)n1 x (1+r2)n2
= 1,000 x (1.02)4 x (1.0545)3
= 1,000 x x
= £1,269.22

8. FV = PV (1+r)n Your turn Question;
Question time
Question;
Investor needs £20,000 in three years time and has £16,000 to invest.
What annual rate of return do they need to achieve to reach their target?
FV = PV (1+r)n

9. Answer time Need to solve r FV = PV (1+r)n 20,000 = 16,000 (1+r)3
Take the third root
= 1+r
r =
Required rate of return = 7.72%

10. More is more Frequency of interest not always annual
Effect of 10% nominal annual interest compounded at different periods
Interest compounded a year
No. of periods in one year
Value of £1 after rate, %
Effective annual %
Annually 1
1.1000
10.00
Half-yearly 2
1.1025
10.25
Quarterly 4
1.1038
10.38
Monthly 12
1.1047
10.47
Daily
365
1.1052
10.52
Interest paid more frequently is worth more, i.e 1/4ly (1ST quarter will earn interest & then be compounded) this makes the effective rate of interest greater than the nominal rate.
Refer to time periods rather than years

11. (1+r/n)n-1 Annual effective rate Another formula to commit to memory
What is the effective rate if the nominal rate is 8% p.a compounded quarterly?
(1+0.08/4)4 -1
= (1.02)4 - 1
= (1.0824) – 1 =
Effective rate is 8.24%
Annual percentage rate (APR) or Annual equivalent rate (AER) APR used for loans, AER used for deposits
APR or AER = effective rate of interest

12. Discounting PV = FV/(1+r)n
Investing now for future liability matching, but how much?
PV = FV/(1+r)n
What amount has to be invested to accumulate £10,000 in five years at annual rate of 5%?
10,000 = PV (1.05)5
10,000 = PV (1.2763)
10,000/ = PV
PV = £7,835.15

13. Regular savings End of year Amount £ Value at end of year 10 £ 1
100 (1.08)9
199.90 2
100 (1.08)8
185.09 3
100 (1.08)7
171.38 4
100 (1.08)6
158.69 5
100 (1.08)5
146.93 6
100 (1.08)4
136.05 7
100 (1.08)3
125.97 8
100 (1.08)2
116.64 9
100 (1.08)
108.00 10
100
100.00
Total
1,448.65

14. Regular savings simplified
Last formula
FV = P ( (1+r)n-1)
BODMAS; brackets off, divide, multiply, add, subtract r
£1,000 invested at the end of each year for ten 3%, what is the FV in ten years?
FV = 100 ( (1.03)10 – 1)
0.03
FV = 100 ( – 1)
FV = (11.464)
FV = £1,146.39

15. TVM applied Which bond would you prefer to buy?
US 10-year Government Bond
Coupon 2%
£100
Ford 10-year Corporate Bond
Coupon 8%
£100 or
Cashflows
Cashflows
100+2
100+8 2 2 2 2 2 2 2 2 2 8 8 8 8 8 8 8 8 8
-100
-100
At issue, most bonds will be priced around 100

16. Shall I choose US government or Ford bond?
Price
How much does the bond cost?
Coupon
What is my annual interest?
Factors to consider
when choosing
Maturity
How long can I invest my 100 for?
Yield
What is the current market demanding?
Credit
How much risk does the issuer carry?

17. Yield curves
Ford corporate curve 8% 6% 3%
US government curve 2%
Yield % 2 10 20
Maturity (years)
If US government becomes more risky, what happens to curve?
If Ford becomes less risky, what happens to curve?

18. Pricing bonds Compounding
Consider an investment of £10 invested at a rate of 10% for three years
x1.10
x1.10
x1.10
Present value
£10.00
Year one
£11.00
Year two
£12.10
Year three
£13.31 FV = PV x
(1+r)n
13.31 10
1.331

19. Pricing bonds Discounting
Consider an investment of £10 in three years’ time. With an investment return of 10%, what is the present value of the receipt?
÷1.10
÷ 1.10
÷ 1.10
Present value
£7.51
Year one
£8.26
Year two
£9.09
Year three
£10.00 1 PV = FV x
(1+r)n
I would pay £7.51 today for £10 in three years

20. Time value of money
A bond pays interest of £10 each year, its yield is 10% per annum
Year
Coupon
Discount factor PV 1 10
0.909
9.09 2
0.826
8.26 3
0.751
7.51 4
0.683
6.83
Which coupon is most valuable and why?

21. Pricing a bond
Consider a 3-year bond with a coupon of 10% and a yield of 9%
Year
Coupon
Discount factor PV 1 10
0.917
9.17 2
0.842
8.42 3
110*
0.772
84.92
Price
(premium)
*Coupon and principal

22. Pricing a bond
Consider a 3-year bond with a coupon of 10% and a yield of 10%
Year
Coupon
Discount factor PV 1 10
0.909
9.09 2
0.826
8.26 3
110*
0.751
82.65
Price
100 (par)
*Coupon and principal

23. Pricing a bond
Consider a 3-year bond with a coupon of 10% and a yield of 11%
Year
Coupon
Discount factor PV 1 10
0.901
9.01 2
0.812
8.12 3
110*
0.731
80.43
Price
97.56 (discount)
*Coupon and principal

24. Which bond would you prefer to buy now?
Yield
3-year bond with a coupon of 10%
Yield %
Price 9
102.51 10
100.00 11
97.56
Bond price
View on Currency
As yields fall, bond prices rise
As bond prices rise, yields fall

25. Which bond would you prefer to buy now?
10-year Government Bond
Coupon 2% (get)
£100
Ford 10-year Corporate Bond
Coupon 8%
£100 or
Government yield 3% (want)
Corporate yield 7% 1 1 PV = FV x PV = FV x
(1 + r)n
(1 + r)n =
91.47 (discount) =
(premium)

26. Your turn again Manufacturing your price
You are working on the UK Corporate Bond Fund. You are considering buying a
bond issued by Mega Manufacturer. The bond has three years to maturity and
pays a coupon of 6%.
Fabulous Fabrications are a direct competitor of Mega Manufacturer and have the
same credit rating of A+. The yield of Fabulous Fabrications bond is 8%.
Year Cash flow Discount factor Present value 1 2 3
Price
Required
a) State, before you do any calculations whether the bond will trade at premium,
par or a discount
b) Calculate a fair value for the Mega Manufacture bond.

27. Manufacturing your price
Suggested solution
The bond should trade at a discount as the yield (8%) is higher than the coupon (6%)
b) Mega Manufacture bond
Year Cash flow Discount factor Present value
94.86

28. This presentation has been created for training purposes
This presentation has been created for training purposes. It is intended for Investment Professionals only, and is not for onward distribution. All content regarding regulatory development is M&G's interpretation of future legislation, and our view is subject to change without notice. This information should not be regarded as confirmation of how your firm may be specifically impacted by regulatory change or relied upon as legal advice. This presentation is not a financial promotion and should not be regarded as a recommendation or as financial advice. Issued by M&G Securities Limited which is authorised and regulated by the Financial Services Authority and provides investment products. The registered office is Laurence Pountney Hill, London, EC4R 0HH. Registered in England No