Valuation of bonds
Redeemable bond – yield calculation
Exercise 1
A bond is redeemable in the year 2016.
The current price is £97 per £100
Interest rate is 5%
What is the current yield?
| Year | Cash flows | 5% discount | 10% discount | |||
| 2012 | 0 | (97) | 1.000 | (97.00) | 1.000 | (97.00) |
| 2013 | 1 | 5 | 0.952 | 4.76 | 0.909 | 4.55 |
| 2014 | 2 | 5 | 0.907 | 4.54 | 0.826 | 4.13 |
| 2015 | 3 | 5 | 0.864 | 4.32 | 0.751 | 3.76 |
| 2016 | 4 | 105 | 0.823 | 86.42 | 0.683 | 71.72 |
| 3.04 | (12.84) |
5% + (((3.04/(3.04+12.84)) x (10-5)) = 5 + 0.96 = 5.96%
Exercise 2
A bond is redeemable in the year 2015
The current price is £106 per £100
Interest is 8%
What is the current yield?
| Year | Cash flows | 8% discount | 3% discount | |||
| 2012 | 0 | (106) | 1.000 | (106.00) | 1.000 | (106.00) |
| 2013 | 1 | 8 | 0.926 | 7.41 | 0.971 | 7.77 |
| 2014 | 2 | 8 | 0.857 | 6.86 | 0.943 | 7.54 |
| 2015 | 3 | 108 | 0.794 | 85.75 | 0.915 | 98.82 |
| (5.98) | 8.13 |
3% + (((8.13/(8.13+5.98)) x (8-3) = 3 + 2.89 = 5.89%
Valuing bonds
As interest rates rise – the value of bonds reduces
As interest rates fall – the value of bonds increases
Example – what is the value of a 5% bond maturing in 4 years time if current interest rates are 4% and 6%?
| Year | Cash flows | 4% discount | 6% discount | |||
| 2012 | 0 | |||||
| 2013 | 1 | 5 | 0.962 | 4.81 | 0.943 | 4.72 |
| 2014 | 2 | 5 | 0.925 | 4.63 | 0.890 | 4.45 |
| 2015 | 3 | 5 | 0.889 | 4.45 | 0.840 | 4.20 |
| 2016 | 4 | 105 | 0.855 | 89.78 | 0.792 | 83.16 |
| 103.67 | 96.53 |
5 x 2.775 = 13.875 5 x 2.673 = 13.365
105 x 0.8555 = 89.775 105 x 0.792 = 83.16
103.65 96.53
Risk
CAPM – Capital Asset Pricing Model
An investor requires a return of 14%
The market return is 10%
The return of treasury stock (government bonds) is 2%
What is the beta factor and measure of risk?
14 = 2 + B(10 – 2 )
14 – 2 = B(8)
12/8 = B
B = 1.5
Share valuation
The dividend growth model
(Di /P) + g
If Di is 5p
g = 10%
You expect a return of 15.75%
How much would you be prepared to pay for the share?
Di/p + g
5/P + 10% = 15.75%
5/P = 0.1575 – 0.10
5/P = 0.0575
5/0.0575 = 87p
