discount rate 10 Cost of capital estimations and the
Some readers may be puzzled as to why, when the original amount borrowed was
£100, the amount to be repaid is equally £100 and the coupon interest rate is 10 per
cent, the cost of the loan notes is not 10 per cent before tax or 7.0 per cent after tax.
We should remember that our purpose in calculating the cost of capital is to derive
a discount rate to apply to investment projects. In previous chapters we have seen that
the appropriate discount rate is the opportunity cost of capital. This means either the
saving that would follow from repaying the capital source, or the cost of further
finance raised from that source. At the present time this amount would be 8.8 per cent
after tax. If the business wishes to cancel the loan notes, it can do so by buying the
notes in the capital market at £93 (per £100 nominal). This would save the annual inter-
est payments of 7.0 per cent on the nominal value, and avoid the necessity to repay the
capital after five years. If further finance is to be raised, presumably the same business
could raise £93 for loan notes that pay £10 at the end of each of the next five years plus
£100 at the end of the fifth year. So in either case, 8.8 per cent is the appropriate rate.
We might also ask why investors were at one time prepared to pay £100 (for £100
nominal value) for loan notes that yield £10 p.a. in interest (a 10 per cent return). The
difference must arise either from interest rates having increased generally and/or
Solving for kLwill give us the required cost of capital figure. We have met this situation
before when deducing the internal rate of return of an investment opportunity. Of course,
kLis the IRR of the loan notes, and hence the solution is only discoverable by trial and error, but
this could be achieved using a spreadsheet. As annual returns of a net £7 are worth £93, a
rate of less than 10 per cent is implied. Let us try 8 per cent.
Year Cash flow Discount factor Present value
££
0 (93.0) 1.000 (93.0)
1 7.0 0.926 6.5
2 7.0 0.857 6.0
3 7.0 0.794 5.6
4 7.0 0.735 5.1
5 107.0 0.681 72.9
3.1It seems that the cost of capital is above 8 per cent; let us try 9 per cent.
Year Cash flow Discount factor Present value
££
0 (93.0) 1.000 (93.0)
1 7.0 0.917 6.4
2 7.0 0.842 5.9
3 7.0 0.772 5.4
4 7.0 0.708 5.0
5 107.0 0.650 69.6
(0.7)Thus the cost lies very close to 8.8 per cent.