129The numbers game
She summed up Column C. The total value of the discounted
cash ows of the bond was €108, give or take a cent in rounding.
Anisa got another coffee from the vending machine and thought
about yesterday’s topics. Investors demanded a return for
ination, opportunity cost and the risk of the borrower. The
rating agencies tried to assess the risk of a bond. If the risk and
the return were married correctly, then you could nd a fair value
for the bond.
Then it hit her. The present value of €150 in cash ows over the
next ve years was €108, if you used a discount rate of 8 per cent.
The YTM was a discount rate. If you thought the bond had a risk
of 8 per cent, then €108 was a fair price. So the YTM was the rate
that linked up the €150 to the €108.
But what would happen if you didn’t think the 8 per cent was
correct? What would happen to the price of the bond if the risk
was higher? Or if ination went up and interest rates went down?
An image of a see-saw formed in Anisa’s mind.
The interest rate and bond price see-saw
Bond prices go up when the interest rate falls
If interest rates go down, the price of bonds goes up. It’s
automatic. There’s no direct connection with ination or how
the company is performing. It’s simply that the future cash ows
you’re being promised are more valuable because the discount
rate is smaller.
It had to follow that the opposite was true. If interest rates went
up, then the value of the money promised to you would go down.
The discount rate went up, so the price of the bond went down.
This analysis was vital if you planned to buy a bond that was
already in issue. Perhaps you thought a bond was cheaply priced
midway through its life and might be worth buying. You’d need
these calculations to tell you that the return was above your
assessment of the risk. Anisa was buzzed-up after two double
You can always get what you want130
espressos. She bent open the book, checked her texts and then
told herself to concentrate.
Bond prices fall when inﬂation rises
She used exactly the same bond as before. The difference this
time was that the discount rate was going to be much higher. It
could be that ination had suddenly gone up so investors were
demanding more compensation for the erosion of their savings.
(We will look more closely at ination in Chapter 20.) Or there
might be a sudden spike in the opportunity cost, so the value
of the coupon didn’t seem sufcient. Or maybe the risk of the
company had gone up – and the rating had been cut – because of
a strike or the loss of a major customer.
She tried the spreadsheet with a discount rate of 12 per cent.
How much would she get for this bond now that conditions had
worsened? She knew she would receive less, but just how bad
would her loss be?
A B C = A 3 B
Year Type of Contract value Discount factor Present value
cash ﬂow of cash ﬂow of cash ﬂow
1 Coupon €10 89.3% €8.93
2 Coupon €10 79.7% €7.97
3 Coupon €10 71.2% €7.12
4 Coupon €10 63.6% €6.36
5 Coupon €10 56.7% €5.67
5 Principal €100 56.7% €56.74
Totals €150 €92.79
The higher discount rate (12 per cent as opposed to 8 per cent
previously) meant that the cash ows from the bond were
discounted more aggressively than before. Now, €150 over the
next ve years was only worth €92.79.