The Devil's Deal

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

ination, 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 ination 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 ination 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 ination had suddenly gone up so investors were

demanding more compensation for the erosion of their savings.

(We will look more closely at ination in Chapter 20.) Or there

might be a sudden spike in the opportunity cost, so the value

of the coupon didn’t seem sufcient. 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.