Question

In the last semester's final finance exam there was this exercise:

(You) got a bit info about a bonds interest yield and the market interest rate and
based on that calculate the market value of the bond and the market interest
rate of the bond + would you invest in this bond if the price was 105,5% of its
face value?

How would I calculate something like this and decide on the final Question asked? Could you Maybe come up with an example. Thanks a lot.

Answer 1

Interest Yield of a bond is the annual return earned on the price paid for the bond. Suppose a bond is purchased for 1000 $ and it has a coupon rate of 5%, then the interest yield will be Coupon/Price of Bond = 0.05*1000/1000 = 5.00%. So, interest yield can also be said to be the Coupon Rate of the bond.

Market Value of a bond is calculated by calculating the Present Value of all the future cash flows which an investor will receive from the bond.

Let us take an example where we are given that a bond with Face Value = 1000 $, gives annual coupon with a coupon rate of 5%, and the market interest rate on a similar bond of similar maturity & risk is 6%. Suppose the maturity of the bond is 5 Years. We are required to calculate the Market Value of the bond.

Now, Market Value of this bond can be computed by calculating the Present Value of the cash flows which will be received by the bond.

Cash Flows of the bond will be as below:

Annual Coupon on the bond will be = Coupon Rate * Face Value = 5% * 1000 = 50 $

In the final year, along with the coupon, the investor will also get the face value; therefore the cash flow received in the final year will be = Coupon + Face Value = 50 +1000 = 1050 $

We need a discount rate to discount the values of each of these cash flows in order to calculate the present value of the cash flows. This discount rate is the market interest rate, which in this example is 6%.

Present Value of Cash Flow 1 = 50/(1+ 0.06)^1 = 47.17

Present Value of Cash Flow 2 = 50/(1+ 0.06)^2 = 44.50

Present Value of Cash Flow 3 = 50/(1+ 0.06)^3 = 41.98

Present Value of Cash Flow 4 = 50/(1+ 0.06)^4 = 39.60

Present Value of Cash Flow 5 = 1050/(1+ 0.06)^5 = 784.62

So, the Present Value of the Cash Flows = Market Value of the Bond = 47.17 + 44.50 + 41.98 + 39.60 + 784.62 = 957.88

NOTE: This bond of Face Value 1000 $ has a present market value of 957.88 $. This means that this bond is sold at a discount from its Face Value.

The fact that the bond was being sold at a discount could be ascertained by the fact that the Coupon Rate of the bond is lesser than the Market Interest Rate. Had the coupon rate been higher than the market interest rate, the bond would have sold at a premium to its face value.

Market Interest Rate of a bond is the Yield to Maturity (YTM) of a bond, and is calculated by using the following formula:

Here, Annual Interest = 50; Par/Face Value = 1000; Market Price = 957.88; No. of Years to Maturity = 5; Using these values in the above formula, we will get:

YTM = 5.97%

If we are asked that will we invest in the bond if it's price is 105.50% of its Face Value; we need to calculate the YTM of the bond; if the YTM is greater than the Market Interest Rate then we should invest in the bond, otherwise we must not.

So in this case, Price of Bond = 105.5% * 1000 = 1055; Par/Face Value = 1000; Years to Maturity = 5; Annual Interest = 5% * 1000 = 50

Using this information in the formula for YTM, we will get the YTM = 3.80%, which is lesser than the market interest rate of 6%, therefore we must not invest in this bond.

This is one example, the conclusions will differ according to different values of the various parameters. But hopefully this example can serve as a template to solve similar problems.