Question

Bond A has a face value of $5,000, a coupon rate of 2%, and a maturity date of five years. Bond B has a face value of $4,000, a coupon rate of 10%, and a maturity date of 10 years. Bond C has a face value of $4,500, a coupon rate of 3%, and a maturity date of four years. If these bonds are being sold for $6,300 each, which should you buy? Assume that the prevailing interest rate is 3%.

Answer 1

Answer - Bond B

Explanation

Bond A

We have to give $6300 for a bond with face value of $5000. We give a higher price than face value only if the coupon rate is more than the prevailing interest rate.

Here, price is higher than face value and coupon rate is lower than the prevailing interest rate.

In other words, if we deposit the $6300 at 3% interest rate, we will get an interest of 3% annually plus $6300 at end of 5 years. But, if we buy bond A, we get interest of 2% (on $5000) annually and $5000 back at end of 5 years. Clearly, without doing maths, we can see that we should not buy Bond A.

Bond C

We have to give $6300 for a bond with face value of $4500. We give a higher price than face value only if the coupon rate is more than the prevailing interest rate.

Here, price is higher than face value and coupon rate is equal to the prevailing interest rate. So, do not buy this either.

Bond B

Cashflow from bond B,

At year 0, cashflow = -6300

From year 1 to year 9, cashflow from bond = $400 each

At year 10, cashflow = 4400

On the other hand, cashflow from investing $6300 at 3% interest rate,

At year 0, cashflow = -6300

From year 1 to year 9, cashflow = 3%*6300 = $189

At year 10, cashflow = 6489

Cash flow difference between these options,

From year 1 to 9 : $211

Year 10: -2029

Present value of the cash flow difference,

That is, present value of cash flow from the bond B is greater than investing 6300 today at prevailing interest rate of 3% by about $88.45

Hence, we should go for Bond B