Home > Student Questions > Discount and Premium Bonds

November 22nd, 2010

I received the following question from a student:

Here is my response:

Discount does not imply you got a “good deal”. Consider these three bonds:

Bond A: 10-year annual bond with \$1000 par amount, 5% coupons and a yield of 5%.
Bond B: 10-year annual bond with \$1000 par amount, 0% coupons and a yield of 5%.
Bond C: 10-year annual bond with \$1000 par amount, 20% coupons and a yield of 5%.

The price of each bond is:
Bond A: 50 a-angle-10 + 1000v^10 = 1000 (priced at par)
Bond B: 1000v^10 = 613.91 (discount bond)
Bond C: 200 a-angle-10 + 1000v^10 = 2158.26 (premium bond)

Which of these bonds is the “best deal”? From a yield perspective they are equivalent – all three bonds earn 5%. So which bond should an investor buy? Well it depends on her cash flow needs.

Bond A pays annual coupons of \$1000 x .05 = \$50
Bond B does not pay an annual coupon
Bond C pays annual coupons of \$1000 x .20 = \$200

Maybe the investor doesn’t need any cash inflow over the next 10 years and is worried that she wouldn’t be able to reinvest any cash inflows at more than 5%. In this case, she would choose bond B. Maybe she needs annual cash flow of \$50, then she would choose A. Maybe she needs a larger annual cash flow of \$200 then she would choose C.

If she bought B, then she bought the bond at a “discount” but her coupon payments were less than bond A’s (in fact her coupons are 0). So that is why she got the discount on the purchase price.

If she bought C, she paid a “premium” but her coupon payments were much larger to account for that premium. To receive those larger coupons she needed to pay more.