Zero rate vs. yield on coupon bearing bond

in Hull's solutions manual of Options, Futures & Derivatives (8th edition), there's question 4.7, in which is asked to put the following in descending order: a) the five-year zero rate, b) the yield on a five-year coupon-bearing bond, c) the forward rate corresponding to the period between 4.75 and 5 years in the future. The yield curve is upward sloping.

The solution is c>a>b.

With an upward sloping yield curve, it makes sense to me that the forward rate at the end of the curve is highest among the three. However, I don't get how to put a and b in order; what's the reasoning behind it?

• Ask yourself, which bond do you want? The 5y zero-coupon-bond or a coupon-bearing-bond? Everything else the same. Which one you'd choose if I gave you one? The one that you want will be more expensive (because I also want it), and therefore the rate will go down. – SmallChess Jun 5 '15 at 5:52
• Well, I'd say the coupon bearing bond because 1 dollar today is more worth than 1 dollar tomorrow and with the coupon bearing bond I get the coupon payments before maturity. For this reason the issuer has to pay less than on the zero-coupon bond. Is this correct? – Alex Jun 5 '15 at 10:28
• This might be relevant: quant.stackexchange.com/questions/15659/… – Helin Jun 6 '15 at 14:05