The floating rate portion of a plain vanilla interest rate swap with yearly payments and a notional principal of one unit has cash flows at the end of each year defining a stream starting at time 1 of \(\left(c_{0}, c_{1}, c_{2}, \ldots, c_{M-1}\right)\), where \(c_{i}\) is the actual spot rate at the beginning of year \(i\). Using the concepts of forwards, argue that the value at time zero of \(c_{i}\) to be received at time \(i+1\) is \(d(0, i+1) r_{i}\), where \(r_{i}\) is the short rate for time \(i\) implied by the current (time zero) term structure and \(d(0, i+1)\) is the implied discount factor to time \(i+1\). The value of the stream is therefore \(\sum_{i=0}^{M-1} d(0, i+1) r_{i}\). Show that this reduces to the formula for \(V\)