# PV of security with interest-dependent cash flows

I struggle with the following exercise, where the correct answer is supposed to be "no":

A riskless security with cash flow $$C_1, C_2, \dots, C_n$$ has a market price of $$\sum_{i=1}^n C_i\,d(i)$$. The discount factor $$d(i)$$ denotes the present value of $$\1$$ at time $$i$$ from now. Is the formula still valid if the cash flow depends on interest rates?

I don't even know another way to valuate a security with known future cash flows other than with the usual formula $$\mathrm{PV} =\sum_{i=1} C_i\,d(i)$$.

If the cash flows depend on the (random) interest rates, then the $$C_i$$ are random variables and so would be the sum $$\sum\limits_{i=1}^n C_id(i)$$. However, initial market prices need to be constants, they cannot be random (because you need to know how much this claim is worth right now). The $$d(i)$$ are real numbers though since they are discount factors (typically prices of default-free zero-coupon bonds, which we can observe in the marketplace). So, what you need to do is to specify a model for the interest rate (say a short rate model) and then, you can compute the the (conditional) expectation of the cash flows $$C_i$$. It basically boils down to pricing a bond with variable coupons.
Recall that in general the no-arbitrage price of any claim paying $$\xi$$ is given by $$\mathbb{E}^\mathbb{Q}\left[\frac{B_t}{B_T}\xi\bigg|\mathcal{F}_t\right]$$.