Solve equation 11.31 for a with NPV set at 0 to get an expression for a*, the value of a that makes the project marginal, in terms of r, X, P and D. Treat X, P and D as parameters and find

∂a*/∂r. What can be said about its sign? What is its sign for the values used in the chapter when discussing discount rate adjustment, X = 1000, D = 75 and P = 12.5? Confirm the answer by evaluating a* for r = 0.055 and r = 0.045, and explain it.