Homework Answers
Let P = price; C = cost; Q = quantity
NPV for the change to new policy will be
NPV = - Cost at the start + Present Value (PV) of incremental cash flows
Cost at the start = Pold*Qold + Cold*(Qnew -Qold) + (Cnew - Cold)*Qold
Incremental cash flow = (Pnew-Cnew)*Qnew - (Pold - Cold)*Qold
PV of incremental cash flow = incremental cash flow/required return
For the break-even quantity of the new policy, this NPV should equal zero.
Solve this using Solver, as follows:
| Formula | Old | New | |
| Price (P) | 86 | 88 | |
| Cost (C) | 46 | 46 | |
| Quantity (Q) | 4,400.00 | 4,370.01 | |
| (P-C)*Q | CF | 1,76,000.00 | 1,84,313.08 |
| Required return (rr) | 2.00% | ||
| CFnew - CFold | Incremental CF (ICF) | 8,313.08 | |
| ICF/rr | PV of inc.CF (Pvicf) | 3,77,867.43 | |
| Pold*Qold + Cnew(Qnew -Qold) + (Cnew -Cold)*Qold) | Cost at start (C1) | 3,77,866.71 | |
| Pvicf - C1 | NPV | 0.00 |
Break-even quantity = 4,370.01 units
Solver SS:
D188 Solver Parameters B D Old 179 Formula New Set Objective: SDS188 180 88 To: O Max Min O Value Of: Price (P) Cost (C) Quantity (Q) CF Required return (rr) Incremental CF (ICF) PV of inc.CF (Pvicf) 46 4,388.41 1,84,313.07 181 182 183 (P-C)*Q 184 185 Cfnew - Cfold 186 ICF/rr Pold*Qold + Cnew(Qnew - 187 Qld) + (Cnew-Cold)*Qold) 188 Pvicf-C1 189 46 4,400.00 1,76,000.00 2.20% 8,313.07 3,77,866.69 By Changing Variable Cells: SE$182 Subject to the Constraints: Add Cost at start (C1) NPV 3,77,866.69 Change -----0.001 Delete
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