The same move, discounted — and the memo that says why

Harbourline’s warehouse, again

Lesson 12.5 laid out Harbourline Logistics’ warehouse move undiscounted: one-time costs of 210,000 at t0 (the 90,000 lease-break penalty, 60,000 of moving costs, 35,000 of contribution lost in the transition month and 25,000 of retention bonuses) against an annual rent saving of 60,000 for four years. Four years of savings total 240,000, so the undiscounted answer was +30,000 → move — and the lesson said, in its own voice, that the answer was provisional because the 240,000 arrives over four years while the 210,000 leaves now.

Harbourline’s required return is 10 %. The savings are an ordinary annuity — 60,000 at the end of each of four years — so:

PV of savings     60,000 × 3.1699 (annuity, 4 yr, 10 %)   =   190,194
Less: one-time costs at t0                                  (210,000)
NPV of the move                                             (19,806)

The move destroys 19,806 of value. Discounted at the return Harbourline’s lenders and shareholders require, four years of 60,000 are worth 190,194 today — less than the 210,000 it costs to get them. Do not move. The undiscounted answer was wrong, and this is the answer to act on: design decision 5, closed.

What rate would make it worth doing

The move breaks even where the PV of the savings equals the one-time costs — where the four-year annuity factor is

$$\frac{210,000}{60,000}=3.50$$

Reading down the four-year row of the annuity table: 3.6299 at 4 %, 3.4651 at 6 % — so the break-even rate is about 5.6 %. Below it the move creates value; above it the move destroys value:

Rate    Factor (4 yr)   PV of savings    NPV
 4 %       3.6299          217,794      +7,794
 6 %       3.4651          207,906      −2,094
10 %       3.1699          190,194     −19,806
12 %       3.0373          182,238     −27,762

No lender or shareholder of a logistics company requires as little as 5.6 %, so the sensitivity confirms the decision rather than softening it. Had the annual saving been 50,000 instead of 60,000, the NPV at 10 % would be $50,000\times 3.1699-210,000=-51,505$ — worse still. The direction is the general lesson: discounting punishes decisions whose costs come first and whose benefits come late, which is what a relocation, an expansion and a boat lift all are.

The investment recommendation

The final’s last written prompt is a memo, and the memo has five parts. For Lakehead’s boat lift:

1. The figure and the decision. NPV +139,397 at 10 % → accept. (Payback 3.48 years and PI 1.148 as secondary checks — named, not relied on.)
2. The rate and why. 10 % is Lakehead’s WACC — the blended return its lenders and shareholders require — so a positive NPV means value created after every provider of capital is paid.
3. The assumptions. Five-year life; 270,000 a year of net cash inflow (90,000 of income plus 180,000 of depreciation); 50,000 salvage; 40,000 of working capital recovered in year 5; tax ignored; the t0 investment undiscounted.
4. Two qualitative factors, each with a direction. Capacity for larger vessels supports the strategy (for); the shoreline permit and the environmental review could delay or add cost (against); crew safety and skills; the lift’s resale if the market does not arrive.
5. One sensitivity. The NPV is still +33,683 at 14 %, so the decision survives a rate four points higher; or, with year 5 unchanged, the annual inflow of years 1–4 could fall to about 226,000 before NPV reached zero.

A memo that gives the figure alone is a calculation. A memo that gives the figure, the rate and why, the assumptions it rests on, the factors the number cannot see and how robust the answer is — that is a recommendation.