Silverline Logistics: a divisional hurdle rate for a new cold-chain venture
Silverline Logistics Ltd runs port drayage and warehousing in Hong Kong, financed 15% debt / 85% equity, with an equity beta of 0.95. The 10-year Hong Kong Government Bond yields 3.8%, the market risk premium is estimated at 5.5%, Silverline's pre-tax cost of debt is 4.9% and the profits tax rate is 16.5%. The board is evaluating a HK$255 million entry into temperature-controlled pharmaceutical logistics through a joint venture. The JV will be financed at a target 35% debt / 65% equity; the CFO has identified a Singapore-listed peer group in the same business with an equity beta of 1.42, a debt-to-equity ratio of 60% and a tax rate of 17%. Debt for the venture would cost 6.4% pre-tax. The project is forecast to generate HK$40 million of annual net cash flow for 10 years. The investment committee proposes to appraise it at Silverline's existing WACC.
1. Calculate the risk-adjusted WACC for the cold-chain venture, showing the ungearing and regearing steps.
Read the worked answer
Step 1 - Silverline's existing WACC (for context)
- Ke = 3.8% + 0.95 × 5.5% = 9.03%
- Kd after tax = 4.9% × (1 − 0.165) = 4.09%
- WACC = 0.85 × 9.03 + 0.15 × 4.09 = 7.68 + 0.61 = 8.29% ≈ 8.3%
Step 2 - Ungear the proxy beta
Ba = Be ÷ [1 + (1 − t) × D/E] = 1.42 ÷ [1 + (1 − 0.17) × 0.60] = 1.42 ÷ (1 + 0.498) = 1.42 ÷ 1.498 = 0.948
This strips out the peer group's financial risk and leaves the asset (business) risk of cold-chain pharma logistics.
Step 3 - Regear to the JV's target gearing
Target D/E = 35/65 = 0.538
Be = 0.948 × [1 + (1 − 0.165) × 0.538] = 0.948 × (1 + 0.449) = 0.948 × 1.449 = 1.374
Step 4 - Cost of equity and WACC
- Ke = 3.8% + 1.374 × 5.5% = 3.8 + 7.56 = 11.36%
- Kd after tax = 6.4% × 0.835 = 5.34%
- WACC = 0.65 × 11.36 + 0.35 × 5.34 = 7.38 + 1.87 = 9.25%
Judgement points
- The peer beta must come from the same business, not from a diversified conglomerate; 0.948 is plausible for a logistics asset but should be cross-checked against a second peer set.
- Deleveraging and releveraging assumes debt is risk-free and the beta of debt is zero - acceptable at these gearing levels.
- If the JV's debt is non-recourse and guaranteed by the partner, the effective gearing is lower than 35% and the discount rate should be adjusted again.
2. Quantify the error if the investment committee uses Silverline's existing WACC, and explain the decision consequence.
Read the worked answer
The two rates are 0.95 percentage points apart, and it changes the answer
10-year annuity factors:
- At 8.3%: (1 − 1.083⁻¹⁰) ÷ 0.083 = 6.620
- At 9.25%: (1 − 1.0925⁻¹⁰) ÷ 0.0925 = 6.349
| At 8.3% (company WACC) | At 9.25% (venture WACC) | |
|---|---|---|
| PV of HK$40m × 10 years | 264.8 | 254.0 |
| Less cost HK$255.0m | (255.0) | (255.0) |
| NPV | +HK$9.8m | −HK$1.0m |
The project flips from accept to reject. Using the company rate overstates NPV by roughly HK$10.8 million, about 4% of the outlay - on a marginal project that is the whole decision.
Why the company rate is wrong here
- Different business risk. Silverline's drayage earnings move with Hong Kong port volumes. Pharma cold-chain earnings move with hospital and distributor contracts - a different systematic risk, and the peer beta (0.948 ungeared, against Silverline's own ungeared beta of about 0.83) says it is higher.
- Different financial risk. 35% gearing versus 15% means shareholders bear more financial risk; the regeared beta captures that.
- Different debt cost. 6.4% versus 4.9% reflects the JV's non-recourse structure and thinner credit.
- One rate for the whole company subsidises new ventures out of the core business - the classic symptom is a diversified group that keeps entering low-return businesses and cannot explain why its group return keeps falling.
Practical safeguard - put the venture WACC in the board paper explicitly, show the sensitivity of NPV to ±50bp, and require management to justify any use of the group rate in writing.
3. The JV partner wants to push gearing to 60% debt to 'capture the tax shield'. Evaluate this using capital structure theory and state what else the board must consider.
Read the worked answer
The tax shield argument is real but incomplete
Under Modigliani–Miller with taxes, firm value rises with debt by t × D: at 16.5% tax and an extra HK$100 million of debt, roughly HK$16.5 million of value. The static trade-off model then subtracts the present value of financial distress costs. WACC falls as gearing rises, but only up to the point where the rising cost of equity and the rising cost of debt (as rating and default risk deteriorate) offset the shield. Beyond that point WACC rises and value falls.
Why 60% is not obviously better for this JV
- The cash flows are contract-based but not risk-free. Pharma logistics contracts can be lost at renewal, and a JV at 60% gearing has little room to absorb a lost contract. The debt is likely non-recourse, so the loss falls on the equity - the partner's 60% gearing shifts risk onto Silverline's shareholders without a matching return.
- The tax shield only has value if there is taxable profit to shelter. A start-up JV with capital allowances and start-up losses may not pay tax for several years, so the shield is deferred and worth less than t × D.
- Guarantees and covenants. If Silverline must guarantee the JV debt or provide a keepwell, the debt is effectively on Silverline's balance sheet and its own 3.5x-style covenants are affected.
- Pecking order and flexibility. High gearing consumes debt capacity that the group may want for the core business or for distress.
Board's checklist before agreeing
- Model WACC at 35%, 45% and 60% gearing using the regearing formula, not intuition, and show the NPV at each.
- Obtain the partner's guarantee terms and confirm whether the debt is truly non-recourse.
- Check the JV's forecast taxable profits against the shield.
- Consider adjusted present value instead of WACC if the JV's debt capacity is fixed and finite: base-case NPV at the all-equity rate plus the present value of the financing side effects.
- Agree an exit and deadlock mechanism before signing - a 60/40 JV with no exit is a financing decision nobody can reverse.