Problem 6.1
Subunit "Sewing and Cutting" → Selling division
Subunit "Sizing and Fitting" → Buying division
Final selling price (per unit): € 300.00
Total costs (for both divisions): TC = 200 + 6Q^2
No market at all → Transfer-price = Marginal cost of producing at the optimal level for the company as a whole.
The marginal cost (MC) is the first derivative of the cost function (TC) with respect to the output quantity (Q).
MC(for both selling and buying) = 12Q
MR (buying) = 300
Net MR (for buying) = 300 - 12Q
Setting marginal costs of the selling division equal to the net marginal return of the buying division gives:
12Q = 300 - 12Q
24Q = 300
Q = 12.5 → 13 (= the optimal number of units sold)
MC(= transfer-price): € 150.00
Profits: € 1,472.00
Problem 6.2
Net Present Value (NPV)
H D L
Initial investment expenditure 1,000,000 900,000 800,000
Cash flow year 1: 225,000 250,000 200,000
Cash flow year 2: 225,000 250,000 220000
Cash flow year 3: 225,000 225,000 242000
Cash flow year 4: 225,000 202,500 266200
Cash flow year 5: 225,000 182,250 292820
Estimated NPV (5%) -25.86775 68.61096 247.5069
Residual income (RI)
Huey (H) 1 2 3 4 5
Net cash flow 225,000 225,000 225,000 225,000 225,000
Depreciation 200000 200000 200000 200000 200000
Subunit "Sewing and Cutting" → Selling division
Subunit "Sizing and Fitting" → Buying division
Final selling price (per unit): € 300.00
Total costs (for both divisions): TC = 200 + 6Q^2
No market at all → Transfer-price = Marginal cost of producing at the optimal level for the company as a whole.
The marginal cost (MC) is the first derivative of the cost function (TC) with respect to the output quantity (Q).
MC(for both selling and buying) = 12Q
MR (buying) = 300
Net MR (for buying) = 300 - 12Q
Setting marginal costs of the selling division equal to the net marginal return of the buying division gives:
12Q = 300 - 12Q
24Q = 300
Q = 12.5 → 13 (= the optimal number of units sold)
MC(= transfer-price): € 150.00
Profits: € 1,472.00
Problem 6.2
Net Present Value (NPV)
H D L
Initial investment expenditure 1,000,000 900,000 800,000
Cash flow year 1: 225,000 250,000 200,000
Cash flow year 2: 225,000 250,000 220000
Cash flow year 3: 225,000 225,000 242000
Cash flow year 4: 225,000 202,500 266200
Cash flow year 5: 225,000 182,250 292820
Estimated NPV (5%) -25.86775 68.61096 247.5069
Residual income (RI)
Huey (H) 1 2 3 4 5
Net cash flow 225,000 225,000 225,000 225,000 225,000
Depreciation 200000 200000 200000 200000 200000
