In: Finance
Otobai Company in Osaka, Japan is considering the introduction of an electrically powered motor scooter for city use. The scooter project requires an initial investment of ¥19 billion. The cost of capital is 12%. The initial investment can be depreciated on a straight-line basis over the 10-year life of the project. Profits are taxed at a rate of 50%. Consider the following project estimates: Market size 1.4 million Market share .1 Unit price ¥ 395,000 Unit variable cost ¥ 320,000 Fixed cost ¥ 3.4 billion Otobai is considering still another production method for its electric scooter. It would require an additional investment of ¥19 billion but would reduce variable costs by ¥44,000 per unit. a. What is the NPV of this alternative scheme? (Do not round intermediate calculations. Enter your answer in billions rounded to 3 decimal places.) NPV ¥ billion b. What is the break-even quantity? (Do not round intermediate calculations. Round your answer to the nearest whole number.) Break-even quantity c. Now go back to the original project shown in the problem table prior to the additional investment. Suppose Otobai's management would like to know the figure for variable cost per unit at which the original electric scooter project would break even. Calculate the level of variable costs at which the project would earn zero profit and at which it would have zero NPV. (Do not round intermediate calculations. Enter your answers in dollars per unit rounded to the nearest whole number.) Zero profit $ Zero NPV $ d. Calculate DOL based on the alternative scheme used in part a. (Do not round intermediate calculations. Round your answer to 2 decimal places.) DOL
All financials below in ¥ billion
a. What is the NPV of this alternative scheme? (Do not round intermediate calculations. Enter your answer in billions rounded to 3 decimal places.) NPV ¥ billion
It would require an additional investment of ¥19 billion but would reduce variable costs by ¥44,000 per unit.
Incremental investment, C0 = 19
Incremental annual depreciation tax shield = Incremental annual depreciation x Tax rate = Incremental investment / Life x Tax rate = 19 / 10 x 50% = 0.95
Production volume = Market size x Market share = 1.4 million x 0.1 = 0.14 million units
Variable Cost saved = 44,000 per unit
Hence, pre tax annual cost saving = 44,000 x 0.14 = 6.16 (in ¥ billion)
Post tax annual variable cost saving = 6.16 x (1 - 50%) = 3.08
C = Incremental post tax annual savings on account of alternative scheme = Incremental annual depreciation tax shield + Post tax annual variable cost saving = 0.95 + 3.08 = 4.03
These savings are in the form of an annuity over N = 10 years, Discount rate, R = Cost of capital = 12%
PV of annuities = C / R x [1 - (1+R)-N]
NPV = -C0 + PV of annuities = -C0 + C / R x [1 - (1+R)-N] = -19 + 4.03 / 12 % x [1 - (1 + 12%)-10] = 3.770398804 = 3.770 (rounded off to three places of decimal)
Hence, NPV: ¥ 3.770 billion
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b. What is the break-even quantity?
Case 1: Interpreting the break even as "Accounting Break Even"
Let's say Q is the break even quantity
Sale Price, SP = ¥ 395,000
Unit variable cost, VC = ¥ 320,000 - 44,000 = ¥ 276,000
Fixed cost = 3.4
Depreciation = (19 + 19) /10 = 3.8
Accounting break even equation:
(SP - VC) x Q = Depreciation + Fixed cost
hence, (395,000 - 276,000) x Q = (3.8 + 3.4) x 109
Hence, accounting break even Q = 60,504.20 = 60,504 (Nearest whole number)
Case 2: Interpreting the break even as "Cash Break Even"
So, we have to find the value of Q at which there is a cash break even i.e. NPV is zero.
For alternative 2: C0 = total investment = 19 + 19 = 38
Let's say annual operating cash flow for zero NPV is C
Hence, NPV = - C0 + PV of annuity C = -38 + C / R x [1 - (1 + R)-N] = 0
Hence, C / 12% x [1 - (1 + 12%)-10] = 38
Hence, C = 6.725398238
VC in alternative scheme = VC in first scheme - reduction = 320,000 - 44,000 = 276,000
Sale Price, SP = 395,000
Annual depreciation = 38 / 10 = 3.8
Break even volume = Q (in billions)
Annual operating cash flow = C = 6.725398238 = [(SP - VC) x Q - Depreciation - Fixed cost] x (1 - Tax rate) + Depreciation = [(395,000 - 276,000 ) x Q - 3.8 - 3.4] x (1 - 50%) + 3.8 = 59,500 x Q + 0.2
Hence, Q = (6.725398238 - 0.2) / 59,500 = 0.000109671 billion = 0.109671 mn units = 109,671 units
Hence, cash break even volume, Q = 109,671
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Part (c)
Calculate the level of variable costs at which the project would earn zero profit and at which it would have zero NPV. (Do not round intermediate calculations. Enter your answers in dollars per unit rounded to the nearest whole number.) Zero profit $ Zero NPV $
Let's assume the variable cost for accounting break even is VC
Hence, accounting break even equation:
(SP - VC) x Q - Fixed cost + annual depreciation = 0
Hence, (395,000 - VC) x 0.14 x 106 = (3.4 + 19 / 10) x 109
Hence, VC = 395,000 - (3.4 + 1.9) x 109 / (0.14 x 106) = 357,142.8571 = 357,143 (rounded off to the nearest whole number).
Hence enter your answer as: Zero profit $ 357,143
Let's say annual operating cash flow for zero NPV is C
Hence, NPV = - C0 + PV of annuity C = -19 + C / R x [1 - (1 + R)-N] = 0
Hence, C / 12% x [1 - (1 + 12%)-10] = 19
Hence, C = 3.362699119
Annual operating cash flow = C = 3.362699119 = [(SP - VC) x Q - Depreciation - Fixed cost] x (1 - Tax rate) + Depreciation = [(395,000 - VC) x 0.14 x 106 / 109 - 1.9 - 3.4] x (1 - 50%) + 1.9
Hence, VC = 395,000 - [(3.3627 - 1.9) / (1 - 50%) + 1.9 + 3.4] x 1,000 / 0.14 = 336,247.14 = 336,247 (rounded off to the nearest integer)
Zero NPV $ 336,247
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Part (d)
For alternative scheme:
DOL = Contribution margin / Operating income
Contribution margin = (SP - VC) x Q = (395,000 - 276,000) x 0.14 x 106 / 109 = 16.66
Operating income = Contribution margin - fixed costs - depreciation = 16.66 - 3.4 - 3.8 = 9.46
Hence, DOL = 16.66 / 9.46 = 1.76