분야
zipThe present value of $1 to be received one year from now, discounted at 18% is: $0.8475
The present value of $1 × (1 – 0.08) (that is, $0.92) to be received one year from now, discounted at 10% is: $0.8364
The former calculation overstates the correct answer by approximately 1.3%. However, for cash flows five or ten years in to the future, discounting by 18% understates the correct present value by approximately 23% and 46%, respectively. The error increases substantially because the incorrect factor (i.e., 1.18) is compounded, causing the denominator of the present value calculation to be greatly overstated so that the present value is greatly understated.
10.
Year 0 Years 1-10
Investment ¥15 B
1. Revenue ¥44.000 B
2. Variable Cost 39.600 B
3. Fixed Cost 2.000 B
4. Depreciation 1.500 B
5. Pre-tax Profit ¥0.900 B
6. Tax @ 50% 0.450 B
7. Net Operating Profit ¥0.450 B
8. Operating Cash Flow ¥1.950 B
11. The spreadsheets show the following results:
NPV
Pessimistic Expected Optimistic
Market Size -1.17 3.43 8.04
Market Share -10.39 3.43 17.26
Unit Price -19.61 3.43 11.11
Unit Variable Cost -11.93 3.43 11.11
Fixed Cost -2.71 3.43 9.58
The principal uncertainties are market share, unit price, and unit variable cost.
12. a.
Year 0 Years 1-10
Investment ¥30 B
1. Revenue ¥37.500 B
2. Variable Cost 26.000
3. Fixed Cost 3.000
4. Depreciation 3.000
5. Pre-tax Profit (1-2-3-4) ¥5.500
6. Tax 2.750
7. Net Operating Profit (5-6) ¥2.750
8. Operating Cash Flow (4+7) 5.750
NPV = + ¥5.33 B
b.
Inflows Outflows
Unit Sales Revenues Investment V. Costs F. Cost Taxes PV PV NPV
(000’s) Yrs 1-10 Yr 0 Yr 1-10 Yr 1-10 Yr 1-10 Inflows Outflows
0 0.00 30.00 0.00 3.00 -3.00 0.00 -30.00 -30.00
100 37.50 30.00 26.00 3.00 2.75 230.42 -225.09 5.33
200 75.00 30.00 52.00 3.00 8.50 460.84 -420.18 40.66
Note that the break-even point can be found algebraically as follows:
NPV = -Investment + [(PVA10/10%) (t Depreciation)] +
[Quantity (Price – V.Cost) – F.Cost](1 – t)(PVA10/10%)
Set NPV equal to zero and solve for Q:
Proof:
1. Revenue ¥31.84 B
2. Variable Cost 22.08
3. Fixed Cost 3.00
4. Depreciation 3.00
5. Pre-tax Profit ¥3.76 B
