Where Positive Net Present Value Comes From
1. The 757 must be a zeroNPV investment for the marginal user. Unless Boeing can charge different prices to different users (which is precluded with a secondary market), Delta will earn economic rents if the 757 is particularly well suited to Delta’s routes (and competition does not force Delta to pass the cost savings through to customers in the form of lower fares). Thus, the decision focuses on the issue of whether the plane is worth more in Delta’s hands than in the hands of the marginal user.
a. With a good secondary market and information on past changes in aircraft prices, it becomes somewhat more feasible to ignore cash flows beyond the first few years and to substitute the expected residual value of the plane.
b. Past aircraft prices may be used to estimate systematic risk (see Chapter 9).
c. The existence of a secondary market makes it more important to take note of the abandonment option (see Chapter 10).
2. The key question is: Will Gamma Airlines be able to earn economic rents on the AkronYellowknife route? The necessary steps include:
a. Forecasting costs, including the cost of building and maintaining terminal facilities, all necessary training, advertising, equipment, etc.
b. Forecasting revenues, which includes a detailed market demand analysis (what types of travelers are expected and what prices can be charged) as well as an analysis of the competition (if Gamma is successful, how quickly would competition spring up?).
c. Calculating the net present value.
The leasing market comes into play because it tells Gamma Airlines the opportunity cost of the planes, a critical component of costs.
If the AkronYellowknife project is attractive and growth occurs at the Ulan Bator hub, Gamma Airlines should simply lease additional aircraft.
3. To a baby with a hammer, everything looks like a nail. The point is that financial managers should not mechanically apply DCF to every problem. Sometimes, part or all of a valuation problem can be solved by direct observation of market values. Sometimes careful thought about economic rents clarifies whether NPV is truly positive.
4. The price of $280 per ounce represents the discounted value of expected future gold prices. Hence, the present value of 1 million ounces produced 8 years from now should be: ($280 ´ 1 million) = $280 million
5. First, consider the sequence of events:
§ At t = 0, the investment of $25,000,000 is made.
§ At t = 1, production begins, so the first year of revenue and expenses is recorded at t = 2.
§ At t = 5, the patent expires and competition may enter. Since it takes one year to achieve full production, competition is not a factor until t = 7. (This assumes the competition does not begin construction until the patent expires.)
§ After t = 7, full competition will exist and thus any new entrant into the market for BGs will earn the 9% cost of capital.
Next, calculate the cash flows:
§ At t = 0: $25,000,000
§ At t = 1: $0
§ At t = 2, 3, 4, 5, 6: Sale of 200,000 units at $100 each, with costs of $65 each, yearly cash flow = $7,000,000.
§ After t = 5, the NPV of new investment must be zero. Hence, to find the selling price per unit (P) solve the following for P:
_{}
Solving, we find P = $85.02 so that, for years t = 7 through t = 12, the yearly cash flow will be: [(200,000)´($85.02  $65)] = $4,004,000.
Finally, the net present value (in millions):
_{}
NPV = $10.69 or $10,690,000
6. The selling price after t = 6 now changes because the required investment is:
[$25,000,000´(1  0.03)^{5}] = $21,468,351
After t = 5, the NPV of new investment must be zero, and hence the selling price per unit (P) is found by solving the following equation for P:
_{}
P = $82.19
Thus, for years t = 7 through t = 12, the yearly cash flow will be:
[200,000 ´ ($82.19 ‑ $65)] = $3,438,000.
Finally, the net present value (in millions) is:
_{}
NPV = $9.18 or $9,180,000
7. a. (See the table below.) The net present value is positive at $3.76 million. However, this seems like a very small margin. Unless there is some factor unaccounted for in the analysis (e.g., strategic position such that the project creates an option for future expansion), management might not proceed with the Polyzone project.

t = 0 
t = 1 
t = 2 
t = 3 
t = 4 
t = 5 
t = 610 
Investment 
100 






Production 
0 
0 
40 
80 
80 
80 
80 
Spread 
1.20 
1.20 
1.20 
1.20 
1.20 
1.10 
0.95 
Net Revenues 
0 
0 
48 
96 
96 
88 
76 
Prod. Costs 
0 
0 
30 
30 
30 
30 
30 
Transport 
0 
0 
4 
8 
8 
8 
8 
Other Costs 
0 
20 
20 
20 
20 
20 
20 
Cash Flow 
100 
20 
6 
38 
38 
30 
18 
NPV (at 8%) = 
$3.76 






b. (See the table below.) The net present value is $14.68 million, and so the project is acceptable.

t = 0 
t = 1 
t = 2 
t – 3 
t = 4 
t = 510 
Investment 
100 





Production 
0 
40 
80 
80 
80 
80 
Spread 
1.20 
1.20 
1.20 
1.20 
1.10 
0.95 
Net Revenues 
0 
48 
96 
96 
88 
76 
Prod. Costs 
0 
30 
60 
30 
30 
30 
Transport 
0 
4 
8 
8 
8 
8 
Other Costs 
0 
20 
20 
20 
20 
20 
Cash Flow 
100 
6 
8 
38 
30 
18 
NPV (at 8%) = 
$14.68 





c. (See the table below.) The net present value is $18.64 million, and so the project is acceptable. However, the assumption that the technological advance will elude the competition for ten years seems questionable.

t = 0 
t = 1 
t = 2 
t – 3 
t = 4 
t = 510 
Investment 
100 





Production 
0 
0 
40 
80 
80 
80 
Spread 
1.20 
1.20 
1.20 
1.20 
1.10 
0.95 
Net Revenues 
0 
0 
48 
96 
88 
76 
Prod. Costs 
0 
0 
25 
25 
25 
25 
Transport 
0 
0 
4 
8 
8 
8 
Other Costs 
0 
20 
20 
20 
20 
20 
Cash Flow 
100 
20 
1 
43 
35 
23 
NPV (at 8%) = 
$18.64 





8. There are four components that contribute to this project’s NPV:
§ The initial investment of $100,000.
§ The depreciation tax shield. Depreciation expense is $20,000 per year for five years and is valued at the nominal rate of interest because it applies to nominal cash flows, i.e., earnings.
§ The aftertax value of the increase in silver yield. Like gold, silver has low convenience yield and storage cost. (You can verify this by checking that the difference between the futures price and the spot price is approximately the interest saving from buying the futures contract.) We conclude, therefore, that the PV of silver delivered (with certainty) in the future is approximately today’s spot price, and so there is no need to forecast the price of silver and then discount.
§ The cost of operating the equipment. This cost is $80,000 per year for ten years and is not valued at the real company cost of capital because we do not assume any future increase in cost due to inflation. We are concerned only with the aftertax cost.
Assume that the nominal interest rate is 11 percent. Then:
_{}
_{}
9. Assume we can ignore dividends paid on the stock market index. On June 30, 2005, each ticket must sell for $100 because this date marks the base period for the return calculation. At this price, investment in a ticket will offer the same return as investment in the index. On January 1, 2005, you know that each ticket will be worth $100 in 6 months. Therefore, on January 1, 2005, a ticket will be worth:
100/(1.10)^{1/2} = $95.35
The price will be the same for a ticket based on the Dow Jones Industrial Average.
10. If available for immediate occupancy, the building would be worth $1 million. But because it will take the company one year to clear it out, the company will incur $200,000 in cleanup costs and will lose $80,000 net rent. Assume both rent and costs are spread evenly throughout the year. Thus (all dollar amounts are in millions):
PV = 1,000  PV(200 + 80) = 1,000  280(0.962) = 731
Since the selling price at each date is the present value of forecasted rents, the only effect of postponing the sale to year 2 is to postpone the sales commission. The commission is currently (0.05 ´ 1000) = 50 and grows in line with property value. To estimate the growth rate of value, we can use the constantgrowth model:
PV = 1000 = 80/(0.08  g) so that g = 0%
Thus, the commission in year 2 is: (50 ´ 1.00^{2}) and:
PV (commission) = 50 ´ (1.00^{2}/1.08^{2}) = 43
The value of the warehouse, net of the sales commission, is:
731  43 = 688 or $688,000
Challenge Questions
1. a. The NPV of such plants is likely to be zero, because the industry is competitive and, after two years, no company will enjoy any technical advantages.
b. The PV of each of these new plants would be $100,000 because the NPV is zero and the cost is $100,000.
c. The PV of revenue from such a plant is:
[100,000 tons ´ (Price  0.85)]/0.10 = 100,000
Therefore, the price of polysyllabic acid will be $0.95 per ton.
d. At t = 2, the PV of the existing plant will be:
[100,000 tons ´ (0.95  0.90)]/0.10 = $50,000
Therefore, the existing plant would be scrapped at t = 2 as long as scrap value at that time exceeds $50,000.
e. No. Book value is irrelevant. NPV of the existing plant is negative after year 2.
f. Yes. Sunk costs are irrelevant. NPV of the existing plant is negative after year 2.
g. Phlogiston’s project causes temporary excess capacity. Therefore, the price for the next two years must be such that the existing plant’s owners will be indifferent between scrapping now and scrapping at the end of year 2. This allows us to solve for price in years 1 and 2.
Today’s scrap value is $60,000. Also, today’s scrap value is equal to the present value of future cash flows. Therefore:
_{}
Solving, we find that the price is $0.97 per ton. Knowing this, we can calculate the PV of Phlogiston’s new plant:
_{}
2. Aircraft will be deployed in a manner that will minimize costs. This means that each aircraft will be used on the route for which it has the greatest comparative advantage. Thus, for example, for Part (a) of this problem, it is clear that Route X will be served with five A’s and five B’s, and that Route Y will be served with five B’s and five C’s. The remaining Ctype aircraft will be scrapped.
The maximum price that anyone would pay for an aircraft is the present value of the total additional costs that would be incurred if that aircraft were withdrawn from service. Using the annuity factor for 5 time periods at 10 percent, we find the PV of the operating costs (all numbers are in millions):
Type 
X 
Y 
A 
5.7 
5.7 
B 
9.5 
7.6 
C 
17.1 
13.3 
Again, consider Part (a). The cost of using an Atype aircraft on Route X (Cost = Price of A + 5.7) must be equal to the cost of using a Btype aircraft on Route X (Cost = Price of B + 9.5). Also, the cost of using a Btype aircraft on Route Y (Price of B + 7.6) equals the cost of using a Ctype on Route Y (Price of C + 13.3). Further, because five Ctype aircraft are scrapped, the price of a Ctype aircraft must be $1.0, the scrap value. Therefore, solving first for the price of B and then for the price of A, we find that the price of an Atype is $10.5 and the price of a Btype is $6.7. Using this approach, we have the following solutions:


Usage 

Aircraft Value (in millions) 


X 
Y 
Scrap 
A 
B 
C 
a. 
5A+5B 
5B+5C 
5C 
$10.5 
$6.7 
$1.0 
b. 
10A 
10B 
10C 
10.5 
6.7 
1.0 
c. 
10A 
5A+5B 
5B+10C 
2.9 
1.0 
1.0 
d. 
10A 
10A 
10B+10C 
2.9 
1.0 
1.0 
3. a.
b. Given that the industry is competitive, the investment in a new plant to produce bucolic acid must yield a zero NPV. First, we solve for the revenues (R) at which a new plant has zero NPV.


0 
1 
2 
3 
1. 
Initial investment 
100 



2. 
Revenues net of tax 

0.6R 
0.6R 
0.6R 
3. 
Operating costs net of tax 

30 
30 
30 
4. 
Depreciation tax shield 

+40 


5. 
Salvage value net of tax 



+15 
Therefore:
We can now use the new revenue to recompute the present values from Part (a) above. (Recall that existing plants must use the original tax depreciation schedule.).
_{}
_{}
c. Existing 2yearold plants have a netoftax salvage value of:
50 – [(0.4)´(50.0  33.3)] = $43.33
d. Solve again for revenues at which the new plant has zero NPV:


0 
1 
2 
3 
1. 
Initial investment 
100 



2. 
Revenues 

+R 
+R 
+R 
3. 
Operating costs 

50 
50 
50 
4. 
Salvage value 



+25 
With revenues of $91:
_{}
_{}