The document discusses an investment by Rainbow Products to purchase a paint-mixing machine that would save $5,000 per year. It examines the payback period, net present value (NPV), and internal rate of return (IRR) of purchasing the $35,000 machine with a 15-year lifespan. Two additional options are considered: purchasing a service contract to keep the machine in new condition forever, or reinvesting 20% of annual savings to increase savings at 4% annually.

1. Investment Analysis and Lockheed Tri Star
1. Rainbow Products is considering the purchase of a paint-mixing machine to reduce labor costs.
The savings are expected to result in additional cash flows to Rainbow of $5,000 per year. The
machine costs $35,000 and is expected to last for 15 years. Rainbow has determined that the cost of
capital for such an investment is 12%.
[A] Compute the payback, net present value (NPV), and internal rate of return (IRR) for this machine.
Should Rainbow purchase it? Assume that all cash flows (except the initial purchase) occur at the end
of the year, and do not consider taxes.
[B] For a $500 per year additional expenditure, Rainbow can get a “Good As New” service
contract that essentially keeps the machine in new condition forever. Net of the cost of the service
contract, the machine would then produce cash flows of $4,500 per year in perpetuity. Should
Rainbow Products purchase the machine with the service contract?
[C] Instead of the service contract, Rainbow engineers have devised a different option to preserve
and actually enhance the capability of the machine over time. By reinvesting 20% of the annual cost
savings back into new machine parts, the engineers can increase the cost savings at a 4% annual rate.
For example, at the end of year one, 20% of the $5,000 cost savings ($1,000) is reinvested in the
machine; the net cash flow is thus $4,000. Next year, the cash flow from cost savings grows by 4% to
$5,200 gross, or $4,160 net, of the 20% reinvestment. As long as the 20% reinvestment continues, the
cash flows continue to grow at 4% in perpetuity. What should Rainbow Products do?
HINT: The formula for the present value (V) of an initial end-of-year perpetuity payout of $C
(growing at g%) per period, with a discount rate of k%, is:
V
C
k g
=
−

2. 2. Suppose you own a concession stand that sells hot dogs, peanuts, popcorn, and beer at a ball park.
You have three years left on the contract with the ball park, and you do not expect it to be renewed.
Long lines limit sales and profits. You have developed four different proposals to reduce the
lines and increase profits.
The first proposal is to renovate by adding another window. The second is to update the
equipment at the existing windows. These two renovation projects are not mutually exclusive; you
could take both projects. The third and fourth proposals involve abandoning the existing stand. The
third proposal is to build a new stand. The fourth proposal is to rent a larger stand in the ball park.
This option would involve $1,000 in up-front investment for new signs and equipment installation;
the incremental cash flows shown in later years are net of lease payments.
You have decided that a 15% discount rate is appropriate for this type of investment. The
incremental cash flows associated with each of the proposals are:
Incremental Cash Flows
Project Investment Year 1 Year 2 Year 3
Add a New Window -$75,000 44,000 44,000 44,000
Update Existing Equipment -50,000 23,000 23,000 23,000
Build a New Stand -125,000 70,000 70,000 70,000
Rent a Larger Stand -1,000 12,000 13,000 14,000
• Using the internal rate of return rule (IRR), which proposal(s) do you recommend?
• Using the net present value rule (NPV), which proposal(s) do you recommend?
• How do you explain any differences between the IRR and NPV rankings? Which rule is
better?
3. MBATech, Inc., is negotiating with the mayor of Bean City to start a manufacturing plant in an
abandoned building. The cash flows for MBAT’s proposed plant are:
Year 0 Year 1 Year 2 Year 3 Year 4
- 1,000,000 371,739 371,739 371,739 371,739
The city has agreed to subsidize MBAT. The form and timing of the subsidy have not been
determined, and depend on which investment criterion is used by MBAT. In preliminary discussions,
MBAT suggested four alternatives:
[A] Subsidize the project to bring its IRR to 25%.
[B] Subsidize the project to provide a two-year payback.
[C] Subsidize the project to provide an NPV of $75,000 when cash flows are discounted at 20%.
[D] Subsidize the project to provide an accounting rate of return (ARR) of 40%. This is defined as:

3. ARR
Average Annual Cash Flow
Investment
of Years
Investment
=
−
÷
#
2
You have been hired by Bean City to recommend a subsidy that minimizes the costs to the
city. Subsidy payments need not occur right away; they may be scheduled in later years if
appropriate. Please indicate how much of a subsidy you would recommend for each year under each
alternative suggested by MBAT.
Which of the four subsidy plans would you recommend to the city if the appropriate discount rate is
20%?
4. You are the CEO of Valu-Added Industries, Inc. (VAI). Your firm has 10,000 shares of common
stock outstanding, and the current price of the stock is $100 per share. There is no debt; thus, the
“market value” balance sheet of VAI looks like:
VAI Market Value Balance Sheet
Assets $1,000,000 Equity $1,000,000
You then discover an opportunity to invest in a new project that produces positive cash flows
with a present value of $210,000. Your total initial costs for investing and developing this project are
only $110,000. You will raise the necessary capital for this investment by issuing new equity. All
potential purchasers of your common stock will be fully aware of the project’s value and cost, and are
willing to pay “fair value” for the new shares of VAI common.
• What is the Net Present Value of this project?
• How many shares of common stock must be issued (at what price) to raise the required
capital?
• What is the effect of this new project on the value of the stock of the existing shareholders,
if any?
Lockheed Tri Star and Capital Budgeting1
In 1971, the American firm Lockheed found itself in Congressional hearings seeking a $250-
million federal guarantee to secure bank credit required for the completion of the L-1011 Tri Star
program. The L-1011 Tri Star Airbus is a wide-bodied commercial jet aircraft with a capacity of up to
400 passengers, competing with the DC-10 trijet and the A-300B airbus.
Spokesmen for Lockheed claimed that the Tri Star program was economically sound and that
their problem was merely a liquidity crisis caused by some unrelated military contracts. Opposing
the guarantee, other parties argued that the Tri Star program had been economically unsound and
doomed to financial failure from the very beginning.
1 Facts and situations concerning the Lockheed Tri Star program are taken from U. E. Reinhardt, "Break-Even
Analysis for Lockheed's Tri Star: An Application of Financial Theory," Journal of Finance 27 (1972), 821-838, and
from House and Senate testimony.

4. The debate over the viability of the program centered on estimated “break-even sales” the
number of jets that would need to be sold for total revenue to cover all accumulated costs.
Lockheed’s CEO, in his July 1971 testimony before Congress, asserted that this break-even point
would be reached at sales somewhere between 195 and 205 aircraft. At this point, Lockheed had
secured only 103 firm orders plus 75 options-to-buy, but they testified that sales would eventually
exceed the break-even point and that the project would thus become “a commercially viable
endeavor.”
Costs
The preproduction phases of the Tri Star project began at the end of 1967 and lasted four
years, after running about six months behind schedule. Various estimates of the up-front costs
ranged between $800 million and $1 billion. A reasonable approximation of these cash outflows
would be $900 million, occurring as follows:
End of Year Time “Index” Cash Flow ($mm)
1967 t=0 -$100
1968 t=1 -$200
1969 t=2 -$200
1970 t=3 -$200
1971 t=4 -$200
According to Lockheed testimony, the production phase was to run from the end of 1971 to
the end of 1977, with about 210 Tri Stars as the planned output. At that production rate, the average
unit production cost2 would be about $14 million per aircraft. The inventory-intensive production
costs would be relatively front-loaded, so that the $490 million ($14 million per plane, 35 planes per
year) annual production costs can be assumed to occur in six equal increments at the end of years
1971-1976 (t=4 through t=9).
Revenues
In 1968, the expected price to be received for the L-1011 Tri Star was about $16 million per
aircraft. These revenue flows would be characterized by a lag of a year to the production cost
outflows; annual revenues of $560 million can be assumed to occur in six equal increments at the end
of years 1972-1977 (t=5 through t=10). Inflation-escalation terms in the contracts ensured that any
future inflation-based cost and revenue increases offset each other nearly exactly, thus providing no
incremental net cash flows.
Deposits toward future deliveries were received from Lockheed customers. Roughly one-
quarter of the price of the aircraft was actually received two years early. For example, for a single Tri
Star delivered at the end of 1972, $4 million of the price is received at the end of 1970, leaving $12
million of the $16 million price as cash flow at the end of 1972. So, for the 35 planes built (and
presumably, sold) in a year, $140 million of the $560 million in total annual revenue is actually
received as a cash flow two years earlier.
2 Excluding preproduction cost allocations. That is, the $14 million cost figure is totally separate from the $900
million of preproduction costs shown in the table above.

5. Discount Rate
Experts estimated that the cost of capital applicable to Lockheed’s assets (prior to Tri Star)
was in the 9%-10% range. Since the Tri Star project was quite a bit riskier (by any measure) than the
typical Lockheed operation, the appropriate discount rate was almost certainly higher than that.
Using 10% should give a reasonable (although possibly generous) estimate of the project’s value.
Break-Even Revisited
In an August 1972 Time magazine article, Lockheed (after receiving government loan
guarantees) revised its break-even sales volume: “[Lockheed] claims that it can get back its
development costs [about $960 million] and start making a profit by selling 275 Tri Stars.”3 Industry
analysts had predicted this (actually, they had estimated 300 units to be the break-even volume) even
prior to the Congressional hearings.4 Based on a “learning curve” effect, production costs at these
levels would average only about $12.5 million per unit, instead of $14 million as above. Had
Lockheed been able to produce and sell as many as 500 aircraft, this average cost figure may have
been even as low as $11 million per aircraft.
Lockheed had testified that it had originally hoped to capture 35%-40% of the total free-world
market of 775 wide bodies over the next decade (270-310 aircraft). This market estimate had been
based on a wildly optimistic assumption of 10% annual growth in air travel; at a more realistic 5%
growth rate, the total world market would have been only 323 aircraft. The Tri Star’s actual sales
performance never approached Lockheed’s high expectations. Lockheed’s share price plummeted
from a high of about $70 to around $3 during this period. There were about 11.3 million shares of
Lockheed common outstanding during this period. Exhibit 1 contains additional information on
Lockheed’s common stock.
Value Added?
As concerns the economic viability of the Tri Star program, there are several interesting
points to consider:5
• At planned (210 units) production levels, what was the true value of the Tri Star
program?
• At a “break-even” production of roughly 300 units, did Lockheed really break even in
value terms?
• At what sales volume did the Tri Star program reach true economic (as opposed to
accounting) break-even?
• Was the decision to pursue the Tri Star program a reasonable one? What were the effects
of this “project” on Lockheed shareholders?
3 Time (August 21, 1972), 62.
4 Mitchell Gordon, "Hitched to the Tri Star—Disaster at Lockheed Would Cut a Wide Swathe," Barron's (March
15, 1971), 5-14.
5 Ignore taxes and depreciation tax shields here. In cases near the "break-even" volume, these would tend to
offset each other nearly completely.

6. LOCKHEED, INC. COMMON STOCK
Monthly Prices, 1967-1973
DollarPriceofaShareofCommon
$71
$3.25
Jan ‘67
$0
$10
$20
$30
$40
$50
$60
$70
$80
Jan ‘68 Jan ‘69 Jan ‘70 Jan ‘71 Jan ‘72 Jan ‘73 Jan ‘74