Question

Conditional Ltd. operates under ideal conditions of uncertainty. It has just purchased a

new machine, at a cost of $3,575.10, paid for entirely from the proceeds of a stock issue.

The interest rate in the economy is 8%. The machine is expected to last for two years,

after which time it will have zero salvage value.

The new machine is an experimental model, and its suitability for use in Conditional’s

operations is not completely known. Conditional assesses a 0.75 probability that there will

be a major machine failure during the first year of operation, and a 0.25 probability that

the machine will operate as planned. If there is a major failure, cash flow for the year will

be $1,000. If the machine operates as planned, cash flow will be $3,000 for the year. If

there is no major failure in the first year, the probability of a major failure in the second

year, and resulting cash flows of $1,000, falls to 0.60. If there is no major failure in the

second year, cash flows for that year will again be $3,000. However, if there is a major

failure in the first year, the lessons learned from correcting it will result in only a 0.10

probability of failure in the second year.

It turns out that there is no major failure in the first year.

1. What is market value of company's stock at t=0, just after the machine is acquired, assuming that the market's expectations are the same as those given in the problem? Explain.

2. Assume that the market's t=0 expectations are the same as given in the problem and that no new information is available to the market until earnings are reported at t=1 (i.e., it is not possible to observe which state occurred except by observing reported financial statement information). What is the dollar increase (decrease) in the market value of the company's stock upon the release of the t=1 financial statements? Explain.

Answer 1

Part (1)

Let's calculate the NPV at each node = C1/(1 + r) + C2/(1 + r)²

Node 1 : NPV = 1,000 / (1 + 8%) + 1,000 / (1 + 8%)² = 1,783.26

Node 2: NPV = 1,000 / (1 + 8%) + 3,000 / (1 + 8%)2 = 3,497.94

Node 3: NPV = 3,000 / (1 + 8%) + 1,000 / (1 + 8%)2 = 3,635.12

Node 4: NPV = 3,000 / (1 + 8%) + 3,000 / (1 + 8%)2 = 5,349.79

Hence, market value of company's stock at t=0, just after the machine is acquired, assuming that the market's expectations are the same as those given in the problem = Expected value = Sum of (NPV x joint probability) across all the four nodes = 1,783.26 x 0.075 + 3,497.94 x 0.675 + 3,635.12 x 0.15 + 5,349.79 x 0.10 = $ 3,575.10

Part (2)

No major failure in year 1.

Now two states are posible:

Major failure in year 2; C2 = 1,000; p2 = 0.60

No major failiure in year 2: C2 = 3000; p2 = 0.4

Hence, expected cash flow in year 2 = Sum of (probability x cash flows) = 0.6 x 1,000 + 0.4 x 3,000 = 1,800

Hence, PV of cash flows at year 1 = Expected cash flow in year 2 / (1 + r) = 1,800 / (1 + 8%) = $  1,666.67

Hence, value of the company's stock = Cash flow from year 1 + PV of future cash flows at year 1 = 3,000 + 1,666.67 =  4,666.67

Hence, the dollar increase (decrease) in the market value of the company's stock upon the release of the t=1 financial statements = 4,666.67 - 3,575.10 = $ 1,091.56