Solutions to sample Midterm 2

Solutions to sample MIDTERM 2

1 a) Applying the SML equation:

.11132 = R_f + 1.04 [.108 - R_f ] => R_f (1 - 1.04) = .11132 - 1.04*0.108

=> R_f = (-.001)/(-0.04) = 2.5%

b) Risk premium for the market portfolio = E(R_m) - R_f = .108 - .025 = 8.3%

c) Risk premium for the stock= E(R_i) - R_f = .11132 - .025 = 8.632%

d) The extra return on the market is -.02 - .108 = -128%. The extra return on the stock will be 1.04 * (-.128) = -13.312%. This means the ex-post E(R) for the stock = .11132 - .13312 = -2.18%

Abnormal return = actual return - ex-post expected return = .0333 - (-0.0218) = 5.51%

2 a) Regardless of what other information is given, we use the yield on 3-month t-bills for the short-term riskfree rate.

R_i = short-term R_f today + beta * [avg. historical stock return - avg. historical short-term R_f]

= 3-month t-bill yld today + beta * [avg. historical stock return - avg. historical return on 3-month t-bills]

= .0185 + 0.88*(0.1218 - 0.0392) = 9.1188%

b) There isn't an equally strong convention governing which t-bond should be used for the long-term riskfree rate, but we stick with using 20-year t-bonds (regardless of what other information is given).

R_i = long-term R_f today + beta * [avg. historical stock return - avg. historical long-term R_f]

long-term R_f today = 20-year t-bond yld today - avg. risk premium for 20-year t-bond = .0552 - (.0577-.0392) = 3.67%

avg. historical long-term R_f = avg. historical short-term R_f = .0392

=> R_i = .0367 + 0.88*(0.1218 - 0.0392) = 10.9388%

3 a) Take the equity beta, and unlever to get the asset beta:

b_a = (D/V) b_d + (E/V) b_e = 0.25*0.11 + 0.75*0.99 = 0.77

b) Now lever up this asset beta using the new debt-to-value ratio:

If D/V = 0.35, then E/V = 0.65 => D/E = 0.35/0.65

b_e = b_a + (D/E)[ b_a - b_d] = 0.77 + (0.35/0.65)*(0.77 - 0.18) = 1.0877

4 a) We really have three separate decisions here:

a) whether to make the initial $13,500,000 investment in clinical trials at time 0

b) whether to invest the additional $7,000,000 investment at time 1 if the earlier trials are not successful.

c) whether to make the $650,000,000 investment to launch the product once trials are successful.

LAUNCH PRODUCT

SUCCESS / AT TIME 1

/ prob 0.35 \ DON'T LAUNCH PRODUCT

/ SUCCESS / AT TIME 2

INVEST IN / INVEST IN / prob 0.2 \ DON'T

/ TRIALS TODAY \ / FURTHER TRIALS \

/ \ / AT TIME 1 \ FAILURE => ABANDON

/ \ FAILURE / prob 0.8

/ prob 0.65 \

\ ABANDON

DON'T INVEST

Consider first whether it is worth launching the product if the trials succeed:

	Expected cashflows each year, starting next year = 45,000,000
	Growth rate for cf = 7%
	PV today of future cashflows = 45,000,000/(.135 - .07) = 692,307,692.31
	NPV of the investment today = 692,307,692.31 - 650,000,000 = 42,307,692.31

=> if the trials succeed, it is worth launching the product

Now consider if it's worth investing in additional trials at time 1:

	With a probability of 0.2, you will launch the product at time 2, and generate a time 2 NPV of $42,307,692.31
	With a probability of 0.8, you abandon the project and end up with zero

=> the NPV at time 1 of making the additional investment = (0.2*42,307,692.31)/1.135 - 7,000,000 = 455,099.97

=> if the first round of trials do not succeed, you will continue the trials

So is it worth launching the first round of trials today?

	With a probability of 0.35, the first round of trials will succeed; you will will launch the product at time 1, and generate a time 1 NPV of $42,307,692.31
	With a probability of 0.65, the first round of trials will not succeed. But you will continue the trials and end up with a time 1 NPV of $455,099.97

=> the NPV at time 0 of launching the first round of trials = (0.35*42,307,692.31 + 0.65*455,099.97)/1.135 - 13,500,000 = -192,945.12

=> they should not launch the clinical trials.

b) You have the opportunity to buy the information at time 1 if the first round of trials don't succeed. If the information is positive, you will go ahead and invest in the second round of trials at time 1, and continue on to launch the product at time 2 once the trials succeed. If the information is negative, you will abandon the trials (and the project).

On the other hand, if you don't buy the information at time 1, then you will make the same decision as before -- namely invest in the second round of trials, and launch the product if the second round of trials succeed.

LAUNCH PRODUCT

SUCCESS / AT TIME 1

/ prob 0.35 \ DON'T

/ POSITIVE => CONTINUE WITH 2ND ROUND AT TIME

INVEST IN / GET INFO / prob 0.2 1; LAUNCH PRODUCT AT TIME 2

TRIALS TODAY \ / AT TIME 1 \

\ / \ NEGATIVE => ABANDON

\ FAILURE / prob 0.8

prob 0.65 \

\ DON'T GET => SAME DECISION AS BEFORE (DO 2ND

INFO ROUND; EARN TIME 1 NPV OF $455,099.97)

If you buy the information at time 1:

	with probability of 0.2, the information is positive; you invest $7,000,000 in the trials at time 1 and pick up a time 2 NPV of $42,307,692.31 when you launch the product.
	with a probability of 0.8, the information is negative; you abandon the project and get nothing

=> the NPV at time 1 of getting the information = 0.2*(42,307,692.31/1.135 - 7,000,00) - 3,500,000 = 2,555,099.97

(We subtract away the time 1 information cost from the expected time 1 "cashflows" resulting from getting the information.)

So when we consider whether to invest in the first round of trials:

	with a probability of 0.35 you end up with a time 1 NPV (from launching the product) of 42,307,692.31
	with a probability of 0.65 you end up with a time 1 NPV (from buying the information) of 2,555,099.97

=> the NPV at time 0 of investing in the first round of trials = (0.35*42,307,692.31 + 0.65*2,555,099.97)/1.135 - 13,500,000 = $1,009,698.05

=> Clearly, they should buy the information. Buying the information increases the NPV of launching the trials enough to make it positive. So now, Baschaproff should launch the clinical trials.

5 a) First we take each firm's equity beta, and unlever to get the asset beta:

Firm P: b_a = (D/V) b_d + (E/V) b_e = (12/40)*0.2 + (28/40)*1.6 = 1.18

Firm Q: b_a = (24/48)*0.3 + (24/48)*2.1 = 1.20

Firm R: b_a = (30/50)*0.4 + (20/50)*2.25 = 1.14

Then we take the average asset beta = (1.18 + 1.2 + 1.14)/3 = 1.1733

b) Using the asset beta estimated in part a, we lever it up to get the estimated equity beta for firm D:

If D/V = 0.4, then E/V = 0.6 => D/E = 0.4/0.6 = 0.6667

b_e = b_a + (D/E)[ b_a - b_d] = 1.1733 + 0.6667*(1.1733 - 0.25) = 1.7889

6 a) Firm-specific news and economy-wide news are both randomly positive or negative; it’s not clear why one type of news is diversifiable and one is not. F Firm-specific news is diversifiable because on a given day it makes some stocks go up and some stocks go down; economy-wide news is not diversifiable because although it is randomly positive or negative (we can't predict it advance whether there will be good news or bad news), once economy-wide news arrives, it makes most stocks move in the same direction.

b) A stock whose expected return is less than the riskfree rate will tend to go down when there is good news about the economy. T E(R) is less than the riskfree rate only when a stock has a negative beta, and a negative beta stock is negatively correlated with the market portfolio. Good news about the economy sends the market up, and a negative beta stock down.

c) If a stock has a beta greater than 1, the stock will tend to fluctuate more than the market when there is good news or bad news about the economy. T A stock with a beta of 1.2 will tend to go up by 1.2% every time the market goes up 1% and down by 1.2% every time the market goes down. So it shows bigger fluctuations.

d) If the economy is expected to do badly enough, the E(R) for the market portfolio can sometimes be less than the riskfree return. F The market portfolio is a risky asset with a positive beta; the expected return always has to be more than the riskfree rate. In other words, the market portfolio always has to have a positive risk premium.

e) If a company increases its debt ratio (holding the investment decision constant), its debt beta will increase. T The risk of a firm's shares has two components, business risk and financial risk. Financial risk increases with debt. So the more debt a firm has, the riskier its shares.

f) If short-term interest rates are expected to increase, the yield on short-term treasuries today > (yield on long-term treasuries today + average historical difference between the two yields). F The terms short-term and long-term are reversed; the yield on long-term treasuries today > (yield on short-term treasuries today + average historical difference between the two yields).

g) Positive NPV projects plot to the left of the SML and negative NPV projects plot to the right. T Positive NPV projects plot above or to the left; negative NPV projects plot below or to the right.

h) If the variables that are used to compute a project's cashflows are estimated carefully to begin with, we will not have to worry about errors in the estimated NPV. F No matter how carefully you estimate a variable, at the end you still have only an estimate. And any estimate contains estimation error. Estimating carefully can reduce estimation error, but it cannot eliminate it.

i) One problem that arises in the context of capital budgeting is that some long-term investments (e. g. R&D expenses) do not show up in the capital budget. T See page 312 in the book.

j) If a project has positive NPV despite a high probability of bankruptcy, stockholders want the project to be accepted; in this situation, they regard bankruptcy as a calculated risk they are prepared to take. T The fact that there is a high probability of bankruptcy is already reflected in the NPV computation. If NPV is positive regardless, then it is a risk stockholders are prepared to take.

k) If stock prices increase sharply, they are then more likely to fall than to go up more. F The market has no memory. Stock prices do not obey the law of gravity.

l) Stock prices follow a random walk with drift; the drift comes from the fact that expected return is positive. T

m) If a market is weak-form efficient, it must automatically be semi-strong form efficient too. F Information about past prices may be fully reflected in today's price, but that does not mean that all other public information must also be fully reflected.

n) In an efficient market, all securities are zero NPV investments. T All securities are correctly priced, which means price is the PV of future cashflows. This makes NPV zero. (Unfortunately, the question on the exam read "In an efficient market, all investments are zero NPV investments". Since positive NPV projects still exist, this is not true. So I'm accepting both True and False as correct answers.)

o) 99% of the time anomalies do not work, but 1% of the time they work and allow you to beat the market. F 99% of the money making rules researchers examine don't work, but those are not called anomalies. "Anomalies" refers only to the 1% that seem to work. So it's wrong to say that 99% of the time anomalies don't work.

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