Case
Solutions Book Exercises
- Course
- Institution
Solutions Book Exercises
[Show more]
Seller
Follow
PVives
Content preview
CHAPTER 9: THE CAPITAL ASSET PRICING MODELCHAPTER 9: THE CAPITAL ASSET PRICING MODEL
PROBLEM SETS
1. E (rP ) = rf + β P [ E (rM ) − rf ]
.12
.18 = .06 + β P [.14 − .06] → β P = = 1.5
.08
2. If the security’s correlation coefficient with the market portfolio doubles (with all
other variables such as variances unchanged), then beta, and therefore the risk
premium, will also double. The current risk premium is: 14% – 6% = 8%
The new risk premium would be 16%, and the new discount rate for the security
would be: 16% + 6% = 22%
If the stock pays a constant perpetual dividend, then we know from the original data
that the dividend (D) must satisfy the equation for the present value of a perpetuity:
Price = Dividend/Discount rate
50 = D/0.14 D = 50 0.14 = $7.00
At the new discount rate of 22%, the stock would be worth: $7/0.22 = $31.82
The increase in stock risk has lowered its value by 36.36%.
3. a. False. β = 0 implies E(r) = rf , not zero.
b. False. Investors require a risk premium only for bearing systematic
(undiversifiable or market) risk. Total volatility, as measured by the standard
deviation, includes diversifiable risk.
c. False. Your portfolio should be invested 75% in the market portfolio and 25%
in T-bills. Then: β P = (0.75 1) + (0.25 0) = 0.75
4. The expected return is the return predicted by the CAPM for a given level of
systematic risk.
E (ri ) = rf + βi [ E (rM ) − rf ]
E (r$1 Discount ) = .04 + 1.5 (.10 − .04) = .13, or 13%
E (rEverything $5 ) = .04 + 1.0 (.10 − .04) = .10, or 10%
9-1
Copyright © 2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
, CHAPTER 9: THE CAPITAL ASSET PRICING MODEL
5. According to the CAPM, $1 Discount Stores requires a return of 13% based on its
systematic risk level of β = 1.5. However, the forecasted return is only 12%.
Therefore, the security is currently overvalued.
Everything $5 requires a return of 10% based on its systematic risk level of β = 1.0.
However, the forecasted return is 11%. Therefore, the security is currently
undervalued.
6. Correct answer is choice a. The expected return of a stock with a β = 1.0 must, on
average, be the same as the expected return of the market which also has a β = 1.0.
7. Correct answer is choice a. Beta is a measure of systematic risk. Since only
systematic risk is rewarded, it is safe to conclude that the expected return will be
higher for Kaskin’s stock than for Quinn’s stock.
8. The appropriate discount rate for the project is:
rf + β × [E(rM ) – rf ] = .08 + [1.8 (.16 – .08)] = .224, or 22.4%
Using this discount rate:
10
$15
NPV = −$40 + t
= −$40 + [$15 Annuity factor (22.4%, 10 years)] = $18.09
t =1 1.224
The internal rate of return (IRR) for the project is 35.73%. Recall from your
introductory finance class that NPV is positive if IRR > discount rate (or,
equivalently, hurdle rate). The highest value that beta can take before the hurdle
rate exceeds the IRR is determined by:
.3573 = .08 + β × (.16 – .08) β = .2773/.08 = 3.47
9. a. Call the aggressive stock A and the defensive stock D. Beta is the sensitivity
of the stock’s return to the market return, i.e., the change in the stock return
per unit change in the market return. Therefore, we compute each stock’s beta
by calculating the difference in its return across the two scenarios divided by
the difference in the market return:
−.02 − .38 .06 − .12
βA = = 2.00 βD = = 0.30
.05 − .25 .05 − .25
9-2
Copyright © 2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller PVives. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $4.31. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
66579 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now