20. Payback and NPV. A project has a life of 10 years and a payback
period of 10 years. What must be true of project NPV?



21. IRR/NPV. Consider this project with an internal rate of return of
13.1 percent. Should you accept or reject the project if the discount
rate is 12 percent?

18. Portfolio Analysis. Use the data in the previous problem and
consider a portfolio with weights of .60 in stocks and .40 in bonds.
a. What is the rate of return on the portfolio in each scenario?
b. What is the expected rate of return and standard deviation of the portfolio?
c. Would you prefer to invest in the portfolio, in stocks only, or in bonds only?

21. CAPM and Expected Return. The following table shows betas for
several companies. Calculate each stock?s expected rate of return
using the CAPM. Assume the risk-free rate of interest is 5 percent.
Use a 9 percent risk premium for the market portfolio.

Company Beta
Cisco 2.03
CitiGroup 1.36
Merck .40
Walt Disney .84

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Request for Question Clarification by livioflores-ga on 05 Jun 2005 07:33 PDT

In problem 18: What is the "previous problem" data?

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Clarification of Question by noah0304-ga on 05 Jun 2005 09:45 PDT

17. Scenario Analysis. Consider the following scenario analysis:
Rate of Return
Scenario 		Probability 	Stocks Bonds
Recession 		.20 			?5% 		+14%
Normal economy 	.60 			+15 		+8
Boom 			.20 			+25		+4
Value of Reserves, Value of Reserves, Value of
per Barrel 50 Million Barrels Dryholes
Boom $4.00 $200,000,000 0
Normal economy $5.00 $250,000,000 0
Recession $6.00 $300,000,000 0

a. Is it reasonable to assume that Treasury bonds will provide higher
returns in recessions than in booms?

Yes, it is reasonable. Interest rates are procyclic; that is, they
rise when the economy is booming and fall when the economy goes into a
recession. During recessions, the government usually tries to keep
interest rates low in order to stimulate investment. Since bond prices
and interest rates go in opposite directions (when interest rates
rise, bond prices fall, and vice versa), then we would expect bond
prices to go up when the economy hits a recession

b. Calculate the expected rate of return and standard deviation for
each investment.
ER = 0.2*(-5) + 0.6*15 + 0.2*25
ER = 13%
Likewise, the expected return on bonds is 8.4%.
Variance = 0.2*(-5-13)^2 + 0.6*(15-13)^2 + 0.2*(25-13)^2
Variance = 96
So the standard deviation of the return on stocks is 9.79% (square
root of 96). Likewise, the standard deviation of the return on bonds
is 3.2%.

c. Which investment would you prefer? 
Although the portfolio of stocks has a higher expected return than
bonds, it also carries a higher variance, so there is no clear-cut
answer to this question.
Personally, since I am very risk averse, I would choose to invest in
bonds only.

Hi!!


20. A project has a life of 10 years and a payback period of 10 years.
What must be true of project NPV?

The payback period is the number of years required to return the
original investment from the net cash flows (net operating income
after taxes plus depreciation).
Since Payback Period calculations do not take into account the time
value of money project's NPV is negative (if required return is - as
always - greater than zero).

If PP = 10 years then (CF1+CF2+...+CF10)-I = 0

We also know that:
NPV = PV - I

Since:
         CF1           CF2                CF10           
PV  = ---------  +  ----------  +...+  ---------- =  
      (1 + r)^1     (1 + r)^2	      (1 + r)^10   

   
If r > 0 then for each i=1 to 10 is:
CFi/(1+r)^i < CFi

Then if (CF1+CF2+...+CF10)-I = 0 we have:

NPV = PV-I < (CF1+CF2+...+CF10)-I = 0

The equality is valid only if r=0%, and this last thing does not
happen in real life for a 10 years project.

              --------------------------

21. Consider this project with an internal rate of return of 13.1
percent. Should you accept or reject the project if the discount rate
is 12 percent?

The IRR rule states that you must accept a project if its IRR is
greater than the discount rate; and reject the project if its IRR is
lower than the discount rate.

In this case IRR = 13.1% > 12% = Discount rate ==> Accept the project.

              ---------------------------

18. Use the data in the previous problem and consider a portfolio with
weights of .60 in stocks and .40 in bonds.

Relevant info:
---------------------------------------------------------------
                                          Rate of Return
Scenario 	Probability            Stocks          Bonds
---------------------------------------------------------------
Recession         .20                    ?5%           +14%
Normal economy    .60                   +15%            +8%
Boom              .20                   +25%            +4%
---------------------------------------------------------------

a. What is the rate of return on the portfolio in each scenario?

-Recession:
Rp = Weight of Stocks * Stocks rate + Weight of Bonds * Bonds rate =
   = 0.60 * (-5%) + 0.40 * 14% =
   = 2.6%

-Normal Economy:
Rp = 0.60 * 15% + 0.40 * 8% =
   = 12.2%

-Boom:
Rp = 0.60 * 25% + 0.40 * 4% =
   = 16.6%


b. What is the expected rate of return and standard deviation of the portfolio?

Expected Return = Weighted sum of the expected returns of each scenario =
                = 0.20*Recession rate + 0.60*Normal rate + 0.20*Boom rate =
                = 0.20 * 2.6% + 0.60 * 12.2% + 0.20 * 16.6% =
                = 11.16%

Variance = 0.2*(2.6-11.16)^2 + 0.6*(12.2-11.16)^2 + 0.2*(16.6-11.16)^2 =
         = 21.2224 

Standard Deviation = SQRT(Variance) = 4.61%


c. Would you prefer to invest in the portfolio, in stocks only, or in bonds only?
In general this is a subjective question, the answer depends on
personal risk aversion.
Your answer to the problem #17 is valid and helpful here, note that
the portfolio diversifies risks and provides a good rate of return
(11.16%) in the middle of the pure stocks (13%) and pure bonds (8.4%)
options; closer to the highest rate. The Standard deviation of the
portfolio is again in the middle of the other options but closer to
the lowest SD (bonds).
Personally i will take the portfolio option.

               ---------------------------

21. The following table shows betas for several companies. Calculate
each stock?s expected rate of return using the CAPM. Assume the
risk-free rate of interest is 5 percent. Use a 9 percent risk premium
for the market portfolio.

-----------------------
Company           Beta
-----------------------
Cisco             2.03
CitiGroup         1.36
Merck             0.40
Walt Disney       0.84
-----------------------

According to the CAPM to find rE (cost of equity) we have that:
rE = rF + rP * BETA 

where:
rE = stock rate
rF = risk free rate
rP = market risk premium = rE - rF 


-Cisco:
rE = 5% + 9% * 2.03 = 23.27%

-CitiGroup:
rE = 5% + 9% * 1.36 = 17.24%

-Merck:
rE = 5% + 9% * 0.40 = 8.6%

-Walt disney:
rE = 5% + 9% * 0.84 = 12.56%

------------------------------------------------------

I hope that this helps you. Feel free to request for a clarification
if you need it.

Regards,
livioflores-ga