Time Value of Money and CAPM model

Problem: PV of cash Flow stream.
A rookie quarterback is negotiating his first NFL contract. His opportunity cost is 10%. He has been offered three possible 4-year contracts. Payments are guaranteed and they would be made at the end of each year. Terms of each contract are as follows:
Year 1 2 3 4
Contract 1 $3,000,000 $3,000,000 $3,000,000 $3,000,000
Contract 2 $2,000,000 $3,000,000 $4,000,000 $5,000,000
Contract 3 $7,000,000 $1,000,000 $1,000,000 $1,000,000
As his advisor, which contract would you recommend that he should accept?

Problem: FV of uneven cash flow
You want to buy a house within 3 years, and you are certainly saving for the down payment. You plan to save $5000 at the end of first year, and you anticipate that your annual savings will increase by 10% annually thereafter. Your expected annual return is 7%. How much will you have for a down payment at the end of year 3?

Problem: Evaluating lump sums and annuities
Crissie just won the lottery, and she must choose between three award options. She can elect to receive a lump sum today $61 million, to receive 10 end-of-year payments of $9.5 million, or to receive 30 end-of-year payments of $5.5 million.
a.If she thinks she can earn 7% annually, which should she choose?
b.If she thinks she can earn 8% annually, which should she choose?
c.If she thinks she can earn 9% annually, which should she choose?
d.Explain how interest rates influence the optimal choice.

Problem: PV and Loan eligibility
You have saved $4000 for a down payment on a new car. The largest monthly payment you can afford is $350. The loan will have a 12% APR based on end-of-months payments. What is the most expensive car you can afford if you finance it for 48 months? For 60 months?

Problem: Expected Returns
Stock X and Y have the following probability distributions of expected future returns:
Probability X Y
0.1 (10%) (35%)
0.2 2 0
0.4 12 20
0.2 20 25
0.1 38 45
a. Calculate the expected rate of return, ry, for stock Y (rx=12%)
b. Calculate the standard deviation of expected returns for stock X (S.D for stock Y=20.35%). Now calculate the coefficient of variation for stock Y. Is it possible that most will regard stock Y as being less risky than stock X? Explain.

Problem: CAPM and required return
Bradford manufacturing company has a beta of 1.45, while Farley Industries has a beta of 0.85. The required return on an index fund that holds the entire stock market is 12%. The risk free rate of interest is 5%. By how much does Bradford's required return exceed Farley's required return?

Problem: Required Rate of return
Suppose rRF=9%, rM=14% and bi=1.3
a.What is ri, the required rate of return on Stock i?
b.Now suppose that rRF(1) increases to 10% or (2) decreases to 8%. The slope of SML remains constant. How much this affect rM and ri?
c.Now assume that rRF remains at 9% but rM (1) increases to 16% or (2) falls to 13%. The slope of SML does not remain constant. How would these changes affect ri?

Problem: Security Market Line
You plan to invest in Kish Hedge fund, which has total capital of $500 million invested in 5 stocks:
Sock Investment Stock's Beta coefficient
A $160 million 0.5
B $120 million 1.2
C $80 million 1.8
D $80 million 1.0
E $60 million 1.6

Kish's beta coefficient can be found as a weighted average of its stocks' betas. The risk free rate is 6%, and you believe the following probability distribution for future market returns is realistic:

Probability Market Return
0.1 -28%
0.2 0
0.4 12%
0.2 30%
0.1 50%

a.What is the equation for Security Market Line (SML)? (Hint : First determine the expected market return)
b.Calculate Kish's required rate of return.
c.Suppose Rick Fish, the president, receives a proposal from a company seeking new capital. The amount needed to take a position in the stock is $50 million, it has an expected return of 15%, and its estimated beta is 1.5. should Kish invest in the new company? At what expected rate of return should Kish be indifferent to purchasing the stock?