In: Finance
Step by step with provided answers. What is the formula step by step? Thank you so much.
10. Given annual returns of 14%, 8%, -10% and 4%, what is the geometric average?
= 3.61%
11. What is the arithmetic average of the returns in question 10?
= 4.00%
12. What is the standard deviation of the returns in question 10?
= 10.20%
16. Moi International wants to issue 20-year, zero coupon bonds that yield 5 percent. What price should they charge for these bonds if they have a par value of $1,000? Assume annual compounding.
= $376.89
17. A stock has an expected return of 15%. The risk-free rate is 3%, and the market risk premium is 8%. What is the beta for this stock?
= 1.50
18. The beta of the overall market is _____ and the beta of a risk-free security of is _____.
= 1; 0.
19. The stock of RWC has a beta of 1.28. The expected return on the market is 8 percent and the risk-free rate is 1.5 percent. What is the expected return on this stock?
=9.82 percent
=Bond price $1,256.82
a. What are the expected dividends in years 1 and 2?
=D1 = $1.40, D2 = 1.9
b. What would you be willing to pay for this stock today?
=P0 = $46.24
10.
Given, R1 = 0.14, R2 = 0.08, R3 = -0.10, R4 = 0.04
Geometric Return = [(1+R1)(1+R2).....(1+Rn)]1/n - 1
= [(1+0.14)(1+0.08)(1-0.10)(1+0.04)]1/4 - 1 = 0.0361 or 3.61%
11.
Arithmetic Average = [R1+R2+....Rn]/n
= [0.14 + 0.08 - 0.10 + 0.04]/4 = 0.04 or 4%
12.
Average Geometric Return = G = 0.0361
Standard Deviation = √ [(R1- G)2 + (R2-G)2 + .....+ (Rn-G)2]/n-1
= √ [(0.14 - 0.0361)2 + (0.08 - 0.0361)2 + (-0.10 - 0.0361)2 + (0.04 - 0.0361)2 ]/3
= √0.0313/3 = 0.1020 or 10.20%
16.
Par Value of Bond = FV = $1000
Interest Rate = r = 5% or 0.05
Number of Years = n = 20
PV = FV/(1+r)n = 1000/(1+0.05)20 = $376.89
17.
Using CAPM model
ERi = Rf + β(ERm - Rf)
where,
ERi = Expected return of stock = 15%
Rf = Risk-free rate = 3%
β = Beta of the stock
ERm - Rf = Market Risk Premium = 8%
=> 15 = 3 + β*8
=> β = 1.5
18.
Beta describes how much a stock's price moves with respect to market
The beta of the overall market is 1 and the beta of a risk-free security of is 0
19.
Using CAPM model
ERi = Rf + β(ERm - Rf)
where,
ERi = Expected return of stock
Rf = Risk-free rate = 1.5
β = Beta of the stock = 1.28
ERm = Expected Return on Market = 8%
=> ERi =1.5 + 1.28(8 - 1.5) = 9.82%
-------------------------------------
Number of periods = n = 22*2 = 44 semiannual periods
Yield I/Y= r = 4.2%/2 = 2.1%
SemiAnnual Payment P = 6%*1000/2 = $30
Face Value FV = $1000
Hence, PV = P/(1+r) + P/(1+r)2 + .... + P/(1+r)n + FV/(1+r)n
= P[1 - (1+r)-n]/r + FV/(1+r)n = 30(1 - 1.021-44)/0.021 + 1000/1.02144 = $1256.82
------------------------------------
Given, D0 = Dividend Now = $1
(a) Growth rate for next 2 years = 40%
=> D1 = 1*(1+0.40) = $1.40
D2 = 1.40*(1+0.40) = $1.96
(b) D3 = D2*(1+0.05) = 1.96(1+0.05) = $2.06
Required Return = r = 9%
Using Gordons Growth model,
P2 = D3/(r - g) = 2.06/(0.09 - 0.05) = 51.5
Present Value = P0 = D1/(1+r) + D2/(1+r)2 + P2/(1+r)2 = 1.40/(1+0.09) + 1.96/(1+0.09)2 + 51.50/(1+0.09)2 = $46.28