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Delia Martin has $10,000 that she can deposit in any of three savings accounts for a 3-year period. Bank A compounds interest on an annual basis, bank B compounds interest twice each year and Bank C compounds interest each quarter. All three banks shave a stated annual interest rate of 4 percent.
a)What amount would Ms Martin have at the end of the third year leaving all interest paid on deposit in each bank?
Bank A (principal+ interest)10,000 x 1.04^ 3=$11248.64
Bank B(principal+ interest)10,000 x 1.02%^6=$11261.62
Bank C(principal+ interest)10,000 x 1.01^12=$11268.25
So, Bank A interests: 11,248.64-10,000=$1,248.64
Bank B interests: 11,261.62-10,000=$1,261.62
Bank C interests: 11,268.25-10,000=$1,268.25
b) What effective annual rate (EAR) would she earn in each of the banks?
Bank AFor bank A compounds interest on an stated annual basis, thus, its annual interest rate is 4%.
c) On the basis of your findings in A and B, which bank should Ms Martin deal with? Why?
I suggest Ms Martin to choose bank C. Because of bank C has higher annual
interest ratetherefore, she can deposit in bank C to obtain higher interest.
d) If a fourth bank -Bank D, also with a 4percent stated interest rate – compounds interest continuously, how much would Ms Martin have at the end of the third year? Does this alternative change your recommendation in c? Explain why or why not?
If deposit in bank D, Ms Martin could gains interest plus principal as below
10000 x 2.7183×0.04 =$11274.83
This result would be affecting the suggestion in question C. Because compound interest will accrue continuously based on the generated interest in a certain term plus principal, and thus, Ms Martin could receiving more interest if she deposits in bank D.
Q2- You have been asked for your advice in selecting a portfolio of assets and have been supplied with the following data:
Asset A Asset BAsset C
No probabilities have been supplied. You have been told that you can create two portfolios – one consisting of assets A and B and the other consisting of assets A and C -by investing equal proportions (i.e.50 percent) in each of the two component assets.
a)What is the expected return for each asset over the 3-year period?
b) What is the standard deviation for each asset’s return?
Asset A√(12%-15%2+14%-15%2+16%-15%2 +18%-15%2) / 4 =2.24
Asset B√(16%-13%2+14%-13%2+12%-13%2 +10%-13%2) / 4 =2.24
Asset C√(12%-15%2+14%-15%2+16%-15%2 +18%-15%2) / 4 =2.24
c) What is the expected return for each of the two portfolios?
A and B18% x 50%+10% x 50%=14%
A and C18% x 50%+18% x 50%=18%
d) How would you characterize the correlations of returns of the two assets making up each of the two portfolio identified in c?
Correlation of A&B = -5 / (2.24 x 2.24) = -1 They are perfect negative correlated.
Correlation of A&C = 5 / (2.24 x 2.24) = 1 They are perfect correlated.
e) What is the standard deviation of each portfolio?
STDEV(A&B) = √0.5 2 x 2.24 2 + 0.5 2 x 2.24 2 + 2 (0.5 x 0.5 x (-1) x 2.24 x 2.24) =0
STDEV(A&C) = √0.5 2 x 2.24 2 + 0.5 2 x 2.24 2 + 2 (0.5 x 0.5 x 1 x 2.24 x
f) Which portfolio would you recommend? Why?
I would recommend A&B portfolio. It has the standard deviation of zero. There is perfect negative correlation between asset A and B. It will completely eliminate risk.
Q 3- Perry Motor’s common stock currently pays an annual dividend of $1.80 per share. The required return on the common stock is 12%. Estimate the value of the common stock under each of the following dividend-growth-rate assumptions.
a) Dividends are expected to grow at an annual rate of 0 percent to infinity.
Stock value = =$15
b) Dividends are expected to grow at a constant annual rate of 5 percent to infinity.
Stock value = =$27