Finance 303 Midterm Study Help

Annuity

You finance a $385,00 loan to buy a house. The loan has an interest rate of 6.4% with payments made annually at the end of the year for 18 years. What is the annual payment?

FV of Annuity

Suppose you deposit $400 at the end of each year for 10 years and your interest rate is 8%. What is the value of your account at the end?

Beta (reversed to solve for the market's variance, then Standard Deviation)

Suppose a stock's beta is 1.5, the covariance of the stock and the market is 0.05. What is the standard deviation of the market? (Hint: reverse the beta equation)

Compound Interest

How much will you have in your account at the end if you put $2,000 for 5 years with monthly compounding at 6% APR (equivalent to a monthly discount rate of 0.5%)?

Annuity Due, then DCF (to discount back to today)

Suppose you receive $300 at the beginning of each year for 6 years, but the first payment occurs 3 years from today (i.e. Year 3). If your discount rate is 5% what is the PV?

Effective Annual Returns (AER)

Suppose you have an APR of 12% compounded monthly. What is the AER?

Bond Valuation

Suppose you have a bond with the following characteristics. A face value of $1,000, 6% semi-annual coupon rate, 15 years to maturity, and a YTM of 5% (equivalent to a semi-annual discount rate of 2.5%). What is the price of your bond?

Rate of Return – Stocks

Suppose you buy a stock for $50, earned four quarterly dividends of $1 each, and the value of your stocks grew by 10%. What was the rate of return of your stock?

DCF

An investment has the following projected cash flows: Year 1 2 3 4 Cashflow $120 $140 $160 $180 With an opportunity cost of capital of 10%, what is the investment's PV?

Fisher Equation

Suppose the real interest rate is 2.2% and the nominal interest rate is 7.5%. What is the inflation rate?

Expected Value

Suppose the following are possible returns for an investment next period: Event Returns Probabilities Boom 18% 30% Base 7% 50% Recession -8% 20% What is the expected return of this investment next period?

Expected Return, then Variance, then Standard Deviation (square root of Variance)

Suppose an investment has the following past returns: 8%, -4%, 12%, 3%, and -1%. What is the standard deviation of this investment?

Expected Return

Suppose an investment had the following past returns: 3%, 12%, -5%, and 10%. What is the expected return using past data?

Beta, then CAPM

Suppose a stock has the following characteristics. The risk-free rate is 2%, the covariance with the stock market is 0.018 and the standard deviation of the market is 15%, and the expected market return is 12%. Under CAPM, what is the required rate of return?

Correlation Coefficient (with Standard Deviation from Variance)

Suppose two stocks: A and B have the following characteristics. The covariance of A and B is 0.008, the variance of A is 0.04 and the variance of B is 0.01. What is the correlation coefficient between A and B?

Expected Return, then Variance, then Standard Deviation, then the 95% range (mean ± 2 standard deviations)

Suppose an investment had the following past returns: 2%, 10%, 15%. Assuming normality, what is 95% probability range of returns (using the range assumptions we learned in this course)?

CAPM, then GGM, then DCF

Suppose a stock has the following characteristics. It is expected to grow its dividends at 10% for 2 years after the upcoming dividend of $1.50 and then 5% forever. The risk-free rate is 2%, expected market return is 7.2%, and beta is 1. What is the PV of this stock?

CAPM

Suppose a stock has the following characteristics. The risk-free rate is 2.5%, the expected market risk premium is 6%, and beta is 1.3. Under CAPM, what is the required rate of return?

GGM

Suppose a stock just paid a dividend of $1.70 and is expected to grow at 5% forever and the required rate of return is 9.5%. What is the intrinsic value of this stock?

Covariance (with Expected Return for each stock's average)

Suppose two stocks: A and B have the following 3 year returns: ● Stock A: 6%, 14%, -2% ● Stock B: 4%, 5%, 1% Using the data above, what is the covariance of stocks A and B?

Annuity, then DCF (to discount the second salary stream back to today)

Suppose you expect a salary of $150,000 for 15 years and then $250,000 for the next 5 years. Assuming a discount rate of 6%, what is the present value of your salary?

Annuity (value of withdrawals at retirement), then FV of Annuity (solve for the yearly deposit)

You turned 25 and want to start saving for retirement at 65. You want to withdraw $100,000 every year for 20 years (with the first withdrawal at 66). The current savings account rate is 4%. How much do you need to start depositing every year (starting at 26) at equal amounts to fulfill your retirement goals?