in order to find rate of interest that applies for a period of six months (for example), we do (1 + interest/discount rate for one period )^(periods)-1, then we convert that number to a percentage
Q: a company is planning to pay 70% of its earnings in the form of a dividend each year far into the future, while retaining what remains of earnings to finance new projects with an expected rate of return of 16.5%. Next year’s earnings are projected as $117 million. The firm has 12 million shares of stock outstanding, and its opportunity cost of capital is 10.2% both for current and for future projects. If we assume that earnings growth is due entirely to new investment, find the stock price per share for this company.
A: 30% retention rate, 16.5% return on new investment, g=retention rate x return on new investment, g=(0.3)(0.165)=0.495 amount of div=(0.7)($117 million)=$81.90 million
Div 1=(81.9 million)/(12 million shares outstanding)=$6.825/share Po=Div1/(Re-g)=6.825/(0.102-0.0495)=130.00
Q: One solution to the maintenance problem in your workspace is to outsource a company that will charge $140,000 per year indefinitely with the first payment one year from now. The alternative is to purchase equipment that costs $315,000 now and also requires $60,000 per year for supplies in years one through four, at which time the equipment becomes worthless and needs to be replaced (we assume that it can be replaced at the original cost, and that the price of supplies remains unchanged). Find the equivalent annual annuity for this alternative using an interest rate of 11.2% and justify your decision (either to outsource or to use the alternative method) by computing the yearly savings.
A: outsource=140,000/year, alternative: CF0: -315,000, CF1:-60,000, CF3:-60,000, CF4: -60,000, solve for NPV, NPV=-500,354.64, N:4, PV:-500,354.64, I/YR: 11.2, FV: 0, solve for PMT, PMT: 161,966.69; 161,966.69-140,000=21,966.69 saved per year by outsourcing, outsourcing is answer.
portfolio weight-the fraction of the total investment in a portfolio held in each individual investment in the portfolio
portfolio weight (wi)=(value of investment i)/(total value of portfolio), which is a percentage
value of investment=shares of a company x $ per share of that company, value of portfolio is amount money in all companys involved
return on portfolio-the weighted average of the return on the investments in a portfolio, where the weights correspond to the portfolio weights,
if apple earns a 10% return and Cocacola earn a 15% return, then 40% (based off calculating portfolio weight) of the portfolio earns 10%, and 60% of the portfolio earns 15%, so the portfolio as a whole earns: (0.40)(10%)+(0.6)(15%)=13%
expected return of a portfolio-the weighted average of expected returns of the investments in a portfolio, where the weights correspond to the portfolio weights
-volatility of a portfolio-the total risk, measured as a standard deviation, of a portfolio
-correlation- a measure of the degree to which returns share common risk. it is calculated as the covariance of the returns divided by the product of the standard deviations of each return.
Dell and Microsoft have high correlation because computers typically ship with Microsoft Windows installed, so both companies benefit from increased spending on computers
-in fact when combining stocks into a portfolio, unless the stocks all have a perfect positive correlation of +1 with each other, the risk of the portfolio will be lower than the weighted average volatility of the individual stocks
-the expected return of a portfolio is equal to the weighted average expected return of its stocks, but the volatility of a portfolio is less than the weighted average volatility. as a result, it’s clear that we can eliminate some volatility by diversifying.