Chapter 15 Part 1 Flashcards
future value formula
Pn = P0(1+r)n P0= the original principal amount (at year 0), n=the number of compounding periods, r= the rate of interest, pn= the future value of P0 compounded over n periods, at a given rate of interest
senmiannual compounding
bonds. Halve the interest rate since it’s paid twice a year and double the compounding times.
present value
P0= Pn/(1+r)n Pn= the future value of P0, compounded over n periods, at a given rate of interest n= the number of compounding periods, r= the rate of interest, P0= the present value of Pn prior to compounding over n periods, at a given rate of interest
To calculate the number of years it will take for your principal to double,
simply divide 72 by the rate of return.
To calculate the rate of return necessaiy to double an investment amount, given a specific period,
divide 72 by the number of years in which you want your money to double.
The internal rate of return (IRR) is expressed as r, the compounded interest rate or yield used to
calculate the present value or future value of an investn1ent as well as the number of years it takes for an investment to double using the Rule of 72.
Chris has $100,000 in his 401 (k). He plans to retire in 24 years and needs $800,000 to supplement other retirement investment. What rate of return must chris receive in order to reach his goal?
Notice thal his investor’s money will need to double more than once o become $800,000. The $100,000 will double to $200,000, $200,000 will double to $100,000 and $400,000 will double to $800,000. Since Chris’ money is invested for 24 yearsb we can determine that the money doubled every eight years. By using the Rule of 72 formula, we can calculate the internal rate of return required. 72 + 8 = 9, which means Chris’ $100,000 will grow to $800,000 if he has an annual rale of return of 9%.
The total return calculation takes into account the
cash flow from dividends or interest, plus any appreciation or depreciation in the value of the investment.
total return =
(ending value - beginning value) + investment income / beginning value
An investor purchases 1,000 shares of VPN at $25 per share. VPN pays an $0.80 annual diuidend. After one year, the stock’s market value has declined to $23 per share. What is the investor’s total return?
The investor’s total purchase was $25,000. After one year, the value of the stock had declined to $23,000. However, the company paid a dividend of$0.80, so the investor received $800. Using the total return formula, 1($23,000- $25,000) + $8001 + $25,000 = ($1,200) + $25,000 = -4.8%. The investor has a loss of 4.8%.
Holding period return (HPR) is
a return that is expressed as a percentage. However, it is not necessarily an annualized return. HPR is considered the total return on an asset or portfolio over a specific holding period.
An investor purchases 1,000 shares of VPN at $25 per share. VPN pays an $0.80 annual dividend. After three months, the investor received her first dividend. One month later, the investor decides to sell the stock at its current market value of $23 per share. What is the investor’s total return?
The investor’s total purchase was $25,000. After four months, the investor sells her shares for $23,000. During her holding period she also received a quarterly dividend of $0.20 per share–a total of$200. Using the holding period return formula, [($23,000 - $25,000) + $200] + $25,000 = ($1,800) + $25,000 = -7.2%. The investor has a loss of 7.2%.
Inflation-adjusted rate of return, also referred to as the real interest rate, measures the
true yield of a fixed-income payment after removing the effects of inflation.
Inflation-Adjusted Return =
Actual return - Rate of inflation
Risk-free return is the
return on an investment that has zero risk. The U.S. Treasury bill (T-bill) rate is most often used to represent the risk-free return rate.
