Ch 5 Concept Review: What is compounding? What is discounting?
According to our text book, “Compounding is the process of accumulating interest on an investment over time to earn more interest”. When you are compounding you are basically leaving your money, and any interest that it has accumulated, for longer than one period since you are reinvesting the interest. While compounding is moving the money forward into the future, discounting is bringing it back to the present. Discounting is the process of finding the present value of a cash flow or even a series of cash flows. Some key differences are that compounding uses compound interest rates and discounting uses discount rates. Also, when compounding the present value amount has already been specified while the future value is given while discounting.
CH 5 LO1: How to determine the future value of an investment made today.
Future value refers to the sum of money an investment will grow to over a certain period of time at a certain given interest rate; future value is the cash value of an investment in the future. The formula to determine future value is: FV1 = PV + INT or PV(1 + I)ⁿ Where FV is future value, PV is present value, INT represents the specified interest rate, and PV(1 + I)ⁿ represents the present value times (1 + I)ⁿ where I represents the interest rate the N represents the number of compounding periods.
Ch 6: What is the difference between an annuity and perpetuity?
There is only 1 difference between annuity and perpetuity and that is the ending period. An annuity will have payments that last for a certain period of time while a perpetuity will last indefinitely. An annuity has multiple cash flows where the cash flows are equally fixed for a certain period of time and the cash flows are shown at the end of each period. The formula used to calculate the present value of perpetuity is:
P V(∞) = C/R
PV(∞) = present value of perpetuity.
C = the first payment
r = interest rate per period
The formula used to calculate the present value of an annuity is:
F V A = C/r, [(1 + r) t -1].
P V A = C/r[1-1/(1=r)t],
FVA = future value of annuity
PVA = present value of annuity
C = amount of equal payments
r = interest rate per period
t = number of payments (number of time periods)
Ch6.1a Describe how to calculate the future value of a series of cash flows.
There are several steps used to determine the future value of a series of cash flows. The first step is to plug the first series of cash flows into your formula C(1+R)^Y with C being your cash flow, R being the interest rate the cash flow earns per period, and Y being the number of periods. Then you plug the second cash flow into the formula along with each subsequent cash flow. Then you will calculate each formula in order to determine the future value of each individual cash flow. The last step is you need to add the future value of each individual cash flow in order to determine the future value of the series.
Ch6.1b: Describe how to calculate the present value of a series of cash flows.
The present value of a series of future cash flows is classified as the amount that you would need in order to duplicate those future cash flows for a given discounted rate. According to our text book there are two ways of calculating the present value of a series of cash flows. The first being we can either discount one period at a time while the second is we can just calculate the present values individually and then add them up.
6.1c: Unless we are explicitly told otherwise, what do we always assume about the timing of cash flows in present and future value problems?
Whether you are working with present or future value problems, the timing of cash flows is very important. In the majority of calculation, it is assumed that the cash flow will occur at the end of a period. Even the formulas that we have learned showing the numbers in either standard present value or future value are setup to calculate with the cash flow in the end of the period.
Ch7: Which Time Value of Money (TVM) inputs are used to calculate the yield on a bond?
The time value of money input used to calculate the yield on a bond is called the Yield to Maturity rate. This is the rate that is required on the market of the bond. Using our formulas, we can actually calculate the present value of the cash flows as an estimate of the bond’s current market value. When interest rates rise then the present value of the bond’s remaining cash flows will decline making the bond useless. Then when interest rates fall the value of the bond rises. To determine the value of the bond we must know how many periods are remaining until the maturity, the face value, the coupon, and the market interest rate for similar bonds.
Ch8: Describe the dividend discount model for stock valuation.
The dividend discount model, also known as the DDM, is used to value the price of a stock. It does this by taking the predicted dividends and discounting them back to the present value. If this present value is higher than the current value, the shares are trading at then the stock is considered undervalued. When using the dividend, discount model its best to remember that the price you are calculating is the value of the stock based solely off the dividends. Also for stocks with a sturdy history of dividend growth its safe to assume that the historical dividend growth rate will continue.