Time Value of Money 4 Financial Management (13th edt) By E.F. Bringham and M.C. Ehrhardt 4-1 Time Value of money Receiving $1 today is worth more than $1 in the future Today’s dollar can be invested to have more dollars tomorrow Opportunity cost is the interest we could have earned on $1 if received earlier Opportunity cost rate is the rate of return on the best available alternative investment of equal risk. 4-2 1 Compounding and Discounting Compounding Translating today’s $1 into its equivalent FV FVn = PV ( 1 + i )n FV1= 100(1+.10)1=110 Discounting Translating tomorrow's $1 into its equivalent PV PVn = FV÷( 1 + i )n PV1= 110÷ (1+.10)1=100 4-3 Compounding and Discounting When making investment …show more content…
PMT {1 - (1 r)-n } r PV (Immediate) = PMT (PVIFA i, n ) 4-20 10 PVIFAi,n (PVIFA Table) PVIF The PV of an annuity of $1 per period n i=2% i=4% i=6% i=8% 1 2 3 4 5 6 7 8 9 0.980 1.942 2.884 3.808 4.713 5.601 6.472 7.326 8.162 0.962 1.886 2.775 3.630 4.452 5.242 6.002 6.733 7.435 0.943 1.833 2.673 3.465 4.212 4.917 5.582 6.210 6.802 0.926 1.783 2.577 3.312 3.993 4.623 5.206 5.747 6.247 i=10% i=10% 0.909 1.736 2.487 3.170 3.791 4.355 4.868 5.335 5.759 0.909 0.826 0.751 0.683 0.621 0.564 0.513 0.467 0.424 4-21 PV of Your Bank Loan Cynthia Smart agrees to repay her PMT loan in 24 monthly PVImm. {1 - (1 r)-n } r installments of $250 each. If the interest rate on the loan is $250 0.75% per month PVImm = {1 - (1 + 0.0075)-24 } 0.0075 (9% per annum), what is the present =$5,472.29 value of her loan payments? 4-22 11 PV of an Annuity Due PVDue PMT {1 - (1 r)-n }(1 r) r PV
The amount of money that I had spent over one week ended up totaling $100.77. To come up with the amount of money that would be spent in a year if I spent $100.77 for 52 weeks, the total would be $5,240.04. Then to determine the amount of money that would be spent over 25 years, it would be $5,240.04 multiplied by 25 years, and that would be $131,001. That is $131,001 that I spent on completely unnecessary expenses. To determine what $131,001 would equal in todays money it requires to be plugged into an equation, PV=FV/(1+i)^n . “FV” stands for the future value, that is the value that we calculated by multiplying by 25 years, $131,001. The “i” stands for the interest
13. What is the formula for the Present Value (PV) for a finite stream of cash flows (1 per year) that lasts for 10 years?
You want to buy a new sports car from City Toyota for $62,000. The contract is in the form of a 48-month annuity due at a 9% APR. What will your monthly payment be? $1531.39
If we were to use the example above with a 5% interest rate, and a present value of
When considering potential investments it is important to know the present value of the investment so the firm knows how much to invest in order to reach a predetermined profit. The first investment opportunity involves an eight point five percent return rate over six years with a predetermined payout of twenty four thousand dollars. The initial investment amount must be determined. In order to do so, the present value will need to be calculated. This is done by using the present value equation, future value/ (1+R)^n. When calculated the company should initially invest fourteen thousand seven hundred and eleven dollars. This initial investment predicts a return on investment of twenty four thousand
An amount is deposited for eight years at 8%. If compounding occurs quarterly, then the table value is found at (adjust rate and number of periods!)
Find out the PV of $ 12,000 as 6 years annuity. Answer – $ Rs 55476
$1000 is borrowed at 12% p.a. compounding monthly and a repayment of $200 is made each month. Use the annuity formula to find the amount owing after 3
What is the present value of a $700 annuity payment over four years if interest rates are 10 percent? Recalculate the present value at 9 percent interest, and again at 11 percent interest.
Suppose that the pension fund manager wants to invest a sum of money that will satisfy this liability stream. Assuming that any amount that can be invested today can earn an annual interest rate of 7.6%, how much must be invested today to satisfy this liability stream?
He talks to her about several annuities that she could buy that would guarantee her an annual fixed income. The annuities are as follows:
Present value is the amount of money required today to produce, using prevailing interest rates, a given amount of money in the future. Future value is the amount of money in the future that a certain amount of money today will yield, given prevailing interest rates. Time value of money calculations are useful for retirement planning purposes. If one assumes that a given amount will be available upon retirement, then one can determine the present value of that future amount. Or, if one sets aside a certain amount today, one can determine the future value of that current sum and therefore plan for retirement expenses. The required rate of return influences the amount to be invested as well as the risk profile, including risk tolerance, investment goals, and horizon.
Annuity immediate, also known as ordinary annuity or annuity in arrears, is the most common annuity form in the territories. It is an annuity with payments of one unit each, made at the end of each year for n years with the rate of interest per period is i. The present value of annuity (a_n) is the sum of each payments’ present values. Its equation is given by a_n=〖1-(1+i)〗^(-n)/i. Future value of the annuity (s_n) refers to the accumulated value of the annuity at time n. Its equation is given by s_n=(〖(1+i)〗^n-1)/i. Another well-known form of annuity is annuity-due. It is an annuity in which the payment is paid at the beginning of the payment periods. Perpetuity is an annuity with no termination date with numerous of payments, such as dividends of stocks. Deferred annuity is an annuity which payments can start after a period of time. It is suitable for some clients who want to stop to pay for a short time interval due to his or her financial problems. Some more examples of annuities are fixed annuities, variable annuities and equity-indexed annuities