Presentation on theme: "Example 1: In the following cash flow diagram, A8=A9=A10=A11=5000, and"— Presentation transcript:
1Example 1: In the following cash flow diagram, A8=A9=A10=A11=5000, and starting with A12, the deposits start decreasing in the amountof 50 (that is, A12=4950, A13=4900). Find theequivalent worth of the following cash flow at t=60. Theinterest rate is 10%.A60A11
3Example 2: Set up an equation to find the value of Z on the left-hand cash-flow diagram that establishes equivalence with theright-hand cash-flow diagram. Both diagrams are drawn ona yearly scale. The interest rate is 12% compounded quarterly.Note that you are only asked to set up an equation, not tofind the actual value of Z.Z Z Z Z Z10005000years
5Example 3: Find the equivalent worth of the following cash-flow at t=0 assuming an inflation rate of 2% per month.if the market interest rate is 12% compounding monthlyif the market interest rate is 12% compounding continuouslyNote the timings of cash flows and that the cash flowsare shown on a monthly scale. Also all amounts are in actualdollars.A3=3000A1=1000A2=2000months
6Example 3: (a) Effective rate for three months: Effective rate for five months:(b) Effective rate for one month:Effective rate for three months:Effective rate for five months:
7Example 4: Suppose that a bank is paying 8% nominal interest, compounded semiannually.a) What is the semiannual effective rate?b) What is the effective rate per year?c) What is the effective rate per month?d) Find the equivalent nominal interest rate, compoundingcontinuously.
9Example 5:Suppose that some years ago your grandfather has created an accountwhich will provide you with a certain amount of cash over a 20 year period.He arranged such that you will receive your first payment one year from nowin the amount of Also suppose that you will receive 6% net increaseevery year over the next 20 years. That is, your first payment will be 3000,second will be 3000(1.06), third will be 3000(1.06)2, and so on in terms ofconstant dollars. Suppose that over the next 20 years, the inflation rate will be5% per year and the inflation-free interest rate will be 3% per year.How much will be your last payment (20th year) in terms of constant dollars?b)How much will be your last payment (20th year) in terms of actual dollars?c)Using constant dollar analysis and the geometric gradient formula, find thepresent worth of your total earnings over 20 years.d)Using actual dollar analysis and the geometric gradient formula, find the
10Example 6:The following equation describes the conversion of a cash flow into an equivalentequal payment series of amount A for 8 years with an interest rate of 10% compoundedannually. Draw the original cash flow diagram.A = [ (P / F, 10%, 1) - 200(P / A1, 5%, 10%, 3) (P / F, 10%, 2)] (A / P, 10%, 8)+ [ (A / G, 10%, 4)] (P / A, 10%, 4) (P / F, 10%, 1) (A / P, 10%, 8)+750(F / A, 10%, 2) (A / F, 10%, 8)
11Example 6:The following equation describes the conversion of a cash flow into an equivalentequal payment series of amount A for 8 years with an interest rate of 10% compoundedannually. Draw the original cash flow diagram.A = [ (P / F, 10%, 1) - 200(P / A1, 5%, 10%, 3) (P / F, 10%, 2)] (A / P, 10%, 8)+ [ (A / G, 10%, 4)] (P / A, 10%, 4) (P / F, 10%, 1) (A / P, 10%, 8)+750(F / A, 10%, 2) (A / F, 10%, 8)
12Example 7:A man borrows a loan of $50,000 from a bank. According to the agreement betweenthe bank and the man, the man will pay nothing for two years and starting at year 3,he will pay equal amounts of A in every 3 months for the next 5 years. If the interestrate is 10% compounded monthly and the inflation rate is 8%,a) Find the payment amount Ab) Find the interest payment and principal payment for the 10th payment.c) Find the total interest paid to the bankd) Suppose you want to pay off the remaining loan in lump sum right after making the15th payment. How much would this lump be? How much would this decrease yourtotal interest payment to the bank?e) Now, assume that, instead of paying equal amounts of A in actual dollars, you wantto pay equal amounts of B in constant dollars. Find this constant dollar paymentamount B.
13Example 7:a) i3 = (1 +0.1/12)3 – 1A = (F | P, i3, 8) * (A | P, i3, 20)b) P9 = A(P | A, i3, 11)Interest = P9* i3Principal Payment = A – Interestc) 20A-50000d) P = A(P | A, i3, 5)Decrease in total interest: 5A - Pe) f3 = ( )˄1/4 - 1i3’ = (i3 - f3) / (1 + f3)B = (F | P, i3’, 8) * (A | P, i3’, 20)
14machine is bought and MARR is 10%, answer the following using Example 8: Assume that you have the following two options for a new machine.Assuming that the salvage value of each option is constant at any time after themachine is bought and MARR is 10%, answer the following usingPW, AE and IRR analysis.OPTION 1OPTION 2Initial Cost$20,000$40,000Annual Savings12,00025,000Salvage Value10,00020,000Life3 yrs.2 yrs.a) Assuming that you will only operate the facility for 2 years, which option will you choose?Assuming that you will close the facility after 5 years, which option will you choose?Which option will you choose if you plan to operate your facility for an indefinite period and each option will be available forever.Assume that you are planning to operate your facility for an indefinite period and option 1 is available forever. However, option 2 is available only now and if you choose option 2 now, you will have to replace it by option 1 at the end of its service life. Which option will you choose now?
15Example 9: Referring to the accompanying cash-flow diagram, answer the following questions:100020003000If i = 0, what is the PW?What is the PW if i ∞ ?If MARR is 10%, what is the discounted payback period?