Download presentation

Presentation is loading. Please wait.

Published byIrea Galloway Modified over 4 years ago

1
Money-Time Relationships Part II – Tricks and Techniques

2
Overview Important assumptions and how to break them Deferred annuities –Slow (but simple) use only P/F –Faster - Combining P/F and P/A Linear Gradients –P/G, A/G, etc. –Sometimes P/F is easier Exponential growth (or decay) Compounding intervals more often than cash flows Variable interest rates require F/P or P/F

3
Important Assumptions FactorAssumptionViolations All (P/F,F/P,P/A,etc.)Constant interest rate for N periods Variable interest rates (5% for 3 years, then 6% for 2 years, then 4% for 6 years) (P/A,i%,N) (F/A,i%,N) Constant cash flowsCash Flows that grow or shrink (P/A,i%,N) A/P (F/A,i%,N) A/F Cash flow interval matches interest compounding interval Interest compounded more often (monthly) than cash flows (quarterly/yearly) (P/A,i%,N) A/P (F/A,i%,N) A/F Cash flows start at end of year 1 and finish at end of year N Cash flow starts at a future year (year 10)

4
Dealing with Violations I ProblemSolution Techniques Changes in i%Find breakdown of problem where i% is piecewise-constant. Use P/F or F/P only. Avoid using P/A, etc. Variable Cash Flows ($A grows or shrinks) If $A is piecewise-constant, with changes in the level, use deferred annuity technique. If $A changes every period, shortcuts exist only for special cases (linear, exponential). For the general case, you can always use P/F or F/P and sum up the results.

5
Dealing with Violations II ProblemSolution Techniques Interest compounded more often (monthly) than cash flows (quarterly/yearly) Use time periods that match the cash flows. Adjust the monthly interest rate I up to the new period. I* = (1+I) 4 -1 I*=(1+I) 12 -1 First Payment of Annual Cash flow starts at a future year, not year 1 (example: need PV of cash flow that starts at year 10 with last payment in year 20) Use deferred annuity formula. Apply appropriate combinations of P/F and P/A. example: (P/F,i%,9)*(P/A,i%,10)

6
Deferred annuities Cash flow starts at beginning of year J+1 Last payment at end of year N 0 J J+1 N $A/year Present Value $P = (P/F,i%,J)*(P/A,i%,N-J)*A $P ?

7
Why not just P/A? 0 J J+1 N $P ? $A/year (P/A,i%,N-J)*$A gives the value of the cash flow in units of year J dollars. This is probably not what you wanted as your final result. Remember: P/A gives a dollar value that is timed one year before the start of the cash flows. You need to use P/F or F/P to move this value to other years! Thats why $P = (P/F,i%,J)(P/A,i%,N-J)*$A

8
Variable cash flows For general cases, use P/F or F/P For linear cases (e.g. –3000,-1000,1000,3000,5000), there is a gradient method involving gradient factors P/G, F/G, etc. For exponential cases, (e.g. 1000,1100,1210,…) there is a convenience interest rate method Use of excel together with P/F or F/P is often the best solution technique. If you are confused, then use P/F or F/P together with a table. This keeps the analysis simple and easy to follow.

9
Exponential Decay Example A watch manufacturer expects a revenue of $100,000 for the first month. The revenue declines by 10% each month and ends after the 12 th month. Calculate the Present Value given i=1%/month. 0123456789101112 $P? $100000 $59049 $31,381

10
Exponential Growth/Decay Slow but simple (Excel + P/F)

11
Exponential Growth/Decay Convenience Interest Rate Method Another way to calculate annuities with a growth (or decay) factor is to adjust the interest rate factor and use a special formula. Common ratio =f = (A k - A k-1 )/ A k-1 = -0.10 Convenience rate i cr =[(1+i)/(1+f)]-1 =[1.01/0.90]-1=0.1222 Special formula PV = A 1 (P/A, i cr %,N)/(1+f) = = ($100000)(6.132)/(0.90)=$681,333

12
Exponential Growth/Decay Convenience Interest Rate Method Common ratio =f = (A k - A k-1 )/ A k-1 = -0.10 Convenience rate i cr =[(1+i)/(1+f)]-1 =[1.01/0.90]-1=0.1222 PV = A 1 (P/A, i cr %,N)/(1+f) = = ($100000)(6.132)/(0.90)=$681,333 Compare with more careful excel+P/F method: $681,235 (difference is due to rounding 6.132)

13
Linear Gradients Cash flow increases or decreases _linearly_ (by the same _amount_ each period) 12 3 45 -3000 -1000 1000 3000 50007000 6 Investment loses 3000 in year 1, 1000 in year 2, but earns 1000,3000,5000,7000 in years 3-6. What is the PV at i=8%?

14
Gradient Factors 012345 ………….N $0 $1 $2 $3 $4 $(N-1) (P/G,i%,N) is the present value (units: year 0$) of this cash flow (F/G,i%,N) is the future value (units: year N$) of this cash flow (A/G,i%,N) is the annuity value (units: $/year) of this cash flow Year

15
Linear Gradients 12 3 45 -3000 -1000 1000 3000 50007000 6 = + -3000 20004000 6000800010000 annuity Simple gradient

16
Linear Gradients 12 3 45 -3000 -1000 1000 3000 50007000 6 Cash flow = annuity (-3000) + gradient (2000/year) Gradient always starts at year 2. PV = -3000 (P/A,8%,6) + 2000(P/G,8%,6) (p.632) = (-3000*4.6229) + 2000 (10.523) =-$13869 + $21046 = $7177

17
60 Seconds Investment Challenge Let i=2%/month. There are two investments, A and B. An investment costs $300 in terms of todays dollars. 01234….N…..24months $0 $1 $2 $3 ….$N… $36 (end) INVESTMENT A INVESTMENT B 0123….N…..36months $21 $0 Do you want to swap $300 for the PV of A, or the PV of B? $21 (end)

18
Investment Challenge: Analysis of A Let i=2%/month. The investment costs $300 in terms of todays dollars. $0 $1 $2 $3 ….$N… $36 (end) INVESTMENT A 0123….N…..36months PV = $1 * (P/G,2%,36) + $1 * (P/A,2%,36) = $392.04 + $25.49 = $417.53 Did you forget that cash flow for P/G begins in year 2? In this example, this mistake cost you money!

19
Investment Challenge: Analysis of B Let i=2%/month. The investment costs $300 in terms of todays dollars. 01234….N…..24months INVESTMENT B $21 $0 Evaluating B is simple, because it has a constant cash flow of $21. It starts in year 1, so we can use the P/A formula. $PV = $21 * (P/A,24,2%) = $21 * 18.9139 = $397.20

20
Compounding intervals more often than cash flows Solution: Change interest rate period to match cash flow period Example: Interest compounded every month at 1%/month, but cash flows are every six months. Use i*=[(1+i)^N]-1=1.01^6-1 =1.06152-1 =6.152%/6-month period

21
Savings account example: Problem Every month your bank pays 0.25% interest on your savings account balance. Every 3 months you deposit $5000. How much do you have after 3 years? Note: this is a F/A problem, except that the compounding interval of 1 month does not match the deposit (cash flow) interval of 3 months.

22
Savings account example: Analysis Step 1: Change interest rate to 3-month rate: i*=[(1+.0025) 3 -1]=.0075187 Step 2: Determine N. If a period is 3-months, then we have N=12 periods in 3 years. Step 3: Notice that the cash flow every period is constant, so we can use the FV formula, $FV = $5000 * (F/A,i*,12) Final Step: Calculate the F/A formula. $FV =$5000 * [(1.0075187) 12 -1]/(0.0075187) =$5000*12.50888=$62544.42

23
Variable interest rates and F/P (or P/F) Rule: Use a separate F/P (or P/F) for each group of years or periods where the interest rate is constant. Example: You have $5000 today. For 3 years you invest it at 4% per year, then for 5 more years at 5% per year, then 2 more for 3% per year. The future value is $FV = $5000 * (F/P,4%,3) * (F/P,5%,5) * (F/P,3%,2) = $5000 * 1.1249 * 1.2763 * 1.0609

24
Summary We learned some tricks for finding present and future values in special situations. The trick that always works is to make a table of all cash flows in excel, apply appropriate P/F or F/P factors, and add up the result. To apply shortcuts for linear or geometric cases, one must pay careful attention to detail. Next week – Chapter 4 –more applications –Return on investment (finding the i%) –comparing machines, investment plans, etc.

Similar presentations

Presentation is loading. Please wait....

OK

Chapter 3 Measuring Wealth: Time Value of Money

Chapter 3 Measuring Wealth: Time Value of Money

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on global warming and climate change Ppt on you can win pdf Ppt on vacuum pump Ppt on viruses and antivirus-shop Ppt on extranuclear inheritance Ppt on family tree Ppt on 5v power supply Ppt on traffic light controller project Ppt on spiritual leadership model Ppt on history of australia timeline