Value of Money Concept$

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1 Value of Money Concept$

2 Time, not timing is the key to investing 2

3 Introduction Time Value of Money Application of TVM in financial planning : - determine capital needs for retirement plan - determine education financing needs - evaluate investments

4 Introduction Time Value of Money PRESENT VALUE (PV) is the principal (original amount) FUTURE VALUE (FV) equals principal (P) plus interest (I) PAYMENT (PMT) a series of occurring cashflow (deposit or receipts) representing either P or P+I

5 Introduction Time Value of Money SIMPLE Interest is calculated only on beginning P COMPOUNDING Interest calculated on beginning P, also on I accumulated ANNUITY annual series of equal cashflow (deposits or receipts).

6 Future Value FV concept. Example, if Arif deposits $1,000 in fixed deposit at 5% pa. How much Arif accumulated after two years? FV = C (1+r) t Capital = $1,000 r = 5% t = 2 years yr 1 yr 2 $1,050 $1, $1,000 x 1.05 $1,050 x 1.05 C (1+r) C (1+r)(1+r) C (1+r) 2

7 Future Value To compute FV, you need : C = capital r = interest rate (rate of return) t = number of years As r h t h, the higher the FV

8 Exercise 1 Future Value How much would Shima have in 5 years time if she invests $20,000 at 12% rate of return? Method 1 (manual calculation) FV = C (1+r) n = $20,000 x (1+0.12) (1+0.12) (1+0.12) (1+0.12) (1+0.12) = $20,000 x (1+0.12) 5 = $ 35,246

9 Future Value Method 2 (financial calculator Compounding) CMPD mode END Input PV, n, r then solve FV

10 Future Value Method 3 (FV table Pocket paper calculator) Lump sum investment $10,000 at r = 12% and n = 5 yrs will result $17,623. So, investment will result = $17,623 x 2 = $35,246

11 Future Value Rule 72 t = 72 r Exercise 2 How long does it take to double my $20,000 at 12% rate of return? t = solve for t = 6 years At what rate can I double my $20,000 in 10 years? 10 = 72 solve for r = 7.2% r Workout - using manual calculation. Workout - using financial calculator.

12 Future Value Rule 72 t = 72 r Workout - compare EPF return 6% against UT return at 12%, 15% and 20%.

13 Future Value What if interest rate is compounded monthly or half yearly? More frequent compounding the bigger the FV Exercise 3 If Shima invests her $20,000 at 12%pa, interest compounded 6 monthly, for 5 years. R = r / m = 12% / 2 (if half yearly) T = m x t = 2 x 5 yrs where m = frequency Method 1 (manual calculation) FV = C (1+r/m) m t FV = $20,000 (1+12% / 2) 2 x 5 = $35,816

14 Future Value Method 2 (financial calculator) - workout CMPD mode END PV = $20,000 n = 5 x 2 r = 12% / 2 then solve FV

15 Future Value - annuity Future value of annuity ORDINARY sum of CONSTANT amount deposited at END of each period for a specified number of years. FV (A) = C [ (1+r) t 1] r

16 Future Value annuity ORDINARY Exercise 4 How much would Baila have in 5 years time if she invests $20,000 every year (end) at 12% interest rate? Method 1 (manual calculation) Capital = $20,000 r = 12% n = 5 years yr 1 yr 2 yr 3 yr 4 yr 5 $20,000 $22,400 $25,088 $28,098 $31,470 $20,000 $22,400 $25,088 $28,098 $42,400 $20,000 $22,400 $25,088 $67,488 $20,000 $22,400 $95,586 $20,000 $127,057

17 Future Value annuity ORDINARY Method 2 (financial calculator) Input PMT, n, r then solve FV (END mode) Method 3 (FV table pocket paper calculator) Not advisable. Pocket calculator for monthly investment (annuity) compounded at monthly rate. Estimate, invest $100 monthly r = 12% n = 5 years Yearly deposit of $20,000 is divided to monthly. Thus, monthly investment of $1,667 at 12% and 5 years = $1,667 x $8,249 = $137,510 $100

18 Effective Rate Calculate Effective Rate (ER) ER = (1+r / m) mt 1 Exercise 5 : Nominal rate Effective rate 1 month 10% pa? 3 months 10% pa? 6 months 10% pa? 12 months 10% pa? Method 1 (manual calculation) Use formula above (long method)

19 Effective Rate Method 2 (financial calculator) Exercise 5 : Nominal rate Effective rate 10.47% 1 month 10% pa? 3 months 10% pa? 10.38% 6 months 10% pa? 10.25% 12 months 10% pa? 10% CNVR mode n = 12 (monthly) I% = 10% (rate per annum) then solve EFF

20 Effective Rate Workout credit card Nominal rate if 1.5% interest charged per month. CNVR mode n = 12 (monthly) I% = 1.5% x 12 (rate per annum) then solve EFF Effective Rate is 19.56% Citibank charges 2% per month What s the Effective Rate?

21 Present Value FV concept. Revisit example where if Arif deposits $1,000 in a fixed deposit account at 5% pa. How much would he get after two years? Arif has RM1, after two years. If the example is the opposite, whereby Arif receives RM1, in two years in an investment of 5% pa, how much must he invest today? So, here PV is computed FV = 1, r = 5% t = 2 years Solve PV =?

22 Present Value If Shima received $35,246 after investing for 5 years at 12%. What was the original investment made? Method 1 (manual calculation) PV = FV. (1+r) n = $35,246 (1+0.12) 5 = $ 20,000

23 Present Value Method 2 (financial calculator Compounding) CMPD mode END Input FV, n, r then solve PV Method 3 (FV table Pocket paper calculator) Lump sum single investment of $10,000 at r = 12% and n = 5 yrs will result $17,623. So, original investment is = ($35,246 / $17,623) x $10,000 = $20,000

24 Present Value Rule 72 t = 72 r Exercise 2 How long does it take to half a $20,000 if inflation rate is 6%? t = 72 6 solve for t = 12 years Workout - using manual calculation. Workout - using financial calculator.

25 Present Value - annuity Present value of annuity ORDINARY (end) PV (A) = C [ 1-1 ] r r(1+r) t Workout total PV of $1000 annuity deposited at year end for 4 years earning return of 10% PV = $ $ $ $1000 (1.1) 1 (1.1) 2 (1.1) 3 (1.1) 4 = $3, Or PV = $1000 [ 1-1 ] (1+0.1) 4

26 Present Value annuity ORDINARY Exercise 4 Revisit Baila case Method 1 (manual calculation) Method 2 (financial calculator) Method 3 (FV table pocket paper calculator)

27 Remember Be J.U.S.T

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