CA Anand Varma
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The purpose of this article is to learn about some common concepts under IFRSs, namely, the
(i) time value of money comprising present value and future value of cash flows,
(ii) simple and compound interest
(iii) effective rate of interest (EIR),
(iv) annuities, plus
their techniques to calculate an IFRS value either in terms of amount, rate or a factor. It is essential to know the above concepts amongst many to enable to apply IFRS accounting.
Following examples illustrating application techniques under IFRS, will facilitate the work of chartered accountants in terms of conceptual clarity, saving in time and generate authenticate financial statements. Wordings shown in italics are typical concepts under IFRS.
A project needs an initial investment of CU 10,000. It is expected to give a return of 2,000 per annum at the end of each year, for six years. The project thus involves a cash outflow of 10,000 in the ‘zero year’ and cash inflows of 2,000 per year, for six years. In order to decide, whether to accept or reject the project, it is necessary that the Present Value of cash inflows received annually for six years is ascertained (assuming market interest rate of 5% p.a. based on similar risk profile, PV of each of the future cash inflows CU 2000 will be 2000÷1.05press=1904.76 at the end of year 1, year 2 =1814.05, year 3 =1727.67, year 4 =1645.40, year 5 =1567.52 and year 6 =1492.43: total PV CU 10,151.83 –or you can also use an ordinary annuity formula and get the total PV in one shot instead of computing PVs year wise and adding manually) and compared with the initial investment of 10,000. The firm will accept the project only when the Present Value of cash inflows at the desired rate of interest exceeds the initial investment or at least equals the initial investment of 10,000; in this case, project may be acceptable. Note that in business perspective itself you feel the need to calculate present value to take a business decision.
Example (i) Assume your entity has provided a service on 31 Dec 2018 for CU 1000 and agrees to be paid on 1 Jan 2020. Time value of money tells us that part of 1000 is interest you will earn after waiting for one year. Perhaps only CU 920 of the 1000 is service revenue earned in 2018 and 80 as interest will be earned in 2019. Calculation of present value CU 920 will remove the interest component, so that the amount of the service revenue can be determined. In other words, you would need to calculate the rate implicit in 1000 by using a PV calculation.
Example (ii) what amount you will need to invest today in order to have CU 15000 at the end of 10 years, assuming investment will earn interest of 10% p.a. compounded half-yearly. Your half yearly rate of effective interest factor comes to 1.05 (10÷100÷2=0.05+1=1.05). Type on calculator 15000÷1.05press=20times=5653.34 as the present value that you need to invest today. 9346.66 would be your interest earnings over 10 years. Table below gives compounding period wise position of your interest earning and the carrying value of your investment:
Comp. periods | Present value end of CP | Interest of comp. periods | Future value |
End of 20^{th} | 15,000 | 714.29 | 15,000.00 |
19 | 14,285.71 | 680.27 | |
18 | 13,605.44 | 647.88 | |
17 | 12,957.56 | 617.02 | |
16 | 12,340.54 | 587.65 | |
15 | 11,752.89 | 559.66 | |
14 | 11,193.23 | 533.01 | |
13 | 10,660.22 | 507.63 | |
12 | 10,152.59 | 483.46 | |
11 | 9,669.13 | 460.43 | |
10 | 9,208.70 | 438.51 | |
9 | 8,770.19 | 417.58 | |
8 | 8,352.61 | 397.79 | |
7 | 7,954.82 | 378.81 | |
6 | 7,576.01 | 360.75 | |
5 | 7,215.26 | 343.59 | |
4 | 6,871.67 | 327.22 | |
3 | 6,544.45 | 311.64 | |
2 | 6,232.81 | 296.81 | |
1 | 5,936.00 | 282.66 | |
0 now | 5,653.34 | 0 | |
Total | 9,346.66 |
Type on calculator 1.05 x 5653.34 press = 20 times will give you the period end carrying value of your investment as 5936.00=6232.81=6544.45 and so on.
Proof of calculations: Future value = present value 5,653.34 + total interest earning 9,346.66 = 15,000.00.
Analysis: Present value and interest earning are each lower in the compounding periods nearer when the investment has been made; PV or investment carrying values and interest earnings keep increasing and are much higher as the investment period progresses. There is no difference in amount of present value 15,000 and future value 15,000 at the end of the 20^{th} period. In GAAPs, interest will be recorded each year on SLM basis at the stated rate of 10% instead of the effective interest rate of 10.25% (i.e. 10÷100=0.1÷2=0.05+1=1.05×1.05=1.1025-1=0.1025×100=10.25%. For example, take CU 13,605.44 being the carrying value of the investment at the end of the 18^{th} comp. period, apply EIR rate of 10.25% to this amount and you will get CU 1,394.56 being the effective interest for the last one year or the 10^{th} year. Add CU 13,605.44 + CU 1,394.56 = CU 15,000 as the future value where it converges with its present value too.
Accounting entries in investor’s books
Date/year | Description of entry | Debit | Credit |
Year 0 present | Investment a/c | 5,653.34 | |
To Bank a/c | 5,653.34 | ||
Inv. made at present value. All FIs are initially recognised at fair value and subsequently carried at amortised cost per IFRS 9 | |||
End of comp period 1 | Investment a/c | 282.66 | |
To Interest earning | 282.66 | ||
End of comp period 20 | Investment a/c | 714.29 | |
To Interest earning | 714.29 | ||
End of com.period 20 | Bank a/c | 15,000 | |
To Investment a/c | 15,000 | ||
Settlement of investment made after 10 years with interest @ 10% |
IFRS tip: stated interest of 10% p.a. requires to be converted to a higher effective interest rate of 10.25%. The effective EIR factor of 1.05 per compounding period remains static for the entire tenure of the investment made even as the semi-annual interest earned amounts keep changing, unlike in GAAPs, interest would be SLM calculated at yearly frequency at the stated rate of 10% p.a. on the amount invested. Compounding frequency plays a key role under IFRS.
Future value is calculated by multiplying the principal amount of CU 10,000 presently available by the interest rate of 4.5% and then adding the interest gained to the principal amount. Following table describes the concept of future value:
Year | Present value of sum available | Interest @1.045 EIR | Future value (carrying value) |
0 now | 10,000 | ||
1 | 450 | 10,450 | |
2 | 470 | 10,920 | |
3 | 492 | 11,412 | |
4 | 513 | 11,925 | |
5 | 537 | 12,462 | |
Total | 2,462 |
Proof of future value calculation: 12,462 at the end of the 5^{th} year i.e. (10,000 + 2,462)
Analysis: In calculating future value, you will notice that interest earnings are lower in the beginning of the investment and keep increasing as the period progresses. Interest is on EIR and not on SLM. Same principle as has been applied in a present value calculation. You can pass the IFRS accounting entries for future value and interest on a similar principle as in (a) above.
You can also calculate present and future value of annuities by using different formulas. Annuities are relevant in loans and lease payments. Annuities may be of similar amounts or different in amounts and can also be either ordinary annuities (end of a period) or annuities due (beginning of a period).
Compound interest: is at the core of Future Value and Present Value calculations in IFRS. It is in a nutshell, interest upon interest. That is, when an interest payment is added to the principal and then the whole thing (principal + interest) earns interest. Two factors determine the power of compound interest:
More time that passes, the greater the contribution is from the interest upon the interest. See this from an example given below and pay attention to the right most column: calculate compound interest for an investment made CU 10,000 with a nominal rate of 5% compounded quarterly:
Carrying value of investment with interest @ 5.09 compounded quarterly has increased much faster compared to the carrying value of investment with simple interest. Rate of compound interest is calculated by using the following equation:
5÷100=0.05÷4=0.0125+1=1.0125×1.0125press=3times=1.02515=1.03797=1.050945-1 =.050945×100=5.09%.
Year | Inv. made | Simple int. @ stated rate 5% | Comp. int. @ 5.09% | Inv. Carrying value com. Int. | Addl. Int. (int. on int.) |
0 | 10,000 | 0 | 0 | 10,000 | 0 |
1 | 10,500 | 500 | 509 | 10,509 | 9 |
2 | 11,000 | 500 | 535 | 11,044 | 35 |
3 | 11,500 | 500 | 562 | 11,606 | 62 |
4 | 12,000 | 500 | 591 | 12,197 | 91 |
5 | 12,500 | 500 | 621 | 12,818 | 121 |
Total | 12,500 | 2,500 | 2,818 | 12,818 | 318 |
Carrying value of investment with interest @ 5.09 compounded quarterly has increased much faster compared to the carrying value of investment with simple interest. Rate of compound interest is calculated by using the following equation:
5÷100=0.05÷4=0.0125+1=1.0125×1.0125press=3times=1.02515=1.03797=1.050945-1 =.050945×100=5.09%.
Money available in the present time is worth more than the same amount in the future due to potential earning capability of the money on hand today. This is because (i) future is always uncertain and risky i.e. no certainty for future cash inflows; (ii) money received today has more purchasing power now than a year hence due to inflation; and (iii) individuals prefer current consumptions to future consumption. Business logic is always first. IFRS only follows it.
For calculating an IFRS value, it is not only necessary to have an expert knowledge of the application of the abovementioned IFRS concepts but to also have a high degree of knowledge of the application of the concepts under market economics (how markets behave and how market prices are set) and risk management (higher the risk you carry lower will be your earning potential and future cash flows).
(CA Anand Varma is a finance and accounting professional and can be reached at [email protected])