Time Value of Money for CS Executive Financial Management

What this chapter covers

Time Value of Money: topics in the order to study them

1. 1Concept and Need for Time Value of MoneyStart with the reasons: preference for current consumption, inflation, risk and investment opportunity. These give you the theory answers and the logic for everything after.
2. 2Simple and Compound InterestYou must see how interest on interest works before using any factor; compounding is the engine of future value.
3. 3Future Value of a Single Sum and AnnuityCompounding forward is the easier direction. Learn the single-sum formula FV = P × (1 + r)^n first, then the annuity as a sum of such terms.
4. 4Present Value of a Single Sum and AnnuityDiscounting is the reverse of compounding and is used far more in later chapters, so learn it once forward is clear.
5. 5Perpetuity and Growing PerpetuityThese are limiting cases of the annuity, so they come easily after present value of an annuity.
6. 6Sinking Fund, Capital Recovery and Loan AmortisationThese apply annuity formulas in reverse, solving for the payment instead of the value, so you need both annuity formulas ready.
7. 7Doubling Period and Rule of 72 and 69Finish with the shortcut rules; they are approximations and make sense only after you know exact compounding.

How to prepare Time Value of Money

1. Read the concept topic once and write the four reasons for time preference in your own words, with one line of explanation each.
2. Derive the compound interest formula from year-by-year working for three years, so you understand A = P × (1 + r)^n instead of memorising it.
3. Practise each problem type in blocks: single-sum future value, annuity future value, single-sum present value, annuity present value. Do five of each.
4. For every question, write the timeline first. Mark the date of each cash flow and whether payments fall at the start or end of the period.
5. Solve the reverse problems: find the payment, the rate or the number of years. Check by substituting your answer back.
6. Practise with and without factor tables, since the question may supply them, and keep your calculator steps consistent.
7. In the last week, redo your wrong answers and write a one-page sheet of formulas with conditions of use.

Common mistakes in Time Value of Money

• Using the annual rate when interest is compounded half-yearly, quarterly or monthly

  Fix: Underline the compounding period first. Divide the rate by the number of periods per year and multiply the years by the same number.

• Treating an annuity due as an ordinary annuity

  Fix: Draw the timeline. For an annuity due, multiply the ordinary annuity factor by (1 + r), or treat the first payment separately.

• Applying the perpetuity formula when the growth rate is not below the discount rate

  Fix: State the condition r > g before using the formula. If r ≤ g, the formula does not apply.

• Mixing up the first cash flow in a growing perpetuity

  Fix: Compute A1 = A0 × (1 + g) first if the question gives today's amount.

• Using future value factors where present value is needed, or the reverse

  Fix: Ask whether you are moving money forward or back. Then pick the factor and sanity-check: present value must be smaller than the future sum for a positive rate.

• Treating Rule of 72 as exact

  Fix: Use it only for estimates, and use the compound formula (1 + r)^n = 2 when an exact answer is asked.

Last-day revision: Time Value of Money

• ✓Compound amount: A = P × (1 + r)^n, where r is the rate per period and n is the number of periods.
• ✓Simple interest: SI = P × r × n; it is not earned on earlier interest.
• ✓Present value of a single sum: PV = FV ÷ (1 + r)^n.
• ✓Future value of an ordinary annuity: A × [(1 + r)^n − 1] ÷ r, with payments at the end of each period.
• ✓Present value of an ordinary annuity: A × [1 − (1 + r)^−n] ÷ r.
• ✓An annuity due has payments at the start of each period; its value is the ordinary annuity value × (1 + r).
• ✓Perpetuity: PV = A ÷ r; growing perpetuity: PV = A1 ÷ (r − g), valid only when r > g.
• ✓Sinking fund payment = target amount ÷ FV annuity factor; capital recovery payment = loan ÷ PV annuity factor.
• ✓When interest is compounded m times a year, use rate ÷ m and years × m.
• ✓Rule of 72: doubling years ≈ 72 ÷ rate in per cent; Rule of 69 is a closer approximation for continuous or frequent compounding.
• ✓Always match the rate period to the cash flow period.

Time Value of Money practice questions

• Ramesh deposits ₹50,000 in a bank for 2 years at 10% per annum compounded annually. What will be the amount at the end of 2 years?
• When the number of compounding periods per year increases, with the nominal annual rate and the time period unchanged, what happens to the f…
• Kaveri Industries borrows ₹5,00,000 at 10% p.a., repayable in 5 equal annual instalments at each year-end. Each instalment is about ₹1,31,89…
• Sundaram Textiles must accumulate ₹10,00,000 at the end of 5 years to redeem a liability. It will deposit equal amounts at the end of each y…
• Ravi deposits Rs 10,000 in a bank for 2 years at 10% per annum compounded annually. What is the amount at the end of 2 years?
• A sum of ₹1,00,000 is invested at 12% per annum for one year. Interest is compounded half-yearly. What is the effective annual rate (EAR) an…
• Mehta Ltd expects to pay a dividend of Rs 5 at the end of next year, growing at 4% per annum forever. If the required return is 14%, the pre…
• In the context of time value of money, what does the process of discounting do?

Time Value of Money in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

• CMA IntermediateTime Value of Money
• CS ProfessionalCalculation of Interest and Annuities
• CA FoundationMathematics of Finance
• FRM Part IPricing Conventions, Discounting, and Arbitrage