Discount rate
Also written Return rate · Reinvestment rate
The rate used to bring a future cash flow back to today's value — the higher this rate, the lower a given future amount is worth in present-day rupees.
In plain language
Money received later is worth less than the same amount received today, because today's money can be invested and grow while the wait continues. To compare the two fairly, the future amount has to be brought back to a present-day value.
The discount rate is the rate used to make that adjustment. The workbook also calls it the return rate, the interest rate, or the reinvestment rate — all names for the same number in the same role, depending on the calculation being done.
The key relationship to hold onto: the higher the discount rate, the lower a future rupee is worth today. A higher rate means more return is being given up by choosing to wait for the money instead of getting it now.
How it works
A future cash flow is discounted using PV = FV / (1+r)^n, where r is the discount rate for each compounding period and n is the number of periods. Raising r shrinks the present value; lowering it raises the present value — the relationship runs in one direction only.
The workbook's own illustration makes the size of the effect concrete: Rs 1,000 received after 3 years, discounted at 5%, is worth Rs 864 today. The same Rs 1,000, discounted at 8% instead, is worth only Rs 794 today — a difference of Rs 70, purely from changing the discount rate, with nothing else in the calculation touched.
A worked example
A father wants to know today's value of Rs 5,00,000 his son will receive in 4 years from a maturing investment. At a discount rate of 7%:
PV = 5,00,000 / (1.07)^4 = Rs 3,81,449
If the father instead uses a discount rate of 10%, reflecting a higher return available elsewhere, the same Rs 5,00,000 four years out is worth less today:
PV = 5,00,000 / (1.10)^4 = Rs 3,41,507
A change of just 3 percentage points in the discount rate changes today's value of the same future amount by nearly Rs 40,000 — the discount rate is doing all the work in both calculations.
Why NISM asks about it
Chapter 2 (Time Value of Money), section 2.1, introduces the discount rate with the Rs 1,000-at-5%-versus-8% example, before section 2.2.1 builds the present value formula around it. Expect a question testing whether a higher discount rate raises or lowers present value, or a direct PV calculation given a discount rate.
Common exam traps
- A higher discount rate always lowers present value, never raises it. If a computed answer moves the other way, the rate was applied to the wrong side of the equation.
- The workbook uses discount rate, return rate, interest rate and reinvestment rate interchangeably — do not expect the exam to always use the same label for the same number.
- The discount rate must match the compounding period, not necessarily the year — a monthly cash flow needs a monthly rate.
Check yourself
1.What happens to the present value of a future cash flow when the discount rate increases?
- a)It increases
- b)It decreases
- c)It remains unchanged
- d)It becomes negative
Show the answer
Answer: (b) It decreases
"The HIGHER the discount rate, the LOWER the present value of future cash flows. A higher rate means that investors have to FOREGO MORE RETURNS by opting to receive the money today." The chapter illustrates this: Rs 1,000 after 3 years is worth Rs 864 at 5 per cent but only Rs 794 at 8 per cent.
2.The present value of a perpetuity is calculated as:
- a)C x (1 + r)^n
- b)C / r
- c)C x r
- d)C / (1 + r)^n
Show the answer
Answer: (b) C / r
"The constant stream of a similar cash flow will ultimately lead to the calculation being made as the CASH FLOW DIVIDED BY THE DISCOUNT RATE", so PV = C / r. There is no exponent and no time period, because a perpetuity has no finite period.
3.Rs 1,000 will be received after 3 years. The chapter says it is worth Rs 864 today when discounted at 5 per cent. What is it worth today at 8 per cent, and which principle does this show?
- a)Rs 864 — the discount rate does not change the present value of a fixed future sum
- b)Rs 760 — 8 per cent a year for 3 years is 24 per cent, taken off Rs 1,000
- c)Rs 794 — the higher the discount rate, the lower the present value of future cash flows
- d)Rs 1,260 — a higher rate raises the value of the cash flow
Show the answer
Answer: (c) Rs 794 — the higher the discount rate, the lower the present value of future cash flows
The chapter's own example: "Rs 1,000 received after 3 years when discounted at 5 per cent is worth Rs 864 today but the same amount discount at 8 per cent is worth only Rs 794."
Working: PV = FV/(1+r)^n = 1,000/(1.08)^3 = 1,000/1.259712 = Rs 793.83, about Rs 794. At 5 per cent: 1,000/1.157625 = Rs 863.84, about Rs 864.
The principle is one of the four points the chapter lists: "The higher the discount rate, the lower the present value of future cash flows. A higher rate means that investors have to forego more returns by opting to receive the money today instead of future cash flows."
Option A is wrong because the example shows the present value falling from Rs 864 to Rs 794 as the rate rises.
Option B is wrong because it takes simple interest off the future sum. Discounting divides by (1+r)^n — it does not subtract r × n.
Option D is wrong because Rs 1,260 is roughly the future value of Rs 1,000 compounded at 8 per cent for 3 years (1,000 × 1.2597). Future inflows are discounted to reach their present value, not compounded.
Where this is taught
Free preparation for NISM Series X-ARelated terms
- Compound interest rateThe rate at which a present sum of money grows into the future once its interest is reinvested and starts earning interest of its own, the forward-looking twin of the discount rate.
- Compounding periodThe interval, such as monthly, quarterly or annually, over which interest is calculated and added to an investment — the more often it happens within a year, the faster the investment grows.
- Fixed annuityAn annuity that pays a fixed, unchanging amount at each regular period, agreed at the time of investing — as against a floating annuity, whose payouts move with an inflation or index benchmark.
- Economic Internal Rate of ReturnThe IRR of a project widened to include the direct and indirect economic benefits it creates, whether or not they reach the fund — as distinct from the financial IRR the fund actually earns.
- PerpetuityA constant cash flow received every period with no end date. Its present value is simply the cash flow divided by the discount rate: PV = C / r.
- EMIThe Equated Monthly Instalment — the fixed monthly payment on a loan that covers both interest and a portion of the principal, calculated so the loan is fully repaid by the end of its term.