Question

(a) Why does money have a time value? Does inflation have anything to do with making a ringgit today worth more than a ringgit tomorrow?

(b) Discuss the present value of an annuity with an example.

(c) You plan to retire in exactly 20 years. Your goal is to create a fund that will allow you to receive RM20,000 at the end of each year for 30 years. You know that you will be able to earn 11% per annum during the 30-year retirement period.

(i) How large a fund will you need when you retire in 20 years to provide the 30-years, RM20,000 retirement annuity?

(ii) How much will you need today as a single amount to provide the fund calculated in part (i) if you earn 9% per annum during the 20 years preceding retirement?

(iii) What effect would an increase in the rate you earn both during and prior to retirement have on the vales found in parts (i) and (ii)? Explain.

Answer 1

Answer (a)

Definition of TVM

The time value of money (TVM) is the concept that money available at the present time is worth more than the identical sum in the future due to its potential earning capacity.

The money has a time value because of its potential earning capacity. It is because money can earn interest over time.

Example

Mr. A has RM 1000 at the beginning of the year and he decides to deposit it into a bank for interest rate 10%. At the end of the year Mr. A will receive RM 1100 (1000 + 1000*10%) i.e., (Principal + Interest)

It can be easily analysed that if Mr A has an option to receive RM 1000 either at the beginning of the year or at the end of the same year.

He will opt for the payment received in the beginning. 1100 > 1000.

This concept is known as time value of money. It is because you have to pay someone to borrow their money to compensate them for the time you have it.

Reasons of TVM

There are certain reasons of time value of money. Some of these are as follows:

Inflation

Interest earning

Uncertain future

Human preference

Inflation refers to continuous rise in prices and diminishing purchasing power. this effect of inflation results in time value of money.

Interest earning over a period of time, interest or additional income can be earned on the present money which increases its worth over the time. This results in time value of money.

Uncertain future Future is full of uncertainties. What is no payment is received in future?

Human preference Taking money in present is natural human behaviour which increases the present value of money.

Impact of inflation on time value of money

Inflation refers to continuous rise in prices. It plays a prominent role in determining time value of money.

To understand this, let us take an example:

Mr. X has RM 500 which he can use to buy a machinery. Somehow, he postpones his decision of buying it in next year. Mr. Y asks for a loan of RM 500 from Mr. X.

So instead of buying that machinery, Mr. X lends RM500 to Mr. Y. At the end of the year, due to inflation the rate of machinery increases by 5%. Therefore, purchasing power of Mr. X is reduced.

Cost of machinery (500 + 500 *5%) is now RM 525. To maintain the purchasing power and buy the machinery Mr. X wants RM 525 from Mr. Y at the end of the year.so that he can buy the machinery.

The worth of present value of RM 500 is more than future value of RM 500.

Therefore, it can be said that inflation plays a vital role in making a ringgit today worth more than a ringgit tomorrow.

Answer (b)

Present value of an annuity refers to current value of future payments from an annuity for given rate of return and discount rate.

Due to time value of money the value of RM500 received today is more than getting RM100 per year for next 5 years.

Formula for present value of annuity

PV _annuity = P {1- (1+r)^-n} / r

Where,

PV _annuity     = present value of annuity

P = periodic payment

r= interest rate / discount rate

n= no of years/ periods

Example

Mr. A. has an option to receive an annuity which offers:

RM50000 per year at the end of next 25 years with 6% discount rate, or

RM650000 lumpsum payment.

Mr. A needs to determine more rational option.

For this, let us calculate present value of annuity.

PV _annuity = P {1- (1+r)^-n} / r

P= 50000

R= 0.06

N= 25

PV _annuity = 50000 {1- (1+0.06)^-25} / 0.06

PV _annuity = 50000 {1- (1.06)^-25} / 0.06

PV _annuity = 50000 {1- 0.232998631} / 0.06

PV _annuity = 50000 * 0.76700136949/ 0.06

PV _annuity = 639168

Present value of annuity is 639168

Lumpsum payment 650000

Mr. A should opt for lump sum.

Answer (c)

(i)

We need to calculate the present value of annuity

PV _annuity = P {1- (1+r)^-n} / r

P = 20000

R= 0.11

N = 30

PV _annuity = 20000 {1- (1+0.11)^-30} / 0.11

PV _annuity = 20000 {1- (1.11)^-30} / 0.11

PV _annuity = 20000 {1- 0.004368281691} / 0.11

PV _annuity = 20000 * 0.95631718308/ 0.11

PV _annuity = 173875.85

We need a fund of RM173875.85

(ii)

We will calculate present value of the fund

PV= FV / (1 + i) ⁿ

Fv= 173875.85

I= 9 %

N =20

PV=173875.85 / (1 + 0.09) ²⁰

= 173875.85/ 5.60441076778

= 31024.82

(III)

In case (I) present value will increase

In case (iI) present value will decrease

ihope it helps, in case of any query feel free to ask.

thank you.