Time Value of Money: Caiib Paper 1 (Module B), Unit 1
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So, here we are providing “Unit 1: Time Value of Money” of “Module B: Business Mathematics” from “Paper 1: Advanced Bank Management (ABM)”.
The Article is Caiib Unit 1: Time Value of Money
Present value (PV) is the current value of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows.
The formula for present value is:
- PV = CF/(1+r)n
- CF = cash flow in future period
- r = the periodic rate of return or interest (also called the discount rate or the required rate of return)
- n = number of periods
Assume that you would like to put money in an account today to make sure your friend has enough money in 5 years to buy a bike. If you would like to give your child 660000 in 5 years, and you know you can get 10% interest per year from a savings account during that time, how much should you put in the account now?
PV = 660000/ (1 + .01)^5 = 409808.073/-
The value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today. It refers to a method of calculating how much the present value (PV) of an asset or cash will be worth at a specific time in the future. There are two ways to calculate FV:
- For an asset with simple annual interest: = Original Investment x (1+(interest rate*number of years))
- For an asset with interest compounded annually: = Original Investment x ((1+interest rate)^number of years)
1) 20,000 invested for 10 years with simple annual interest of 5% would have a future value of
FV = 20000(1+(0.05*10))
2) 20,000 invested for 10 years at 5%, compounded annually has a future value of :
FV = 20000(1+0.5)^10)
An annuity is a series of payments made at equal intervals. Examples of annuities are regular deposits to a savings account, monthly home mortgage payments, monthly insurance payments and pension payments. Annuities can be classified by the frequency of payment dates.
- Ordinary Annuity: Payments are required at the end of each period. For example, straight bonds usually pay coupon payments at the end of every six months until the bond’s maturity date.
- Annuity Due: Payments are required at the beginning of each period. Rent is an example of annuity due. You are usually required to pay rent when you first move in at the beginning of the month, and then on the first of each month thereafter.
Present Value of an Annuity
The present value an annuity is the sum of the periodic payments each discounted at the given rate of interest to reflect the time value of money.
PV of an Ordinary Annuity = R (1 − (1 + i)^-n)/i
PV of an Annuity Due = R (1 − (1 + i)^-n)/i × (1 + i)
- i is the interest rate per compounding period;
- n are the number of compounding periods; and
- R is the fixed periodic payment.
1. Calculate the present value on Jan 1, 2018 of an annuity of 10,000 paid at the end of each month of the calendar year 2018. The annual interest rate is 24%.
Periodic Payment R = 10,000
Number of Periods n = 12
Interest Rate i = 24%/12 = 2%
PV = 10000 × (1-(1+2%)^(-12))/2%
= 10000 × (1-1.02^-12)/2%
= 10000 × (1-0.7885)/2%
= 5000 × 0.11255/2%
= 5000 × 21.15
♦Net Present Value
The net present value or net present worth applies to a series of cash flows occurring at different times. The present value of a cash flow depends on the interval of time between now and the cash flow. It also depends on the discount rate. NPV accounts for the time value of money. These three possibilities of net present value are briefly explained below:
- Positive NPV: If present value of cash inflows is greater than the present value of the cash outflows, the net present value is said to be positive and the investment proposal is considered to be acceptable.
- Zero NPV: If present value of cash inflow is equal to present value of cash outflow, the net present value is said to be zero and the investment proposal is considered to be acceptable.
- Negative NPV: If present value of cash inflow is less than present value of cash outflow, the net present value is said to be negative and the investment proposal is rejected.
Net present value method
Net present value method (also known as discounted cash flow method) is a popular capital budgeting technique that takes into account the time value of money. It uses net present value of the investment project as the base to accept or reject a proposed investment in projects like purchase of new equipment, purchase of inventory, expansion or addition of existing plant assets and the installation of new plants etc.
To be at Net Present Value you also need to subtract money that went out (the money you invested or spent):
- Add the Present Values you receive
- Subtract the Present Values you pay
Company A is considering a new piece of equipment. It will cost Rs. 6,000 and will produce a cash flow of Rs. 1,000 every year for the next 12 years (the first cash flow will be exactly one year from today).
What is the NPV if the appropriate discount rate is 10%?
You can either discount each individual cash flow or recognise that the Rs. 1,000 cash flows are just a twelve year annuity. So,
PV = a/i[l -1/(1 +i)n] PV= 1,000/0.1 [1 – 1/(1.1)12] PV = Rs. 6,814
Adding this to the original investment gives an NPV of
NPV = Rs. 6,814 – Rs. 6,000
NPV =Rs. 814
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