Question

Explain why we have to discount the cash flows in order to evaluate the net present value. What is the role of the discount rate? Use a numerical example in you excel file and calculate the NPV using the NPV EXCEL function, the usage of the PV & SUM EXCEL functions and the mathematical formula for the present value calculation.

Answer 1

We have to discount the cash flows to be received in future because money has time value and the cash flow received in future is less valuable than the same amount if received today.

Concept of time value of money: If you invested $1today, it shall have more value than $1 at some future time.

Suppose you invested $10000 today @10% interest rate compounded annually for two years it shall become 12100 [i.e.10000*(1.1)^{^2}]

formula of compounded amount i.e. P*(1+r)^t

where r= rate of interest

P=Principal amount t=number of periods

here we have calculated the future value of $10000 hence r shall be called the compounding rate

if we have to calculate the present value with the same rate, r shall be called the discoundting rate.

Formula of discounting=P/(1+r)^{^t}

Calculation of present value of 12100 to be received after two years=12100/(1.1^{^2})

=10000

Calculation of NPV:

NPV=Present value of all future cash flows-Initial investment

Example: Solved using mathmatical formula:

Year	Cash flow	PV factor	PV
0	-50000	1	-50000
1	12000	0.909091	10909.09
2	11000	0.826446	9090.909
3	18000	0.751315	13523.67
4	13000	0.683013	8879.175
5	17000	0.620921	10555.66
NPV	2958.504

Where cash flow in year 0=Initial investment

PV factor=1/(1+r)^{^t}

Solved using excel PV function: