NPV

Page 1

Consider the cash flow given below. The interest rate is 5%. calculate the PV of each payment in the neighbouring cell and find the sum of all PVs.Also calculate NPV by using NPV function and verify that it matches with the sum of all PVs.

Further a range of interest rates is given below. Calculate the NPV correspondig to each of these and plot a graph showing how NPV varies with interest rates

Interest Rate 8%

YearPresent Value

0 -800 ₹ -800.001 100 ₹ 92.59 -£92.592 150 ₹ 128.603 200 ₹ 158.774 250 ₹ 183.765 300 ₹ 204.17

Present value of all payments ₹ -32.11

Present value returned by Excel's NPV function -32.11

Interest Rate NPV0% 200.001% 165.862% 133.363% 102.414% 72.925% 44.796% 17.967% -7.658% -32.119% -55.48

10% -77.8311% -99.2112% -119.6713% -139.2614% -158.0415% -176.0316% -193.28

Payment at end of year

0% 2% 4% 6% 8% 10% 12% 14% 16% 18%

-250.00

-200.00

-150.00

-100.00

-50.00

0.00

50.00

100.00

150.00

200.00

250.00

NPV

NPV

Page 2

Consider the cash flow given below. The interest rate is 5%. calculate the PV of each payment in the neighbouring cell and find the sum of all PVs.

Further a range of interest rates is given below. Calculate the NPV correspondig to each of these and plot a graph showing how NPV varies with interest rates

Paste the Graph here

0% 2% 4% 6% 8% 10% 12% 14% 16% 18%

-250.00

-200.00

-150.00

-100.00

-50.00

0.00

50.00

100.00

150.00

200.00

250.00

NPV

NPV, IRR

Page 3

There are two projects (A and B) available to you for investment. If the current market rate is 12%, which one will you prefer on the basis of

1) NPV2) IRR

CHOOSING BETWEEN PROJECTSInterest rate 12%

Year Project A Project B0 -500 -5001 100 2502 100 2503 150 2004 200 1005 400 50

NPV

IRR

NPV, IRR

Page 4

There are two projects (A and B) available to you for investment. If the current market rate is 12%, which one will you prefer on the basis of

CHOOSING BETWEEN PROJECTS

XIRR, XNPV

Page 5

Uptil now you have seen that NPV and IRR functions work only when the cash flow occurs at regular intervals.If you are faced with a general situation where payments occur at unequal intervals, then 'X'versions of these functions bail you out.

USING IRR, XIRR and XNPV Functions

Interest Rate 15%Year Payment Dates Payment

0 -10000 1-Jan-98 -10,0001 1500 1-Jul-99 3,0002 1500 1-Feb-00 3,0003 1500 1-Jun-01 3,0004 1500 1-Mar-02 3,0005 1500 1-Aug-03 3,0006 1500 1-Oct-04 3,0007 1500 1-Sep-05 3,0008 1500 1-May-06 3,0009 1500 1-Dec-07 1,000

10 1500 1-Jan-08 3,000

XIRRIRR XNPV

XIRR, XNPV

Page 6

Uptil now you have seen that NPV and IRR functions work only when the cash flow occurs at regular intervals.

USING IRR, XIRR and XNPV Functions

Goal Seek

Page 7

Find the roots of "x^2+3x+2" using GoalSeek tool

Root Give the initial value in this cell

x^2+3x+2

Goal Seek

Page 8

Give the initial value in this cell

Homework

Page 9

Consider two projects whose cashflows are given below.

(a) Find the NPV at the market rate of 5% and IRR of the two projects?(b) Do the recomendations on the basis of NPV and IRR conflicts?(c) Compute the crossover rate, that is the rate for which NPV of project A is equal to the NPV of project B.(d) For what rates the NPV and IRR recommendations agree?

Year Project A Project B0 -100 -1501 30 422 30 423 30 424 30 425 30 42

Homework

Page 10

(c) Compute the crossover rate, that is the rate for which NPV of project A is equal to the NPV of project B.