Question

2. The company must choose between two mutually exclusive projects. The cost of capital is 9%. (Maximum acceptable payback period is 4 years.)The cash flows are as follows: Project X Project Y Year O 15550.000.550.000 Year I SO 540.000 Year 2 S10,000 $30,000 Year 3 $20,000 $20,000 Year 4 $30.000 Si0.000 Year 5 S40,000 SO Averags $20,000 $20,000 A. Calculate the following: Project Y Project X a. Payback Period: b. NPV: b. IRR: B. Which project would you recommend? Why?

Answer 1

A .

payback period

project x

PAYBACK PERIOD = INITIAL INVESTMENT / ANNUAL CASHFLOW

(WHEN CASHFLOWS ARE CONSTANT)

year cash flow time (years )

1 50,000 - 0 1

2 50,000 -10000 2

3 30,000 - 20000 3

4 10000 - 30000 4 months

( 30000 is the actual cashflow for the year but the remaining amount is 10000 which is to be recovered , hence this will be done in one third of the whole year as the amount is also one third of the cashflow which is to be received during the same year )

payback period = 3.333 years

project Y

year cash flow time (years )

1 50,000 - 40,000    1

2 10,000 -30000 4 months

  ( 30000 is the actual cashflow for the year but the remaining amount is 10000 which is to be recovered , hence this will be done in one third of the whole year as the amount is also one third of the cashflow which is to be received during the same year )  

payback period = 1.333 years  

NPV

= { CF1/(1+r) + CF2/ (1+r)^2 +.......... CFn/(1+r)^n } - initial investment  

project X

NPV = { 0 + 10000 / (1.09)^2 + 20000 / (1.09)^3 + 30000/(1.09)^4 + 40000/(1.09)^5 } - 50000

= [ 0+ 8416.7999 + 15443.669 + 21252.75633 + 25997.255 ] - 50000

= 71110.48132 - 50000

= 21,110.48132

project Y

NPV = { 40000 / (1.09)^1 + 30000 / (1.09)^2 + 20000/(1.09)^3 + 10000/(1.09)^4 + 0 } - 50000

= [ 36697.24771+25250.39980+15443.66960+7084.252111+0 ] - 50000

= 84,475.56922 - 50000

= 34,475.56922

IRR (It is a rate at which NPV of a project equals to zero )

project X

0 =NPV= { CF1/(1+r) + CF2/ (1+r)^2 +.......... CFn/(1+r)^n } - initial investment

0 = { 0 + 10000 / (1+r)^2 + 20000 / (1+r)^3 + 30000/(1+r)^4 + 40000/(1+r)^5 } - 50000

this question is usually or normally solved through trial and error method , the above equation can be solved for various values of r and hence cab ne reached to the desired answer or IRR    

on solving the above equation we will get , IRR = 19.4047 %

project Y

0 =NPV= { CF1/(1+r) + CF2/ (1+r)^2 +.......... CFn/(1+r)^n } - initial investment

0 = {40000 / (1+r) + 30000 / (1+r)^2 + 20000/(1+r)^3 + 10000/(1+r)^4 + 0 } - 50000

this question is usually or normally solved through trial and error method , the above equation can be solved for various values of r and hence cab ne reached to the desired answer or IRR    

on solving the above equation we will get , IRR = 46.172263 %

B . since the projects are mutually exclusive and due to higher NPV of $ 34,475.56922 it is recommended to invest in project Y .