Question

A project has annual cash flows of $3,000 for the next 10 years and then $6,000 each year for the following 10 years. The IRR of this 20-year project is 13.22%. If the firm's WACC is 12%, what is the project's NPV? Do not round intermediate calculations. Round your answer to the nearest cent.

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Answer 1

Step 1:Computation of Present value of Cashinflows:

Computation of Present value of Cash flows accruing from year 1 to 10

We know that Present value of Ordinary Annuity = C* [ { 1-( 1+i) ^-n} /i]

Here C = Cash flow per period

i= Rate of interest

n = No.of years

Present value of Cash flows accruing from year 1 to 10 at the end of year 0= C* [ { 1-( 1+i) ^-n} /i]

= $ 3000[ { 1-( 1+0.12)^-10 } /0.12]

= $ 3000[ { 1-( 1.12)^-10} /0.12]

= $ 3000[ { 1-0.32197} /0.12]

= $ 3000[ 0.67803/0.12]

= $ 3000( 5.65025)

= $ 16950.75

Present value of Cash flows accruing from year 11 to 20 at the end of year 10= C* [ { 1-( 1+i) ^-n} /i]

= $ 6000[ { 1-( 1+0.12)^-10 } /0.12]

= $ 6000[ { 1-( 1.12)^-10} /0.12]

= $ 6000[ { 1-0.32197} /0.12]

= $ 6000[ 0.67803/0.12]

= $ 6000( 5.65025)

= $ 33901.50

Hence Present value of Cash accruing from year 11 to 20 at the end of 10th year is $ 33901.50

Let us findout the Present value of Cash flows accruing from year 11 to 20 as on today ( t= 0)

We know that Future Value = Present value( 1+i)^n

Here i = Rate of interest and n = No.of years.

$ 33901.50 = Present value ( 1+0.12)^10

$ 33901.50= Present value ( 1.12)^10

$ 33901.50/3.10585 = Present value

$ 10915.3694 = Present value.

Total Present value of Cashinflows = PV of Cash inflows accruing from year 1 to 10+ PV of Cash inflows accruing from year 11 to 20

= $ 16950.75+$ 10915.3694

= $ 27866.12

Step 2:Computation of Initial Outlay:

Given IRR = 13.22%

We know at IRR , NPV should be 0.That means PV of Cash inflows is equal to the cash outflow

So to findout initial outlay we need to discount the future Cashinflows at 13.22%

Present value of Cash flows accruing from year 1 to 10 at the end of year 0= C* [ { 1-( 1+i) ^-n} /i]

= $ 3000[ { 1-( 1+0.1322)^-10 } /0.1322]

= $ 3000[ { 1-( 1.1322)^-10} /0.1322]

= $ 3000[ { 1-0.28891} /0.1322]

= $ 3000[ 0.71109/0.1322]

= $ 3000( 5.37890)

= $ 16136.70

Present value of Cash flows accruing from year 11 to 20 at the end of year 10= C* [ { 1-( 1+i) ^-n} /i]

= $ 6000[ { 1-( 1+0.1322)^-10 } /0.1322]

=$ 6000[ { 1-( 1.1322)^-10} /0.1322]

= $ 6000[ { 1-0.28891} /0.1322]

= $ 6000[ 0.71109/0.1322]

= $ 6000( 5.37890)

= $ 32273.40

Hence Present value of Cash accruing from year 11 to 20 at the end of 10th year is $ 32273.40

Let us findout the Present value of Cash flows accruing from year 11 to 20 as on today ( t= 0)

We know that Future Value = Present value( 1+i)^n

Here I = Rate of interest and n = No.of years.

$ 32273.40= Present value ( 1+0.1322)^10

$ 32273.40= Present value ( 1.1322)^10

$ 32273.40/3.4612 = Present value

$ 9324.3388 = Present value.

Total Present value of Cashinflows = PV of Cash inflows accruing from year 1 to 10+ PV of Cash inflows accruing from year 11 to 20

= $ 16136.70+$ 9324.3388

= $ 25461.04

  

Computation of NPV:

We know that NPV = Present value of Cash inflows -Initial Outlay

= $ 27866.12-$ 25461.04

= $ 2405.08

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