(A) What is the internal rate of return on a project with the following cash flo
ID: 2791271 • Letter: #
Question
(A) What is the internal rate of return on a project with the following cash flows:
(i) What is the project’s internal rate of return? (ii) If your company’s WACC of 12%, what value does this project represent? (iii) Assuming the project is minimally risky, should you invest? Why or why not?
(B) Your company’s executive deems the project in (A) to be vital to company operations, but identifies an alternative that has the following cash flows. Using IRR, which of the two alternatives should you choose? Why?
(C) What are the simple and discounted payback periods for both of the alternative projects in (A) and (B)?
Cash Flow Cash Flow Year (000's) Ye 0 -S 200.0 11 Year (000's) $ 225.00 1 $ 400.0012225.00 13 $ 225.00 14 $ 225.00 4 $ 125.0015 $225.00 16 $ 225.00 17 $ 225.00 18 $ 225.00 19 $ 225.00 $ 225.00 20$ 225.00 $ 225.00 2 -$ 300.00 3 $ 100.00 $ 200.00 $ 225.00 $ 225.00 $ 225.00 10 | $ 225.0 21Explanation / Answer
Project A:
NPV=-200-400/(1+r)-300/(1+r)^2-100/(1+r)^3+125/(1+r)^4+200/(1+r)^5+225/(1+r)^6.........225/(1+r)^21
IRR is the rate at which NPV=0
So,
0=-200-400/(1+r)-300/(1+r)^2-100/(1+r)^3+125/(1+r)^4+200/(1+r)^5+225/(1+r)^6.........225/(1+r)^21
=>r=14.94%
Alternatively,
=IRR({-200;-400;-300;-100;125;200;225;225;225;225;225;225;225;225;225;225;225;225;225;225;225;225})
=14.94%
At r=12%, NPV=215.822
Yes, we should accept the project if the project is minimially risky because NPV is greater than zero and IRR is greater than WACC
Cumulative cash flows in year 0:-200
Cumulative cash flows in year 1:-200-400=-600
Cumulative cash flows in year 2:-600-300=-900
Cumulative cash flows in year 3:-900-100=-1000
Cumulative cash flows in year 4:-1000+125=-875
Cumulative cash flows in year 5:-875+200=-675
Cumulative cash flows in year 6:-675+225=-450
Cumulative cash flows in year 7:-450+225=-225
Cumulative cash flows in year 8:-225+225=0
So, simple payback is year 8=8 years
Cumulative discounted cash flows in year 0:-200
Cumulative discounted cash flows in year 1:-200-400/1.12
Cumulative discounted cash flows in year 2:-200-400/1.12-300/1.12^2
Cumulative discounted cash flows in year 3:-200-400/1.12-300/1.12^2-100/1.12^3
Cumulative discounted cash flows in year 4:-200-400/1.12-300/1.12^2-100/1.12^3+125/1.12^4
Cumulative discounted cash flows in year 5:-200-400/1.12-300/1.12^2-100/1.12^3+125/1.12^4+200/1.12^5
Cumulative discounted cash flows in year 6:-200-400/1.12-300/1.12^2-100/1.12^3+125/1.12^4+200/1.12^5+225/1.12^6
Cumulative discounted cash flows in year 7:-200-400/1.12-300/1.12^2-100/1.12^3+125/1.12^4+200/1.12^5+225/1.12^6+225/1.12^7
Cumulative discounted cash flows in year 8:-200-400/1.12-300/1.12^2-100/1.12^3+125/1.12^4+200/1.12^5+225/1.12^6+225/1.12^7+225/1.12^8
Cumulative discounted cash flows in year 9:-200-400/1.12-300/1.12^2-100/1.12^3+125/1.12^4+200/1.12^5+225/1.12^6+225/1.12^7+225/1.12^8+225/1.12^9
Cumulative discounted cash flows in year 10:-200-400/1.12-300/1.12^2-100/1.12^3+125/1.12^4+200/1.12^5+225/1.12^6+225/1.12^7+225/1.12^8+225/1.12^9+225/1.12^10
Cumulative discounted cash flows in year 11:-200-400/1.12-300/1.12^2-100/1.12^3+125/1.12^4+200/1.12^5+225/1.12^6+225/1.12^7+225/1.12^8+225/1.12^9+225/1.12^10+225/1.12^11
Cumulative discounted cash flows in year 12:-200-400/1.12-300/1.12^2-100/1.12^3+125/1.12^4+200/1.12^5+225/1.12^6+225/1.12^7+225/1.12^8+225/1.12^9+225/1.12^10+225/1.12^11+225/1.12^12
Cumulative discounted cash flows in year 13:-200-400/1.12-300/1.12^2-100/1.12^3+125/1.12^4+200/1.12^5+225/1.12^6+225/1.12^7+225/1.12^8+225/1.12^9+225/1.12^10+225/1.12^11+225/1.12^12+225/1.12^13=-40.33
Cumulative discounted cash flows in year 14:-200-400/1.12-300/1.12^2-100/1.12^3+125/1.12^4+200/1.12^5+225/1.12^6+225/1.12^7+225/1.12^8+225/1.12^9+225/1.12^10+225/1.12^11+225/1.12^12+225/1.12^13+225/1.12^14=5.71
So, discounted payback=13+40.33/(225/1.12^14)=13.876
Project B:
Cumulative cash flows in year 0:-300
Cumulative cash flows in year 1:-300-400=-700
Cumulative cash flows in year 2:-700-400=-1100
Cumulative cash flows in year 3:-1100-200=-1300
Cumulative cash flows in year 4:-1300+125=-1175
Cumulative cash flows in year 5:-1175+225=-950
Cumulative cash flows in year 6:-950+250=-700
Cumulative cash flows in year 7:-700+300=-400
Cumulative cash flows in year 8:-400+300=-100
Cumulative cash flows in year 9:-100+300=200
So, simple payback is year 8+100/300=8.33 years
Cumulative discounted cash flows in year 0:-300
Cumulative discounted cash flows in year 1:-300-400/1.12
Cumulative discounted cash flows in year 2:-300-400/1.12-400/1.12^2
Cumulative discounted cash flows in year 3:-300-400/1.12-400/1.12^2-200/1.12^3
Cumulative discounted cash flows in year 4:-300-400/1.12-400/1.12^2-200/1.12^3+125/1.12^4
Cumulative discounted cash flows in year 5:-300-400/1.12-400/1.12^2-200/1.12^3+125/1.12^4+225/1.12^5
Cumulative discounted cash flows in year 6:-300-400/1.12-400/1.12^2-200/1.12^3+125/1.12^4+225/1.12^5+250/1.12^6
Cumulative discounted cash flows in year 7:-300-400/1.12-400/1.12^2-200/1.12^3+125/1.12^4+225/1.12^5+250/1.12^6+300/1.12^7
Cumulative discounted cash flows in year 8:-300-400/1.12-400/1.12^2-200/1.12^3+125/1.12^4+225/1.12^5+250/1.12^6+300/1.12^7+300/1.12^8
Cumulative discounted cash flows in year 9:-300-400/1.12-400/1.12^2-200/1.12^3+125/1.12^4+225/1.12^5+250/1.12^6+300/1.12^7+300/1.12^8+300/1.12^9
Cumulative discounted cash flows in year 10:-300-400/1.12-400/1.12^2-200/1.12^3+125/1.12^4+225/1.12^5+250/1.12^6+300/1.12^7+300/1.12^8+300/1.12^9+300/1.12^10
Cumulative discounted cash flows in year 11:-300-400/1.12-400/1.12^2-200/1.12^3+125/1.12^4+225/1.12^5+250/1.12^6+300/1.12^7+300/1.12^8+300/1.12^9+300/1.12^10+300/1.12^11
Cumulative discounted cash flows in year 12:-300-400/1.12-400/1.12^2-200/1.12^3+125/1.12^4+225/1.12^5+250/1.12^6+300/1.12^7+300/1.12^8+300/1.12^9+300/1.12^10+300/1.12^11+300/1.12^12
Cumulative discounted cash flows in year 13:-300-400/1.12-400/1.12^2-200/1.12^3+125/1.12^4+225/1.12^5+250/1.12^6+300/1.12^7+300/1.12^8+300/1.12^9+300/1.12^10+300/1.12^11+300/1.12^13
Cumulative discounted cash flows in year 14:-300-400/1.12-400/1.12^2-200/1.12^3+125/1.12^4+225/1.12^5+250/1.12^6+300/1.12^7+300/1.12^8+300/1.12^9+300/1.12^10+300/1.12^11+300/1.12^13+300/1.12^14
Cumulative discounted cash flows in year 15:-300-400/1.12-400/1.12^2-200/1.12^3+125/1.12^4+225/1.12^5+250/1.12^6+300/1.12^7+300/1.12^8+300/1.12^9+300/1.12^10+300/1.12^11+300/1.12^13+300/1.12^14+300/1.12^15
Cumulative discounted cash flows in year 16:-300-400/1.12-400/1.12^2-200/1.12^3+125/1.12^4+225/1.12^5+250/1.12^6+300/1.12^7+300/1.12^8+300/1.12^9+300/1.12^10+300/1.12^11+300/1.12^13+300/1.12^14+300/1.12^15+300/1.12^16=-2.83675
Cumulative discounted cash flows in year 17:-300-400/1.12-400/1.12^2-200/1.12^3+125/1.12^4+225/1.12^5+250/1.12^6+300/1.12^7+300/1.12^8+300/1.12^9+300/1.12^10+300/1.12^11+300/1.12^13+300/1.12^14+300/1.12^15+300/1.12^16+300/1.12^17=40.85655
So, discounted payback=16+2.83675/(300/1.12^17)=16.06492
Incremental
(Project B-Project A)'s NPV=-100+0/(1+r)-100/(1+r)^2-100/(1+r)^3+0/(1+r)^4+25/(1+r)^5+25/(1+r)^6+75/(1+r)^7.........75/(1+r)^21
IRR would be the rate at which the NPV would be zero
0=-100+0/(1+r)-100/(1+r)^2-100/(1+r)^3+0/(1+r)^4+25/(1+r)^5+25/(1+r)^6+75/(1+r)^7.........75/(1+r)^21
r=13.5%
So, IRR of incremental project is 13.5%
As IRR is greater than WACC would accept incremental project or choose B over A
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